[arch-commits] Commit in sagemath-doc/trunk (sagemath-singular4.patch)

Antonio Rojas arojas at archlinux.org
Tue Jan 24 13:44:39 UTC 2017


    Date: Tuesday, January 24, 2017 @ 13:44:38
  Author: arojas
Revision: 208836

Remove unused patch

Deleted:
  sagemath-doc/trunk/sagemath-singular4.patch

--------------------------+
 sagemath-singular4.patch | 3731 ---------------------------------------------
 1 file changed, 3731 deletions(-)

Deleted: sagemath-singular4.patch
===================================================================
--- sagemath-singular4.patch	2017-01-24 13:42:48 UTC (rev 208835)
+++ sagemath-singular4.patch	2017-01-24 13:44:38 UTC (rev 208836)
@@ -1,3731 +0,0 @@
-diff --git a/src/bin/sage b/src/bin/sage
-index 46da103..96de4bc 100755
---- a/src/bin/sage
-+++ b/src/bin/sage
-@@ -472,7 +472,7 @@ fi
- 
- if [ "$1" = '-singular' -o "$1" = '--singular' ]; then
-     shift
--    exec singular "$@"
-+    exec Singular "$@"
- fi
- 
- if [ "$1" = '-sqlite3' -o "$1" = '--sqlite3' ]; then
-diff --git a/src/doc/de/tutorial/interfaces.rst b/src/doc/de/tutorial/interfaces.rst
-index c452b11..037cfc3 100644
---- a/src/doc/de/tutorial/interfaces.rst
-+++ b/src/doc/de/tutorial/interfaces.rst
-@@ -197,6 +197,7 @@ Sages Singular-Schnittstelle (ohne die ``....:``):
- 
-     sage: R1 = singular.ring(0, '(x,y)', 'dp')
-     sage: R1
-+    polynomial ring, over a field, global ordering
-     //   characteristic : 0
-     //   number of vars : 2
-     //        block   1 : ordering dp
-diff --git a/src/doc/en/constructions/rings.rst b/src/doc/en/constructions/rings.rst
-index d301a38..58abf8a 100644
---- a/src/doc/en/constructions/rings.rst
-+++ b/src/doc/en/constructions/rings.rst
-@@ -56,6 +56,7 @@ Here's an example using the Singular interface:
-     sage: R = singular.ring(97, '(a,b,c,d)', 'lp')
-     sage: I = singular.ideal(['a+b+c+d', 'ab+ad+bc+cd', 'abc+abd+acd+bcd', 'abcd-1'])
-     sage: R
-+    polynomial ring, over a field, global ordering
-     //   characteristic : 97
-     //   number of vars : 4
-     //        block   1 : ordering lp
-diff --git a/src/doc/en/developer/coding_in_other.rst b/src/doc/en/developer/coding_in_other.rst
-index 6432644..f40cbc3 100644
---- a/src/doc/en/developer/coding_in_other.rst
-+++ b/src/doc/en/developer/coding_in_other.rst
-@@ -401,6 +401,7 @@ interface to Singular::
- 
-     sage: singular.LIB("brnoeth.lib")
-     sage: singular.ring(5,'(x,y)','lp')
-+        polynomial ring, over a field, global ordering
-         //   characteristic : 5
-         //   number of vars : 2
-         //        block   1 : ordering lp
-diff --git a/src/doc/en/tutorial/interfaces.rst b/src/doc/en/tutorial/interfaces.rst
-index eeb98ed..3cd29da 100644
---- a/src/doc/en/tutorial/interfaces.rst
-+++ b/src/doc/en/tutorial/interfaces.rst
-@@ -196,6 +196,7 @@ Singular (do not type the ``....:``):
- 
-     sage: R1 = singular.ring(0, '(x,y)', 'dp')
-     sage: R1
-+    polynomial ring, over a field, global ordering
-     //   characteristic : 0
-     //   number of vars : 2
-     //        block   1 : ordering dp
-diff --git a/src/doc/fr/tutorial/interfaces.rst b/src/doc/fr/tutorial/interfaces.rst
-index a1fc5cf..6d4dde9 100644
---- a/src/doc/fr/tutorial/interfaces.rst
-+++ b/src/doc/fr/tutorial/interfaces.rst
-@@ -198,6 +198,7 @@ fournie par Sage (n'entrez pas les ``....:``) :
- 
-     sage: R1 = singular.ring(0, '(x,y)', 'dp')
-     sage: R1
-+    polynomial ring, over a field, global ordering
-     //   characteristic : 0
-     //   number of vars : 2
-     //        block   1 : ordering dp
-diff --git a/src/doc/ja/tutorial/interfaces.rst b/src/doc/ja/tutorial/interfaces.rst
-index 99158bb..18e83e9 100644
---- a/src/doc/ja/tutorial/interfaces.rst
-+++ b/src/doc/ja/tutorial/interfaces.rst
-@@ -172,6 +172,7 @@ Singularは,グレブナー基底,多変数多項式のgcd,平面曲線の
- 
-     sage: R1 = singular.ring(0, '(x,y)', 'dp')
-     sage: R1
-+    polynomial ring, over a field, global ordering
-     //   characteristic : 0
-     //   number of vars : 2
-     //        block   1 : ordering dp
-diff --git a/src/doc/pt/tutorial/interfaces.rst b/src/doc/pt/tutorial/interfaces.rst
-index 7feea55..4aabfa6 100644
---- a/src/doc/pt/tutorial/interfaces.rst
-+++ b/src/doc/pt/tutorial/interfaces.rst
-@@ -196,6 +196,7 @@ digite ``...``):
- 
-     sage: R1 = singular.ring(0, '(x,y)', 'dp')
-     sage: R1
-+    polynomial ring, over a field, global ordering
-     //   characteristic : 0
-     //   number of vars : 2
-     //        block   1 : ordering dp
-diff --git a/src/doc/ru/tutorial/interfaces.rst b/src/doc/ru/tutorial/interfaces.rst
-index 4be09f9..41b04ca 100644
---- a/src/doc/ru/tutorial/interfaces.rst
-+++ b/src/doc/ru/tutorial/interfaces.rst
-@@ -190,6 +190,7 @@ Singular предоставляет массивную и продуманную
- 
-     sage: R1 = singular.ring(0, '(x,y)', 'dp')
-     sage: R1
-+    polynomial ring, over a field, global ordering
-     //   characteristic : 0
-     //   number of vars : 2
-     //        block   1 : ordering dp
-diff --git a/src/module_list.py b/src/module_list.py
-index 0dee41b..ec842b7 100644
---- a/src/module_list.py
-+++ b/src/module_list.py
-@@ -58,6 +58,12 @@ linbox_libs = list(linbox_pc['libraries'])
- linbox_library_dirs = list(linbox_pc['library_dirs'])
- linbox_cflags = pkgconfig.cflags('linbox').split()
- 
-+# Singular
-+singular_pc = pkgconfig.parse('Singular')
-+singular_libs = list(singular_pc['libraries'])
-+singular_library_dirs = list(singular_pc['library_dirs'])
-+singular_cflags = pkgconfig.cflags('Singular').split()
-+
- # PNG image library
- png_pc = pkgconfig.parse('libpng')
- png_libs = list(png_pc['libraries'])
-@@ -88,6 +94,9 @@ aliases = dict(
-     LINBOX_CFLAGS=linbox_cflags,
-     LINBOX_LIBRARIES=linbox_libs,
-     LINBOX_LIBDIR=linbox_library_dirs,
-+    SINGULAR_CFLAGS=singular_cflags,
-+    SINGULAR_LIBRARIES=singular_libs,
-+    SINGULAR_LIBDIR=singular_library_dirs
- )
- 
- #########################################################
-@@ -112,12 +121,6 @@ except ValueError:
-     pass
- 
- #########################################################
--### Singular
--#########################################################
--
--singular_libs = ['singular', 'flint', 'ntl', 'gmpxx', 'gmp', 'readline', 'm']
--
--#########################################################
- ### Library order
- #########################################################
- 
-@@ -130,8 +133,8 @@ singular_libs = ['singular', 'flint', 'ntl', 'gmpxx', 'gmp', 'readline', 'm']
- # listed here will be added at the end of the list (without changing
- # their relative order). There is one exception: stdc++ is always put
- # at the very end of the list.
--library_order_list = [
--    "singular", "ec", "ecm",
-+library_order_list = singular_libs + [
-+    "ec", "ecm",
- ] + linbox_libs  + gsl_libs + [
-     "pari", "flint", "ratpoints", "ecl", "glpk", "ppl",
-     "arb", "mpfi", "mpfr", "mpc", "gmp", "gmpxx",
-@@ -190,20 +193,7 @@ ext_modules = [
-                language='c++',
-                libraries = ["flint", "gmp", "gmpxx", "m", "ntl"]),
- 
--    Extension('sage.algebras.letterplace.free_algebra_letterplace',
--              sources = ['sage/algebras/letterplace/free_algebra_letterplace.pyx'],
--              libraries = singular_libs,
--              language="c++"),
--
--    Extension('sage.algebras.letterplace.free_algebra_element_letterplace',
--              sources = ['sage/algebras/letterplace/free_algebra_element_letterplace.pyx'],
--              libraries = singular_libs,
--              language="c++"),
--
--    Extension('sage.algebras.letterplace.letterplace_ideal',
--              sources = ['sage/algebras/letterplace/letterplace_ideal.pyx'],
--              libraries = singular_libs,
--              language="c++"),
-+    Extension('*', sources = ['sage/algebras/letterplace/*.pyx']),
- 
-     Extension('sage.algebras.quatalg.quaternion_algebra_cython',
-                sources = ['sage/algebras/quatalg/quaternion_algebra_cython.pyx'],
-@@ -675,35 +665,7 @@ ext_modules = [
-               sources = ['sage/libs/readline.pyx'],
-               libraries = ['readline']),
- 
--    Extension('sage.libs.singular.singular',
--              sources = ['sage/libs/singular/singular.pyx'],
--              libraries = singular_libs,
--              language="c++"),
--
--    Extension('sage.libs.singular.polynomial',
--              sources = ['sage/libs/singular/polynomial.pyx'],
--              libraries = singular_libs,
--              language="c++"),
--
--    Extension('sage.libs.singular.ring',
--              sources = ['sage/libs/singular/ring.pyx'],
--              libraries = singular_libs,
--              language="c++"),
--
--    Extension('sage.libs.singular.groebner_strategy',
--              sources = ['sage/libs/singular/groebner_strategy.pyx'],
--              libraries = singular_libs,
--              language="c++"),
--
--    Extension('sage.libs.singular.function',
--              sources = ['sage/libs/singular/function.pyx'],
--              libraries = singular_libs,
--              language="c++"),
--
--    Extension('sage.libs.singular.option',
--              sources = ['sage/libs/singular/option.pyx'],
--              libraries = singular_libs,
--              language="c++"),
-+    Extension('*', sources = ['sage/libs/singular/*.pyx']),
- 
-     Extension('sage.libs.symmetrica.symmetrica',
-               sources = ["sage/libs/symmetrica/symmetrica.pyx"],
-@@ -970,9 +932,7 @@ ext_modules = [
-               sources = ['sage/matrix/matrix_modn_sparse.pyx']),
- 
-     Extension('sage.matrix.matrix_mpolynomial_dense',
--              sources = ['sage/matrix/matrix_mpolynomial_dense.pyx'],
--              libraries = singular_libs,
--              language="c++"),
-+              sources = ['sage/matrix/matrix_mpolynomial_dense.pyx']),
- 
-     Extension('sage.matrix.matrix_rational_dense',
-               sources = ['sage/matrix/matrix_rational_dense.pyx'],
-@@ -1569,19 +1529,13 @@ ext_modules = [
-               sources = ['sage/rings/polynomial/multi_polynomial.pyx']),
- 
-     Extension('sage.rings.polynomial.multi_polynomial_ideal_libsingular',
--              sources = ['sage/rings/polynomial/multi_polynomial_ideal_libsingular.pyx'],
--              libraries = singular_libs,
--              language="c++"),
-+              sources = ['sage/rings/polynomial/multi_polynomial_ideal_libsingular.pyx']),
- 
-     Extension('sage.rings.polynomial.plural',
--              sources = ['sage/rings/polynomial/plural.pyx'],
--              libraries = ['m', 'readline', 'singular', 'givaro', 'gmpxx', 'gmp'],
--              language="c++"),
-+              sources = ['sage/rings/polynomial/plural.pyx']),
- 
-     Extension('sage.rings.polynomial.multi_polynomial_libsingular',
--              sources = ['sage/rings/polynomial/multi_polynomial_libsingular.pyx'],
--              libraries = singular_libs,
--              language="c++"),
-+              sources = ['sage/rings/polynomial/multi_polynomial_libsingular.pyx']),
- 
-     Extension('sage.rings.polynomial.multi_polynomial_ring_generic',
-               sources = ['sage/rings/polynomial/multi_polynomial_ring_generic.pyx']),
-diff --git a/src/sage/arith/misc.py b/src/sage/arith/misc.py
-index a7fa5a1..c943bc5 100644
---- a/src/sage/arith/misc.py
-+++ b/src/sage/arith/misc.py
-@@ -3246,7 +3246,7 @@ def binomial(x, m, **kwds):
- 
-         sage: K.<x,y> = Integers(7)[]
-         sage: binomial(y,3)
--        -y^3 + 3*y^2 - 2*y
-+        6*y^3 + 3*y^2 + 5*y
-         sage: binomial(y,3).parent()
-         Multivariate Polynomial Ring in x, y over Ring of integers modulo 7
- 
-diff --git a/src/sage/categories/pushout.py b/src/sage/categories/pushout.py
-index 60dfc3a..37a0914 100644
---- a/src/sage/categories/pushout.py
-+++ b/src/sage/categories/pushout.py
-@@ -3201,6 +3201,7 @@ class BlackBoxConstructionFunctor(ConstructionFunctor):
-         sage: FG(ZZ).parent()
-         Gap
-         sage: FS(QQ['t'])
-+        polynomial ring, over a field, global ordering
-         //   characteristic : 0
-         //   number of vars : 1
-         //        block   1 : ordering lp
-diff --git a/src/sage/interfaces/expect.py b/src/sage/interfaces/expect.py
-index f9de7d0..c86a9bd 100644
---- a/src/sage/interfaces/expect.py
-+++ b/src/sage/interfaces/expect.py
-@@ -1212,6 +1212,7 @@ If this all works, you can then make calls like:
- 
-             sage: R.<x> = QQ[]; f = x^3 + x + 1;  g = x^3 - x - 1; r = f.resultant(g); gap(ZZ); singular(R)
-             Integers
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 0
-             //   number of vars : 1
-             //        block   1 : ordering lp
-diff --git a/src/sage/interfaces/interface.py b/src/sage/interfaces/interface.py
-index 816acfa..95b4a91 100644
---- a/src/sage/interfaces/interface.py
-+++ b/src/sage/interfaces/interface.py
-@@ -733,6 +733,7 @@ class InterfaceElement(Element):
-             PolynomialRing( Rationals, ["x"] )
-             sage: S = singular.ring(0, ('x'))
-             sage: loads(dumps(S))
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 0
-             //   number of vars : 1
-             //        block   1 : ordering lp
-diff --git a/src/sage/interfaces/singular.py b/src/sage/interfaces/singular.py
-index 5ebe7d2..0887e0c 100644
---- a/src/sage/interfaces/singular.py
-+++ b/src/sage/interfaces/singular.py
-@@ -64,6 +64,7 @@ factorization::
- 
-     sage: R1 = singular.ring(0, '(x,y)', 'dp')
-     sage: R1
-+    polynomial ring, over a field, global ordering
-     //   characteristic : 0
-     //   number of vars : 2
-     //        block   1 : ordering dp
-@@ -241,6 +242,7 @@ Groebner basis for some ideal, using Singular through Sage.
- 
-     sage: singular.lib('poly.lib')
-     sage: singular.ring(32003, '(a,b,c,d,e,f)', 'lp')
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 32003
-             //   number of vars : 6
-             //        block   1 : ordering lp
-@@ -611,6 +613,7 @@ class Singular(ExtraTabCompletion, Expect):
-             // dimension (affine) = 0
-             // degree (affine)  = 8
-             // ** right side is not a datum, assignment ignored
-+            ...
- 
-         rather than ignored
- 
-@@ -995,6 +998,7 @@ class Singular(ExtraTabCompletion, Expect):
- 
-             sage: R = singular.ring(0, '(x,y,z)', 'dp')
-             sage: R
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 0
-             //   number of vars : 3
-             //        block   1 : ordering dp
-@@ -1034,7 +1038,7 @@ class Singular(ExtraTabCompletion, Expect):
-             sage: R = singular.ring(7, '(a,b)', 'ds')
-             sage: S = singular.ring('real', '(a,b)', 'lp')
-             sage: singular.new('10*a')
--            1.000e+01*a
-+            (1.000e+01)*a
-             sage: R.set_ring()
-             sage: singular.new('10*a')
-             3*a
-@@ -1074,6 +1078,7 @@ class Singular(ExtraTabCompletion, Expect):
-             sage: R = singular.ring(7, '(a,b)', 'ds')
-             sage: S = singular.ring('real', '(a,b)', 'lp')
-             sage: singular.current_ring()
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 0 (real)
-             //   number of vars : 2
-             //        block   1 : ordering lp
-@@ -1081,6 +1086,7 @@ class Singular(ExtraTabCompletion, Expect):
-             //        block   2 : ordering C
-             sage: singular.set_ring(R)
-             sage: singular.current_ring()
-+            polynomial ring, over a field, local/mixed ordering
-             //   characteristic : 7
-             //   number of vars : 2
-             //        block   1 : ordering ds
-@@ -1122,12 +1128,14 @@ class Singular(ExtraTabCompletion, Expect):
- 
-             sage: r = PolynomialRing(GF(127),3,'xyz', order='invlex')
-             sage: r._singular_()
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 127
-             //   number of vars : 3
-             //        block   1 : ordering rp
-             //                  : names    x y z
-             //        block   2 : ordering C
-             sage: singular.current_ring()
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 127
-             //   number of vars : 3
-             //        block   1 : ordering rp
-@@ -1345,6 +1353,7 @@ class SingularElement(ExtraTabCompletion, ExpectElement):
-             sage: cpQ=copy(Q)
-             sage: cpQ.set_ring()
-             sage: cpQ
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 0
-             //   number of vars : 2
-             //        block   1 : ordering dp
-@@ -1600,7 +1609,10 @@ class SingularElement(ExtraTabCompletion, ExpectElement):
-         # using Singular's term order
-         from sage.rings.polynomial.term_order import termorder_from_singular
-         from sage.all import PolynomialRing
--        if singular.eval('typeof(basering)')=='ring':
-+        # Meanwhile Singulars quotient rings are also of 'ring' type, not 'qring' as it was in the past.
-+        # To find out if a singular ring is a quotient ring or not checking for ring type does not help
-+        # and instead of that we we check if the quotient ring is zero or not:
-+        if (singular.eval('ideal(basering)==0')=='1'):
-             return PolynomialRing(BR, names=singular.eval('varstr(basering)'), order=termorder_from_singular(singular))
-         P = PolynomialRing(BR, names=singular.eval('varstr(basering)'), order=termorder_from_singular(singular))
-         return P.quotient(singular('ringlist(basering)[4]')._sage_(P), names=singular.eval('varstr(basering)'))
-@@ -1722,11 +1734,18 @@ class SingularElement(ExtraTabCompletion, ExpectElement):
-             singular_poly_list = self.parent().eval("string(coef(%s,%s))"%(\
-                     self.name(),variable_str)).split(",")
- 
--        if singular_poly_list == ['1','0'] :
--            return R(0)
-+        # Directly treat constants
-+        if singular_poly_list[0] in ['1', '(1.000e+00)']:
-+            return R(singular_poly_list[1])
- 
-         coeff_start = len(singular_poly_list) // 2
- 
-+        # Singular 4 puts parentheses around floats and sign outside them
-+        charstr = self.parent().eval('charstr(basering)').split(',',1)
-+        if charstr[0] in ['real', 'complex']:
-+              for i in range(coeff_start, 2*coeff_start):
-+                  singular_poly_list[i] = singular_poly_list[i].replace('(','').replace(')','')
-+
-         if isinstance(R,(MPolynomialRing_polydict,QuotientRing_generic)) and (ring_is_fine or can_convert_to_singular(R)):
-             # we need to lookup the index of a given variable represented
-             # through a string
-@@ -1778,7 +1797,7 @@ class SingularElement(ExtraTabCompletion, ExpectElement):
-                         exp = int(1)
- 
-                 if kcache is None:
--                    sage_repr[exp]=k(singular_poly_list[coeff_start+i])
-+                    sage_repr[exp] = k(singular_poly_list[coeff_start+i])
-                 else:
-                     elem = singular_poly_list[coeff_start+i]
-                     if elem not in kcache:
-@@ -1861,7 +1880,7 @@ class SingularElement(ExtraTabCompletion, ExpectElement):
-         ::
- 
-             sage: singular.eval('ring R = integer, (x,y,z),lp')
--            '// ** redefining R **'
-+            '// ** redefining R (ring R = integer, (x,y,z),lp;)'
-             sage: I = singular.ideal(['x^2','y*z','z+x'])
-             sage: I.sage()
-             Ideal (x^2, y*z, x + z) of Multivariate Polynomial Ring in x, y, z over Integer Ring
-@@ -1883,7 +1902,8 @@ class SingularElement(ExtraTabCompletion, ExpectElement):
-         Note that the current base ring has not been changed by asking for another ring::
- 
-             sage: singular('basering')
--            //   coeff. ring is : Integers
-+            polynomial ring, over a domain, global ordering
-+            //   coeff. ring is : integer
-             //   number of vars : 3
-             //        block   1 : ordering lp
-             //                  : names    x y z
-@@ -1967,6 +1987,7 @@ class SingularElement(ExtraTabCompletion, ExpectElement):
-             sage: R = singular.ring(7, '(a,b)', 'ds')
-             sage: S = singular.ring('real', '(a,b)', 'lp')
-             sage: singular.current_ring()
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 0 (real)
-             //   number of vars : 2
-             //        block   1 : ordering lp
-@@ -1974,6 +1995,7 @@ class SingularElement(ExtraTabCompletion, ExpectElement):
-             //        block   2 : ordering C
-             sage: R.set_ring()
-             sage: singular.current_ring()
-+            polynomial ring, over a field, local/mixed ordering
-             //   characteristic : 7
-             //   number of vars : 2
-             //        block   1 : ordering ds
-@@ -2229,6 +2251,7 @@ def reduce_load():
-     By :trac:`18848`, pickling actually often works::
- 
-         sage: loads(dumps(singular.ring()))
-+        polynomial ring, over a field, global ordering
-         //   characteristic : 0
-         //   number of vars : 1
-         //        block   1 : ordering lp
-@@ -2252,13 +2275,15 @@ def generate_docstring_dictionary():
-         sage: from sage.interfaces.singular import generate_docstring_dictionary
-         sage: generate_docstring_dictionary()
-     """
-+    from sage.env import SAGE_LOCAL
-+
-     global nodes
-     global node_names
- 
-     nodes.clear()
-     node_names.clear()
- 
--    singular_docdir = os.environ["SAGE_LOCAL"]+"/share/singular/"
-+    singular_docdir = SAGE_LOCAL+"/share/singular/"
- 
-     new_node = re.compile("File: singular\.hlp,  Node: ([^,]*),.*")
-     new_lookup = re.compile("\* ([^:]*):*([^.]*)\..*")
-diff --git a/src/sage/interfaces/tests.py b/src/sage/interfaces/tests.py
-index e41f15c..af9797a 100644
---- a/src/sage/interfaces/tests.py
-+++ b/src/sage/interfaces/tests.py
-@@ -39,7 +39,7 @@ Test that write errors to stderr are handled gracefully by GAP
-     0
-     sage: subprocess.call("echo syntax error | ipython", **kwds) in (0,1)
-     True
--    sage: subprocess.call("echo syntax error | singular", **kwds)
-+    sage: subprocess.call("echo syntax error | Singular", **kwds)
-     0
- """
- from __future__ import print_function
-diff --git a/src/sage/libs/singular/decl.pxd b/src/sage/libs/singular/decl.pxd
-index 7a5af56..8235e9d 100644
---- a/src/sage/libs/singular/decl.pxd
-+++ b/src/sage/libs/singular/decl.pxd
-@@ -1,3 +1,8 @@
-+# distutils: extra_compile_args = SINGULAR_CFLAGS
-+# distutils: libraries = SINGULAR_LIBRARIES
-+# distutils: library_dirs = SINGULAR_LIBDIR
-+# distutils: language = c++
-+
- """
- Declarations of Singular's C/C++ Functions
- 
-@@ -25,9 +30,6 @@ AUTHOR:
- 
- from sage.libs.gmp.types cimport mpz_t, mpz_ptr
- 
--cdef extern from "factor.h":
--    cdef int libfac_interruptflag
--
- cdef extern from "factory/factory.h":
- 
-     #
-@@ -45,15 +47,14 @@ cdef extern from "factory/factory.h":
-     cdef int SW_USE_NTL_GCD_P
-     cdef int SW_USE_NTL_SORT
- 
--
--cdef extern from "libsingular.h":
-+cdef extern from "singular/Singular/libsingular.h":
- 
-     #
-     # OPTIONS
-     #
- 
--    cdef unsigned int singular_options "test"
--    cdef unsigned int singular_verbose_options "verbose"
-+    cdef unsigned int singular_options "si_opt_1"           # previously 'test'
-+    cdef unsigned int singular_verbose_options "si_opt_2"   # previously 'verbose'
- 
-     # actual options
-     cdef int OPT_PROT
-@@ -116,56 +117,81 @@ cdef extern from "libsingular.h":
-         mpz_t n
-         int s
- 
--    # finite extension field elements
-+    # See singular/libpolys/coeffs/coeffs.h for documentation
-+    cdef enum n_coeffType:
-+        n_unknown
-+        n_Zp
-+        n_Q
-+        n_R
-+        n_GF
-+        n_long_R
-+        n_algExt
-+        n_transExt
-+        n_long_C
-+        n_Z
-+        n_Zn
-+        n_Znm
-+        n_Z2m
-+        n_CF
- 
--    ctypedef struct napoly "polyrec"
-+    ctypedef struct ring "ip_sring"
-+    ctypedef struct AlgExtInfo
- 
--    # algebraic numbers
-+    ctypedef struct n_Procs_s:
- 
--    ctypedef struct lnumber "slnumber":
--        napoly *z
--        napoly *n
--        int s
-+        number* cfDiv(number *, number *, const n_Procs_s* r)
-+        number* cfAdd(number *, number *, const n_Procs_s* r)  # algebraic number addition
-+        number* cfSub(number *, number *, const n_Procs_s* r)
-+        number* cfMult(number *, number *, const n_Procs_s* r)  # algebraic number multiplication
- 
--    ctypedef struct ring "ip_sring"
-+        number*  (*cfInit)(int i, const n_Procs_s* r ) # algebraic number from int
-+        number*  (*cfParameter)(int i, const n_Procs_s* r)
-+        int     (*cfParDeg)(number* n, const n_Procs_s* r)
-+        int     (*cfSize)(number* n, const n_Procs_s* r)
-+        int     (*cfInt)(number* n, const n_Procs_s* r)
-+        int     (*cdDivComp)(number* a,number* b, const n_Procs_s* r)
-+        number*  (*cfGetUnit)(number* a, const n_Procs_s* r)
-+        number*  (*cfExtGcd)(number* a, number* b, number* *s, number* *t , const n_Procs_s* r)
- 
--    ctypedef struct n_Procs_s:
-+        void (*cfDelete)(number **, const n_Procs_s*)
-+
-+        number*  (*cfInpNeg)(number* a,  const n_Procs_s* r)
-+        number*  (*cfInvers)(number* a,  const n_Procs_s* r)
-+        number*  (*cfCopy)(number* a,  const n_Procs_s* r) # deep copy of algebraic number
-+        number*  (*cfRePart)(number* a, const n_Procs_s* cf)
-+        number*  (*cfImPart)(number* a, const n_Procs_s* cf)
-+        void    (*cfWrite)(number* a, const n_Procs_s* r)
-+        void    (*cfNormalize)(number* a,  const n_Procs_s* r)
- 
--        number* nDiv(number *, number *)
--        number* nAdd(number *, number *)
--        number* nSub(number *, number *)
--        number* nMul(number *, number *)
--
--        void    (*nNew)(number* * a)
--        number*  (*nInit)(int i)
--        number*  (*nPar)(int i)
--        int     (*nParDeg)(number* n)
--        int     (*nSize)(number* n)
--        int     (*n_Int)(number* n, ring *)
--        int     (*nDivComp)(number* a,number* b)
--        number*  (*nGetUnit)(number* a)
--        number*  (*nExtGcd)(number* a, number* b, number* *s, number* *t)
--
--        number*  (*nNeg)(number* a)
--        number*  (*nInvers)(number* a)
--        number*  (*nCopy)(number* a)
--        number*  (*nRePart)(number* a)
--        number*  (*nImPart)(number* a)
--        void    (*nWrite)(number* a)
--        void    (*nNormalize)(number* a)
--
--        bint (*nDivBy)(number* a, number* b)
--        bint (*nEqual)(number* a,number* b)
--        bint (*nIsZero)(number* a)
--        bint (*nIsOne)(number* a)
--        bint (*nIsMOne)(number* a)
--        bint (*nGreaterZero)(number* a)
--        void (*nPower)(number* a, int i, number* * result)
-+
-+
-+        bint (*cfDivBy)(number* a, number* b, const n_Procs_s* r)
-+        bint (*cfEqual)(number* a,number* b, const n_Procs_s* )
-+        bint (*cfIsZero)(number* a, const n_Procs_s* ) # algebraic number comparison with zero
-+        bint (*cfIsOne)(number* a, const n_Procs_s* )  # algebraic number comparison with one
-+        bint (*cfIsMOne)(number* a, const n_Procs_s* )
-+        bint (*cfGreaterZero)(number* a, const n_Procs_s* )
-+        void (*cfPower)(number* a, int i, number* * result,  const n_Procs_s* r) # algebraic number power
-+
-+
-+        ring *extRing
-+        int ch
-+        mpz_ptr    modBase;
-+        unsigned long modExponent;
-+
-+        #n_coeffType type
-+        int type
- 
-     # polynomials
- 
-+    const char ** n_ParameterNames(const n_Procs_s* r)
-+
-+    int n_NumberOfParameters(const n_Procs_s* r)
-+
-     ctypedef struct poly "polyrec":
-         poly *next
-+        number *coef
-+        unsigned long exp[1]
- 
-     # ideals
- 
-@@ -193,22 +219,33 @@ cdef extern from "libsingular.h":
-         p_Procs_s *p_Procs #polxnomial procs
-         ideal *qideal #quotient ideal
- 
--        char **parameter # parameter names
--        ring *algring # base extension field
-         short N # number of variables
--        short P # number of parameters
--        int ch # characteristic (0:QQ, p:GF(p),-p:GF(q), 1:NF)
--        unsigned int ringtype # field etc.
--        mpz_ptr ringflaga
--        unsigned long ringflagb
-+
-         int pCompIndex # index of components
-         unsigned long bitmask # mask for getting single exponents
- 
--        n_Procs_s*    cf
-+
-+        n_Procs_s*    cf # coefficient field/ring
-         int ref
- 
-+        # return total degree of p
-+
-+        long (*pLDeg)(poly *p, int *l, ring *r)
-+        long (*pLDegOrig)(poly *p, int *l, ring *r)
-+        long (*pFDeg)(poly *p, ring *r)
-+        long (*pFDegOrig)(poly *p, ring *r)
-+
-+
-+    long p_Deg(poly *p, ring *r)    
-+    long p_WTotaldegree(poly *p, ring *r)
-+    long p_Totaldegree(poly *p, ring *r)
-+    long p_WDegree(poly *p, ring *r)
-+    
-     # available ring orders
- 
-+    ctypedef struct AlgExtInfo:
-+        ring * r
-+
-     cdef enum rRingOrder_t:
-         ringorder_no
-         ringorder_a
-@@ -368,7 +405,6 @@ cdef extern from "libsingular.h":
- 
-     cdef ring *currRing
-     cdef ideal *currQuotient
--
-     # omalloc bin for numbers
- 
-     cdef omBin *rnumber_bin
-@@ -393,7 +429,7 @@ cdef extern from "libsingular.h":
-     cdef idhdl *currRingHdl
- 
-     cdef int errorreported
--    cdef int verbose
-+    cdef int si_opt_2    #  previously 'verbose'
-     cdef void * currentVoice
-     cdef int myynest
- 
-@@ -408,6 +444,10 @@ cdef extern from "libsingular.h":
- 
-     int siInit(char *)
- 
-+    ctypedef short (*cfInitCharProc)(coeffs, void *)
-+
-+    n_coeffType nRegister(n_coeffType n, cfInitCharProc p)
-+
-     # external resource init
- 
-     void feInitResources(char *name)
-@@ -439,7 +479,25 @@ cdef extern from "libsingular.h":
- 
-     # construct ring with characteristic, number of vars and names
- 
--    ring *rDefault(int char, int nvars, char **names)
-+    ring *rDefault(int char , int nvars, char **names)
-+    ring *rDefault(const n_Procs_s* cf, int nvars, char **names)
-+    ring *rDefault(int ch             , int nvars, char **names,int ord_size, int *ord, int *block0, int *block1, int **wvhdl)
-+    ring *rDefault(const n_Procs_s* cf, int nvars, char **names,int ord_size, int *ord, int *block0, int *block1, int **wvhdl)
-+
-+
-+
-+
-+    # see coeffs.h
-+    ctypedef struct  GFInfo:
-+        int GFChar;
-+        int GFDegree;
-+        const char* GFPar_name;
-+
-+
-+    # parameter is pointer to gGFInfo
-+    #
-+    n_Procs_s* nInitChar(n_coeffType t, void * parameter)
-+
- 
-     # ring destructor
- 
-@@ -541,7 +599,7 @@ cdef extern from "libsingular.h":
- 
-     # return whether a polynomial is homogenous
- 
--    int pIsHomogeneous(poly *p)
-+    int p_IsHomogeneous(poly *p, const  ring *r)
- 
-     # return string representation of p
- 
-@@ -614,6 +672,8 @@ cdef extern from "libsingular.h":
- 
-     long p_Totaldegree(poly *p, ring *r)
- 
-+    long pLDeg1_Totaldegree(poly * p,int *l, ring * r)
-+
-     # iterate through the monomials of p
- 
-     poly *pNext(poly *p)
-@@ -651,29 +711,26 @@ cdef extern from "libsingular.h":
- 
-     # gcd of f and g
- 
--    poly *singclap_gcd ( poly *f, poly *g )
-+    poly *singclap_gcd ( poly *f, poly *g, ring * r )
- 
-     # resultant of f and g in x
- 
--    poly *singclap_resultant ( poly *f, poly *g , poly *x)
-+    poly *singclap_resultant ( poly *f, poly *g , poly *x, ring * r)
- 
-     # extended gcd of f and g
- 
--    int singclap_extgcd( poly *f, poly *g, poly *res, poly *pa, poly *pb )
-+    int singclap_extgcd( poly *f, poly *g, poly *res, poly *pa, poly *pb, ring * r )
- 
-     # full polynomial division (as opposed to monomial division)
- 
--    poly *singclap_pdivide ( poly *f, poly *g )
-+    poly *singclap_pdivide ( poly *f, poly *g, ring * r )
- 
-     # factorization
- 
--    ideal *singclap_factorize ( poly *f, intvec ** v , int with_exps)
--
--    # TRUE if p is square free
--    int singclap_isSqrFree(poly *p)
-+    ideal *singclap_factorize ( poly *f, intvec ** v , int with_exps, ring * r)
- 
-     # return determinant of i
--    poly *singclap_det(matrix *i)
-+    poly *singclap_det(matrix *i, ring * r)
- 
-     # normal form calculation of p with respect to i, q is quotient
-     # ring.
-@@ -685,9 +742,7 @@ cdef extern from "libsingular.h":
- 
-     poly *pDiff(poly *p, int i)
- 
--    # return total degree of p
- 
--    int (*pLDeg)(poly *p, int *l, ring *r)
- 
-     # TRUE if p is a vector
- 
-@@ -716,13 +771,11 @@ cdef extern from "libsingular.h":
- 
-     number *nlRInit(int)
- 
--    # rational number from numerator and denominator
- 
--    number *nlInit2gmp(mpz_t n, mpz_t d)
- 
-     # rational number from numerator and denominator
- 
--    number *nlInit2(int i, int j)
-+    number *nlInit2(int i, int j,const n_Procs_s* cf)
- 
-     # simplify rational number (cancel common factors)
- 
-@@ -732,65 +785,6 @@ cdef extern from "libsingular.h":
- 
-     number *nlCopy(number *)
- 
--    # get numerator
--
--    number *nlGetNumerator(number *n, ring *r)
--
--    # get denominator
--
--    number *nlGetDenom(number *n, ring *r)
--
--    # delete rational number
--
--    void nlDelete(number **n, ring *r)
--
--    # i-th algebraic number paraemeter
--
--    number *naPar(int i)
--
--    # algebraic number power
--
--    void naPower(number *, int, number **)
--
--    # algebraic number multiplication
--
--    number *naMult(number *, number *)
--
--    # algebraic number addition
--
--    number *naAdd(number *, number *)
--
--    # deep copy of algebraic number
--
--    number *naCopy(number *)
--
--    # algebraic number from int
--
--    number *naInit(int, ring *r)
--
--    # algebraic number destructor
--
--    void naDelete(number **, ring*)
--
--    # algebraic number comparison with zero
--
--    int naIsZero(number *)
--
--    # algebraic number comparison with one
--
--    int naIsOne(number *)
--
--    # get current coefficent
--
--    number *napGetCoeff(napoly *z)
--
--    # get exponent of i-th variable
--
--    int napGetExpFrom(napoly *, int i, ring* r)
--
--    # normalize a number
--
--    void naNormalize(number *)
- 
-     # number to integer handle
- 
-@@ -800,19 +794,6 @@ cdef extern from "libsingular.h":
- 
-     long SR_HDL(number *)
- 
--    # map Q -> Q(a)
--    number *naMap00(number *c)
--
--    # init integer
--    number *nrzInit(int i, ring *r)
--
--    # init ZmodN from GMP
--    number *nrnMapGMP(number *v)
--
--    #init 2^m from a long
--    number *nr2mMapZp(number *)
--
--
-     # get C int from ZmodN
-     int nrnInt(number *v)
- 
-@@ -824,9 +805,6 @@ cdef extern from "libsingular.h":
- 
-     void id_Delete(ideal **, ring *)
- 
--    # mappinf from ideal i1 in r1 by i2 to r2
--
--    ideal *fast_map(ideal *i1, ring *r1, ideal *i2, ring *r2)
- 
-     # lifting
- 
-@@ -842,7 +820,7 @@ cdef extern from "libsingular.h":
- 
-     # rank of free module for m
- 
--    long idRankFreeModule(ideal *m, ring *r)
-+    long id_RankFreeModule(ideal *m, ring *r)
- 
-     # buchberger's algorithm
- 
-@@ -1003,54 +981,127 @@ cdef extern from "libsingular.h":
-     void setFlag(leftv *A, int F)
-     void resetFlag(leftv *A, int F)
- 
--cdef extern from "singular/prCopy.h":
-+
-+
-+
-+cdef extern from "singular/coeffs/rmodulo2m.h":
-+
-+    #init 2^m from a long
-+    number *nr2mMapZp(number *,const n_Procs_s* src,const n_Procs_s* dst)
-+
-+
-+cdef extern from "singular/kernel/maps/fast_maps.h":
-+
-+    # mappinf from ideal i1 in r1 by i2 to r2
-+
-+    ideal *fast_map_common_subexp(ideal *i1, ring *r1, ideal *i2, ring *r2)
-+
-+
-+
-+cdef extern from "singular/polys/ext_fields/algext.h":
-+
-+    naInitChar(n_Procs_s* cf, void * infoStruct)
-+
-+    ctypedef number* (*nMapFunc)(number *c,const n_Procs_s* src,const n_Procs_s* dst)
-+
-+    nMapFunc naSetMap(const n_Procs_s* src, const n_Procs_s* dst)
-+
-+cdef extern from "singular/coeffs/rmodulon.h":
-+
-+    # init ZmodN from GMP
-+    number *nrnMapGMP(number *v,const n_Procs_s* src,const n_Procs_s* dst)
-+
-+    nMapFunc nrnSetMap(const n_Procs_s* src,const n_Procs_s* dst)
-+
-+cdef extern from "singular/coeffs/rmodulon.h":
-+    # see rmodulon.h
-+
-+    ctypedef struct ZnmInfo:
-+       mpz_ptr base;
-+       unsigned long exp;
-+
-+
-+cdef extern from "singular/coeffs/rintegers.h":
-+
-+    # init integer
-+    number *nrzInit(int i, const n_Procs_s* cf)
-+
-+
-+cdef extern from "singular/polys/weight.h":
-+
-+
-+    double wFunctionalBuch(int *degw, int *lpol, int npol, double *rel, double wx, double wNsqr)
-+
-+
-+cdef extern from "singular/polys/prCopy.h":
-     poly *prCopyR_NoSort(poly *p, ring *r, ring *dest_r)
-     poly *prCopyR(poly *p, ring *r, ring *dest_r)
- 
-     cdef int LANG_TOP
- 
-+cdef extern from "singular/polys/nc/nc.h":
-     # Non-commutative functions
-     ctypedef enum nc_type:
--      nc_error # Something's gone wrong!
--      nc_general # yx=q xy+...
--      nc_skew # yx=q xy
--      nc_comm # yx= xy
--      nc_lie,  # yx=xy+...
--      nc_undef, # for internal reasons */
--      nc_exterior #
-+        nc_error
-+        nc_general
-+        nc_skew
-+        nc_comm
-+        nc_lie
-+        nc_undef
-+        nc_exterior
- 
--
--cdef extern from "singular/gring.h":
-     void ncRingType(ring *, nc_type)
-     nc_type ncRingType_get "ncRingType" (ring *)
-     int nc_CallPlural(matrix* CC, matrix* DD, poly* CN, poly* DN, ring* r)
-     bint nc_SetupQuotient(ring *, ring *, bint)
- 
--cdef extern from "singular/sca.h":
-+
-+cdef extern from "singular/coeffs/longrat.h":
-+
-+    # get numerator
-+
-+    number *nlGetNumerator(number *n, const n_Procs_s* cf)
-+
-+    # get denominator
-+
-+    number *nlGetDenom(number *n, const n_Procs_s* cf)
-+
-+
-+    # rational number from numerator and denominator
-+
-+    number *nlInit2gmp(mpz_t n, mpz_t d,const n_Procs_s* cf)
-+
-+
-+    # delete rational number
-+
-+    void nlDelete(number **n, const n_Procs_s* cf)
-+
-+
-+cdef extern from "singular/polys/nc/sca.h":
-     void sca_p_ProcsSet(ring *, p_Procs_s *)
-     void scaFirstAltVar(ring *, int)
-     void scaLastAltVar(ring *, int)
- 
--cdef extern from "singular/ring.h":
-+cdef extern from "singular/polys/monomials/ring.h":
-     bint rIsPluralRing(ring* r)
-     void rPrint "rWrite"(ring* r)
-     char* rOrderingString "rOrdStr"(ring* r)
-     void pDebugPrint "p_DebugPrint" (poly*p, ring* r)
- 
--cdef extern from "singular/stairc.h":
-+cdef extern from "singular/kernel/combinatorics/stairc.h":
-     # Computes the monomial basis for R[x]/I
-     ideal *scKBase(int deg, ideal *s, ideal *Q)
- 
--cdef extern from "singular/lists.h":
-+cdef extern from "singular/Singular/lists.h":
-     ctypedef struct lists "slists":
-         int    nr
-         leftv  *m
-         void (*Init)(int n)
- 
--cdef extern from "singular/kstd1.h":
-+cdef extern from "singular/kernel/GBEngine/kstd1.h":
-     cdef extern int Kstd1_deg   # degBound, default 0
-     cdef extern int Kstd1_mu    # multBound, default 0
- 
--cdef extern from "singular/syz.h":
-+cdef extern from "singular/kernel/GBEngine/syz.h":
-     ctypedef struct syStrategy "ssyStrategy":
-         short references
-diff --git a/src/sage/libs/singular/function.pyx b/src/sage/libs/singular/function.pyx
-index 74ecee3..9265099 100644
---- a/src/sage/libs/singular/function.pyx
-+++ b/src/sage/libs/singular/function.pyx
-@@ -43,7 +43,7 @@ available, use the :func:`lib` function as shown below::
-     sage: primdecSY = singular_function('primdecSY')
-     Traceback (most recent call last):
-     ...
--    NameError: Function 'primdecSY' is not defined.
-+    NameError: Singular library function 'primdecSY' is not defined
- 
-     sage: singular_lib('primdec.lib')
-     sage: primdecSY = singular_function('primdecSY')
-@@ -202,7 +202,7 @@ cdef class RingWrap:
-             sage: ring(l, ring=P).npars()
-             0
-         """
--        return self._ring.P
-+        return n_NumberOfParameters(self._ring.cf)
- 
-     def ordering_string(self):
-         """
-@@ -236,7 +236,7 @@ cdef class RingWrap:
-             sage: ring(l, ring=P).par_names()
-             []
-         """
--        return [self._ring.parameter[i] for i in range(self.npars())]
-+        return [n_ParameterNames(self._ring.cf)[i] for i in range(self.npars())]
- 
-     def characteristic(self):
-         """
-@@ -252,7 +252,7 @@ cdef class RingWrap:
-             sage: ring(l, ring=P).characteristic()
-             0
-         """
--        return self._ring.ch
-+        return self._ring.cf.ch
- 
-     def is_commutative(self):
-         """
-@@ -1061,7 +1061,7 @@ cdef class LibraryCallHandler(BaseCallHandler):
-             res = <leftv*> omAllocBin(sleftv_bin)
-             res.Init()
-             res.Copy(&iiRETURNEXPR)
--            iiRETURNEXPR.Init();
-+            iiRETURNEXPR.Init()
-             return res
-         raise RuntimeError("Error raised calling singular function")
- 
-@@ -1104,7 +1104,7 @@ cdef class KernelCallHandler(BaseCallHandler):
-         cdef leftv *arg2
-         cdef leftv *arg3
- 
--        cdef int number_of_arguments = len(argument_list)
-+        cdef Py_ssize_t number_of_arguments = len(argument_list)
- 
-         # Handle functions with an arbitrary number of arguments, sent
-         # by an argument list.
-@@ -1147,7 +1147,9 @@ cdef class KernelCallHandler(BaseCallHandler):
-         global error_messages
- 
-         errorreported += 1
--        error_messages.append("Wrong number of arguments")
-+        error_messages.append(
-+                "Wrong number of arguments (got {} arguments, arity code is {})"
-+                .format(number_of_arguments, self.arity))
-         return NULL
- 
-     cdef bint free_res(self):
-@@ -1184,6 +1186,7 @@ cdef class SingularFunction(SageObject):
-             currRingHdl = ggetid("my_awesome_sage_ring")
-             if currRingHdl == NULL:
-                 currRingHdl = enterid("my_awesome_sage_ring", 0, RING_CMD, &IDROOT, 1)
-+                currRingHdl.data.uring = <ring *>omAlloc0Bin(sip_sring_bin)
-             currRingHdl.data.uring.ref += 1
- 
-     cdef BaseCallHandler get_call_handler(self):
-@@ -1248,9 +1251,9 @@ cdef class SingularFunction(SageObject):
-             sage: size(1,2)
-             Traceback (most recent call last):
-             ...
--            RuntimeError: Error in Singular function call 'size':
--             Wrong number of arguments
--            sage: size('foobar')
-+            RuntimeError: error in Singular function call 'size':
-+            Wrong number of arguments (got 2 arguments, arity code is 300)
-+            sage: size('foobar', ring=P)
-             6
- 
-         Show the usage of the optional ``attributes`` parameter::
-@@ -1298,9 +1301,9 @@ cdef class SingularFunction(SageObject):
-             sage: _ = triangL(I)
-             Traceback (most recent call last):
-             ...
--            RuntimeError: Error in Singular function call 'triangL':
--             The input is no groebner basis.
--             leaving triang.lib::triangL
-+            RuntimeError: error in Singular function call 'triangL':
-+            The input is no groebner basis.
-+            leaving triang.lib::triangL
- 
-             sage: G= Ideal(I.groebner_basis())
-             sage: triangL(G,attributes={G:{'isSB':1}})
-@@ -1510,8 +1513,8 @@ cdef inline call_function(SingularFunction self, tuple args, object R, bint sign
- 
-     if errorreported:
-         errorreported = 0
--        raise RuntimeError("Error in Singular function call '%s':\n %s"%
--            (self._name, "\n ".join(error_messages)))
-+        raise RuntimeError("error in Singular function call %r:\n%s"%
-+            (self._name, "\n".join(error_messages)))
- 
-     res = argument_list.to_python(_res)
- 
-@@ -1552,7 +1555,7 @@ cdef class SingularLibraryFunction(SingularFunction):
-     cdef BaseCallHandler get_call_handler(self):
-         cdef idhdl* singular_idhdl = ggetid(self._name)
-         if singular_idhdl==NULL:
--            raise NameError("Function '%s' is not defined."%self._name)
-+            raise NameError("Singular library function {!r} is not defined".format(self._name))
-         if singular_idhdl.typ!=PROC_CMD:
-             raise ValueError("Not a procedure")
- 
-@@ -1587,15 +1590,19 @@ cdef class SingularKernelFunction(SingularFunction):
-             sage: f = SingularKernelFunction("std")
-             sage: f(I)
-             [y - 1, x + 1]
-+            sage: SingularKernelFunction("no_such_function")
-+            Traceback (most recent call last):
-+            ...
-+            NameError: Singular kernel function 'no_such_function' is not defined
-         """
-         super(SingularKernelFunction,self).__init__(name)
-         self.call_handler = self.get_call_handler()
- 
-     cdef BaseCallHandler get_call_handler(self):
--        cdef int cmd_n = -1
-+        cdef int cmd_n = 0
-         arity = IsCmd(self._name, cmd_n) # call by reverence for CMD_n
--        if cmd_n == -1:
--            raise NameError("Function '%s' is not defined."%self._name)
-+        if not cmd_n:
-+            raise NameError("Singular kernel function {!r} is not defined".format(self._name))
- 
-         return KernelCallHandler(cmd_n, arity)
- 
-@@ -1647,18 +1654,18 @@ def singular_function(name):
-         sage: factorize()
-         Traceback (most recent call last):
-         ...
--        RuntimeError: Error in Singular function call 'factorize':
--         Wrong number of arguments
-+        RuntimeError: error in Singular function call 'factorize':
-+        Wrong number of arguments (got 0 arguments, arity code is 303)
-         sage: factorize(f, 1, 2)
-         Traceback (most recent call last):
-         ...
--        RuntimeError: Error in Singular function call 'factorize':
--         Wrong number of arguments
-+        RuntimeError: error in Singular function call 'factorize':
-+        Wrong number of arguments (got 3 arguments, arity code is 303)
-         sage: factorize(f, 1, 2, 3)
-         Traceback (most recent call last):
-         ...
--        RuntimeError: Error in Singular function call 'factorize':
--         Wrong number of arguments
-+        RuntimeError: error in Singular function call 'factorize':
-+        Wrong number of arguments (got 4 arguments, arity code is 303)
- 
-     The Singular function ``list`` can be called with any number of
-     arguments::
-@@ -1675,10 +1682,10 @@ def singular_function(name):
- 
-     We try to define a non-existing function::
- 
--        sage: number_foobar = singular_function('number_foobar');
-+        sage: number_foobar = singular_function('number_foobar')
-         Traceback (most recent call last):
-         ...
--        NameError: Function 'number_foobar' is not defined.
-+        NameError: Singular library function 'number_foobar' is not defined
- 
-     ::
- 
-@@ -1809,21 +1816,22 @@ def lib(name):
-         sage: primes(2,10, ring=GF(127)['x,y,z'])
-         (2, 3, 5, 7)
-     """
--    global verbose
--    cdef int vv = verbose
-+    global si_opt_2
- 
--    if get_verbose() <= 0:
--        verbose &= ~Sy_bit(V_LOAD_LIB)
-+    cdef int vv = si_opt_2
- 
-     if get_verbose() <= 0:
--        verbose &= ~Sy_bit(V_REDEFINE)
-+         si_opt_2 &= ~Sy_bit(V_LOAD_LIB)
-+         si_opt_2 &= ~Sy_bit(V_REDEFINE)
- 
--    cdef bint failure = iiLibCmd(omStrDup(name), 1, 1, 1)
--    verbose = vv
-+    cdef char* cname = omStrDup(name)
-+    sig_on()
-+    cdef bint failure = iiLibCmd(cname, 1, 1, 1)
-+    sig_off()
-+    si_opt_2 = vv
- 
-     if failure:
--        raise NameError("Library '%s' not found."%(name,))
--
-+        raise NameError("Singular library {!r} not found".format(name))
- 
- 
- def list_of_functions(packages=False):
-@@ -1832,11 +1840,12 @@ def list_of_functions(packages=False):
- 
-     INPUT:
- 
--    - ``packages`` - include local functions in packages.
-+    - ``packages`` -- include local functions in packages.
- 
-     EXAMPLE::
- 
--        sage: 'groebner' in sage.libs.singular.function.list_of_functions()
-+        sage: from sage.libs.singular.function import list_of_functions
-+        sage: 'groebner' in list_of_functions()
-         True
-     """
-     cdef list l = []
-@@ -1856,7 +1865,6 @@ def list_of_functions(packages=False):
-     return l
- 
- 
--#cdef ring*?
- cdef inline RingWrap new_RingWrap(ring* r):
-     cdef RingWrap ring_wrap_result = RingWrap.__new__(RingWrap)
-     ring_wrap_result._ring = r
-diff --git a/src/sage/libs/singular/groebner_strategy.pyx b/src/sage/libs/singular/groebner_strategy.pyx
-index b4c2be9..a5843e3 100644
---- a/src/sage/libs/singular/groebner_strategy.pyx
-+++ b/src/sage/libs/singular/groebner_strategy.pyx
-@@ -23,7 +23,7 @@ cdef extern from *: # hack to get at cython macro
- 
- from sage.libs.singular.decl cimport ideal, ring, poly, currRing
- from sage.libs.singular.decl cimport rChangeCurrRing
--from sage.libs.singular.decl cimport new_skStrategy, delete_skStrategy, idRankFreeModule
-+from sage.libs.singular.decl cimport new_skStrategy, delete_skStrategy, id_RankFreeModule
- from sage.libs.singular.decl cimport initEcartBBA, enterSBba, initBuchMoraCrit, initS, pNorm, id_Delete, kTest
- from sage.libs.singular.decl cimport omfree, redNF, p_Copy, redtailBba
- 
-@@ -117,7 +117,7 @@ cdef class GroebnerStrategy(SageObject):
-         cdef ideal *i = sage_ideal_to_singular_ideal(L)
-         self._strat = new_skStrategy()
- 
--        self._strat.ak = idRankFreeModule(i, R._ring)
-+        self._strat.ak = id_RankFreeModule(i, R._ring)
-         #- creating temp data structures
-         initBuchMoraCrit(self._strat)
-         self._strat.initEcart = initEcartBBA
-@@ -353,7 +353,7 @@ cdef class NCGroebnerStrategy(SageObject):
-         cdef ideal *i = sage_ideal_to_singular_ideal(L)
-         self._strat = new_skStrategy()
- 
--        self._strat.ak = idRankFreeModule(i, R._ring)
-+        self._strat.ak = id_RankFreeModule(i, R._ring)
-         #- creating temp data structures
-         initBuchMoraCrit(self._strat)
-         self._strat.initEcart = initEcartBBA
-diff --git a/src/sage/libs/singular/polynomial.pyx b/src/sage/libs/singular/polynomial.pyx
-index b40dc07..e243fae 100644
---- a/src/sage/libs/singular/polynomial.pyx
-+++ b/src/sage/libs/singular/polynomial.pyx
-@@ -22,8 +22,8 @@ plusminus_pattern = re.compile("([^\(^])([\+\-])")
- from sage.libs.singular.decl cimport number, ideal
- from sage.libs.singular.decl cimport currRing, rChangeCurrRing
- from sage.libs.singular.decl cimport p_Copy, p_Add_q, p_Neg, pp_Mult_nn, p_GetCoeff, p_IsConstant, p_Cmp, pNext
--from sage.libs.singular.decl cimport p_GetMaxExp, pp_Mult_qq, pPower, p_String, p_GetExp, pLDeg
--from sage.libs.singular.decl cimport n_Delete, idInit, fast_map, id_Delete
-+from sage.libs.singular.decl cimport p_GetMaxExp, pp_Mult_qq, pPower, p_String, p_GetExp, p_Deg, p_Totaldegree, p_WTotaldegree, p_WDegree
-+from sage.libs.singular.decl cimport n_Delete, idInit, fast_map_common_subexp, id_Delete
- from sage.libs.singular.decl cimport omAlloc0, omStrDup, omFree
- from sage.libs.singular.decl cimport p_GetComp, p_SetComp
- from sage.libs.singular.decl cimport pSubst
-@@ -198,7 +198,7 @@ cdef int singular_polynomial_call(poly **ret, poly *p, ring *r, list args, poly
-     from_id.m[0] = p
- 
-     rChangeCurrRing(r)
--    cdef ideal *res_id = fast_map(from_id, r, to_id, r)
-+    cdef ideal *res_id = fast_map_common_subexp(from_id, r, to_id, r)
-     ret[0] = res_id.m[0]
- 
-     # Unsure why we have to normalize here. See #16958
-@@ -250,20 +250,19 @@ cdef int singular_polynomial_cmp(poly *p, poly *q, ring *r):
-             return 0
-         elif p_IsConstant(q,r):
-             # compare 0, const
--            return 1-2*r.cf.nGreaterZero(p_GetCoeff(q,r)) # -1: <, 1: > #
-+            return 1-2*r.cf.cfGreaterZero(p_GetCoeff(q,r), r.cf) # -1: <, 1: > #
-     elif q == NULL:
-         if p_IsConstant(p,r):
-             # compare const, 0
--            return -1+2*r.cf.nGreaterZero(p_GetCoeff(p,r)) # -1: <, 1: >
--    #else
-+            return -1+2*r.cf.cfGreaterZero(p_GetCoeff(p,r), r.cf) # -1: <, 1: >
- 
-     while ret==0 and p!=NULL and q!=NULL:
-         ret = p_Cmp( p, q, r)
- 
-         if ret==0:
--            h = r.cf.nSub(p_GetCoeff(p, r),p_GetCoeff(q, r))
-+            h = r.cf.cfSub(p_GetCoeff(p, r),p_GetCoeff(q, r),r.cf)
-             # compare coeffs
--            ret = -1+r.cf.nIsZero(h)+2*r.cf.nGreaterZero(h) # -1: <, 0:==, 1: >
-+            ret = -1+r.cf.cfIsZero(h,r.cf)+2*r.cf.cfGreaterZero(h, r.cf) # -1: <, 0:==, 1: >
-             n_Delete(&h, r)
-         p = pNext(p)
-         q = pNext(q)
-@@ -332,7 +331,7 @@ cdef int singular_polynomial_div_coeff(poly** ret, poly *p, poly *q, ring *r) ex
-         raise ZeroDivisionError
-     sig_on()
-     cdef number *n = p_GetCoeff(q, r)
--    n = r.cf.nInvers(n)
-+    n = r.cf.cfInvers(n,r.cf)
-     ret[0] = pp_Mult_nn(p, n, r)
-     n_Delete(&n, r)
-     sig_off()
-@@ -524,14 +523,22 @@ cdef object singular_polynomial_str_with_changed_varnames(poly *p, ring *r, obje
-     return s
- 
- cdef long singular_polynomial_deg(poly *p, poly *x, ring *r):
--    cdef int deg, _deg, i
--
--    deg = 0
-+    cdef int  i
-+    cdef long _deg, deg
-+    
-+    deg = -1
-+    _deg = -1 
-     if p == NULL:
-         return -1
-     if(r != currRing): rChangeCurrRing(r)
-     if x == NULL:
--        return pLDeg(p,&deg,r)
-+        while p:  
-+            _deg = p_WTotaldegree(p,r)
-+          
-+            if _deg > deg:
-+                deg = _deg
-+            p = pNext(p)
-+        return deg
- 
-     for i in range(1,r.N+1):
-         if p_GetExp(x, i, r):
-@@ -603,5 +610,3 @@ cdef int singular_polynomial_subst(poly **p, int var_index, poly *value, ring *r
-     p[0] = pSubst(p[0], var_index+1, value)
-     if unlikely(count >= 15 or exp > 15): sig_off()
-     return 0
--
--
-diff --git a/src/sage/libs/singular/ring.pyx b/src/sage/libs/singular/ring.pyx
-index 2feddbd..f7105af 100644
---- a/src/sage/libs/singular/ring.pyx
-+++ b/src/sage/libs/singular/ring.pyx
-@@ -18,11 +18,14 @@ from __future__ import print_function
- from sage.libs.gmp.types cimport __mpz_struct
- from sage.libs.gmp.mpz cimport mpz_init_set_ui, mpz_init_set
- 
--from sage.libs.singular.decl cimport number, lnumber, napoly, ring, currRing
--from sage.libs.singular.decl cimport rChangeCurrRing, rCopy0, rComplete, rDelete
-+from sage.libs.singular.decl cimport number, poly, ring, currRing
-+from sage.libs.singular.decl cimport rChangeCurrRing, rCopy0, rComplete, rDelete, idInit
- from sage.libs.singular.decl cimport omAlloc0, omStrDup, omAlloc, omAlloc0Bin,  sip_sring_bin, rnumber_bin
- from sage.libs.singular.decl cimport ringorder_dp, ringorder_Dp, ringorder_lp, ringorder_rp, ringorder_ds, ringorder_Ds, ringorder_ls, ringorder_M, ringorder_C, ringorder_wp, ringorder_Wp, ringorder_ws, ringorder_Ws, ringorder_a
--from sage.libs.singular.decl cimport p_Copy
-+from sage.libs.singular.decl cimport p_Copy, prCopyR
-+from sage.libs.singular.decl cimport n_unknown,  n_Zp,  n_Q,   n_R,   n_GF,  n_long_R,  n_algExt,n_transExt,n_long_C,   n_Z,   n_Zn,  n_Znm,  n_Z2m,  n_CF
-+from sage.libs.singular.decl cimport n_coeffType, cfInitCharProc
-+from sage.libs.singular.decl cimport rDefault, GFInfo, ZnmInfo, nInitChar, AlgExtInfo, nRegister, naInitChar
- 
- from sage.rings.integer cimport Integer
- from sage.rings.integer_ring cimport IntegerRing_class
-@@ -109,30 +112,42 @@ cdef ring *singular_ring_new(base_ring, n, names, term_order) except NULL:
-         sage: P.<x,y,z> = Zmod(25213521351515232)[]; P
-         Multivariate Polynomial Ring in x, y, z over Ring of integers modulo 25213521351515232
-     """
-+    cdef long cexponent
-+    cdef GFInfo* _param
-+    cdef ZnmInfo _info
-     cdef ring* _ring
-     cdef char **_names
-+    cdef char **_ext_names
-     cdef char *_name
-     cdef int i,j
-     cdef int nblcks
-     cdef int offset
-+    cdef int nvars
-     cdef int characteristic
--    cdef int ringtype = 0
-+    cdef int modbase
-+
-+    cdef n_coeffType ringtype = n_unknown
-     cdef MPolynomialRing_libsingular k
-     cdef MPolynomial_libsingular minpoly
--    cdef lnumber *nmp
--    cdef int * m
-+    cdef AlgExtInfo extParam
-+    cdef n_coeffType _type = n_unknown
- 
--    cdef __mpz_struct* ringflaga
--    cdef unsigned long ringflagb
-+    #cdef cfInitCharProc myfunctionptr;
- 
--    is_extension = False
-+    _ring  = NULL
- 
-     n = int(n)
-     if n<1:
-         raise ArithmeticError("The number of variables must be at least 1.")
- 
-+    nvars = n
-     order = TermOrder(term_order, n)
- 
-+    cdef nbaseblcks = len(order.blocks())
-+    nblcks = nbaseblcks + order.singular_moreblocks()
-+    offset = 0
-+
-+
-     _names = <char**>omAlloc0(sizeof(char*)*(len(names)))
-     for i from 0 <= i < n:
-         _name = names[i]
-@@ -149,20 +164,110 @@ cdef ring *singular_ring_new(base_ring, n, names, term_order) except NULL:
-     ##         p   -p : Fp(a)           *names         FALSE             (done)
-     ##         q    q : GF(q=p^n)       *names         TRUE              (todo)
- 
--    if base_ring.is_field() and base_ring.is_finite() and base_ring.is_prime_field():
-+    _wvhdl  = <int **>omAlloc0((nblcks + 2) * sizeof(int *))
-+    _order  = <int *>omAlloc0((nblcks + 2) * sizeof(int))
-+    _block0 = <int *>omAlloc0((nblcks + 2) * sizeof(int))
-+    _block1 = <int *>omAlloc0((nblcks + 2) * sizeof(int))
-+
-+
-+
-+    cdef int idx = 0
-+    for i from 0 <= i < nbaseblcks:
-+        s = order[i].singular_str()
-+        if s[0] == 'M': # matrix order
-+            _order[idx] = ringorder_M
-+            mtx = order[i].matrix().list()
-+            wv = <int *>omAlloc0(len(mtx)*sizeof(int))
-+            for j in range(len(mtx)):
-+                wv[j] = int(mtx[j])
-+            _wvhdl[idx] = wv
-+        elif s[0] == 'w' or s[0] == 'W': # weighted degree orders
-+            _order[idx] = order_dict.get(s[:2], ringorder_dp)
-+            wts = order[i].weights()
-+            wv = <int *>omAlloc0(len(wts)*sizeof(int))
-+            for j in range(len(wts)):
-+                wv[j] = int(wts[j])
-+            _wvhdl[idx] = wv
-+        elif s[0] == '(' and order[i].name() == 'degneglex':  # "(a(1:n),ls(n))"
-+            _order[idx] = ringorder_a
-+            if len(order[i]) == 0:    # may be zero for arbitrary-length orders
-+                nlen = n
-+            else:
-+                nlen = len(order[i])
-+
-+            _wvhdl[idx] = <int *>omAlloc0(len(order[i])*sizeof(int))
-+            for j in range(nlen):  _wvhdl[idx][j] = 1
-+            _block0[idx] = offset + 1     # same like subsequent rp block
-+            _block1[idx] = offset + nlen
-+
-+            idx += 1;                   # we need one more block here
-+            _order[idx] = ringorder_rp
-+
-+        else: # ordinary orders
-+            _order[idx] = order_dict.get(s, ringorder_dp)
-+
-+        _block0[idx] = offset + 1
-+        if len(order[i]) == 0: # may be zero in some cases
-+            _block1[idx] = offset + n
-+        else:
-+            _block1[idx] = offset + len(order[i])
-+        offset = _block1[idx]
-+        idx += 1
-+
-+    # TODO: if we construct a free module don't hardcode! This
-+    # position determines whether we break ties at monomials first or
-+    # whether we break at indices first!
-+    _order[nblcks] = ringorder_C
-+
-+
-+    if isinstance(base_ring, RationalField):
-+        characteristic = 0
-+        _ring = rDefault( characteristic ,nvars, _names, nblcks, _order, _block0, _block1, _wvhdl)
-+
-+    elif isinstance(base_ring, NumberField) and base_ring.is_absolute():
-+        characteristic = 1
-+        try:
-+            k = PolynomialRing(RationalField(), 1, [base_ring.variable_name()], 'lex')
-+        except TypeError:
-+            raise TypeError, "The multivariate polynomial ring in a single variable %s in lex order over Rational Field is supposed to be of type %s"%(base_ring.variable_name(), MPolynomialRing_libsingular)
-+
-+        minpoly = base_ring.polynomial()(k.gen())
-+
-+        _ext_names = <char**>omAlloc0(sizeof(char*))
-+        extname = k.gen()
-+        _name = k._names[0]
-+        _ext_names[0] = omStrDup(_name)
-+        _cfr = rDefault( 0, 1, _ext_names )
-+
-+        _cfr.qideal = idInit(1,1)
-+        rComplete(_cfr, 1)
-+        _cfr.qideal.m[0] = prCopyR(minpoly._poly, k._ring, _cfr)
-+        extParam.r =  _cfr
-+
-+        # _type = nRegister(n_algExt, <cfInitCharProc> naInitChar);
-+        _cf = nInitChar( n_algExt,  <void *>&extParam) #
-+
-+        if (_cf is NULL):
-+            raise RuntimeError, "Failed to allocate _cf ring."
-+
-+        _ring = rDefault (_cf ,nvars, _names, nblcks, _order, _block0, _block1, _wvhdl)
-+
-+    elif isinstance(base_ring, IntegerRing_class):
-+        _cf = nInitChar( n_Z, NULL) # integer coefficient ring
-+        _ring = rDefault (_cf ,nvars, _names, nblcks, _order, _block0, _block1, _wvhdl)
-+
-+    elif (isinstance(base_ring, FiniteField_generic) and base_ring.is_prime_field()):
-+        #or (is_IntegerModRing(base_ring) and base_ring.characteristic().is_prime()):
-+
-         if base_ring.characteristic() <= 2147483647:
-             characteristic = base_ring.characteristic()
-         else:
-             raise TypeError("Characteristic p must be <= 2147483647.")
- 
--    elif isinstance(base_ring, RationalField):
--        characteristic = 0
-+        # example for simpler ring creation interface without monomial orderings:
-+        #_ring = rDefault(characteristic, nvars, _names)
- 
--    elif isinstance(base_ring, IntegerRing_class):
--        ringflaga = <__mpz_struct*>omAlloc(sizeof(__mpz_struct))
--        mpz_init_set_ui(ringflaga, 0)
--        characteristic = 0
--        ringtype = 4 # integer ring
-+        _ring = rDefault( characteristic , nvars, _names, nblcks, _order, _block0, _block1, _wvhdl)
- 
-     elif isinstance(base_ring, FiniteField_generic):
-         if base_ring.characteristic() <= 2147483647:
-@@ -175,145 +280,90 @@ cdef ring *singular_ring_new(base_ring, n, names, term_order) except NULL:
-         except TypeError:
-             raise TypeError("The multivariate polynomial ring in a single variable %s in lex order over %s is supposed to be of type %s" % (base_ring.variable_name(), base_ring,MPolynomialRing_libsingular))
-         minpoly = base_ring.polynomial()(k.gen())
--        is_extension = True
- 
--    elif isinstance(base_ring, NumberField) and base_ring.is_absolute():
--        characteristic = 1
--        try:
--            k = PolynomialRing(RationalField(), 1, [base_ring.variable_name()], 'lex')
--        except TypeError:
--            raise TypeError("The multivariate polynomial ring in a single variable %s in lex order over Rational Field is supposed to be of type %s" % (base_ring.variable_name(), MPolynomialRing_libsingular))
--        minpoly = base_ring.polynomial()(k.gen())
--        is_extension = True
-+        ch = base_ring.characteristic()
-+        F = ch.factor()
-+        assert(len(F)==1)
-+
-+        modbase = F[0][0]
-+        cexponent = F[0][1]
-+
-+        _ext_names = <char**>omAlloc0(sizeof(char*))
-+        _name = k._names[0]
-+        _ext_names[0] = omStrDup(_name)
-+        _cfr = rDefault( modbase, 1, _ext_names )
-+
-+        _cfr.qideal = idInit(1,1)
-+        rComplete(_cfr, 1)
-+        _cfr.qideal.m[0] = prCopyR(minpoly._poly, k._ring, _cfr)
-+        extParam.r =  _cfr
-+        _cf = nInitChar( n_algExt,  <void *>&extParam)
-+
-+        if (_cf is NULL):
-+            raise RuntimeError, "Failed to allocate _cf ring."
-+
-+        _ring = rDefault (_cf ,nvars, _names, nblcks, _order, _block0, _block1, _wvhdl)
- 
-     elif is_IntegerModRing(base_ring):
-+
-         ch = base_ring.characteristic()
--        if ch.is_power_of(2):
-+        isprime = ch.is_prime()
-+
-+        if not isprime and ch.is_power_of(2):
-             exponent = ch.nbits() -1
--            # it seems Singular uses ints somewhere
--            # internally, cf. #6051 (Sage) and #138 (Singular)
--            if exponent <= 30:
--                ringtype = 1
--            else:
--                ringtype = 3
--            characteristic = exponent
--            ringflaga = <__mpz_struct*>omAlloc(sizeof(__mpz_struct))
--            mpz_init_set_ui(ringflaga, 2)
--            ringflagb = exponent
-+            cexponent = exponent
-+
-+            if exponent <= 30:  ringtype = n_Z2m
-+            else:               ringtype = n_Znm
-+
-+            if ringtype == n_Znm:
-+
-+              F = ch.factor()
-+
-+              modbase = F[0][0]
-+              cexponent = F[0][1]
-+
-+              _info.base = <__mpz_struct*>omAlloc(sizeof(__mpz_struct))
-+              mpz_init_set_ui(_info.base, modbase)
-+              _info.exp = cexponent
-+              _cf = nInitChar( n_Znm, <void *>&_info )
-+
-+            elif  ringtype == n_Z2m:
-+                _cf = nInitChar( n_Z2m, <void *>cexponent )
-+
- 
--        elif base_ring.characteristic().is_prime_power()  and ch < ZZ(2)**160:
-+        elif not isprime and ch.is_prime_power() and ch < ZZ(2)**160:
-             F = ch.factor()
-             assert(len(F)==1)
- 
--            ringtype = 3
--            ringflaga = <__mpz_struct*>omAlloc(sizeof(__mpz_struct))
--            mpz_init_set(ringflaga, (<Integer>F[0][0]).value)
--            ringflagb = F[0][1]
--            characteristic = F[0][1]
-+            modbase = F[0][0]
-+            cexponent = F[0][1]
-+
-+            _info.base = <__mpz_struct*>omAlloc(sizeof(__mpz_struct))
-+            mpz_init_set_ui(_info.base, modbase)
-+            _info.exp = cexponent
-+            _cf = nInitChar( n_Znm, <void *>&_info )
- 
-         else:
--            # normal modulus
-             try:
-                 characteristic = ch
-             except OverflowError:
-                 raise NotImplementedError("Characteristic %d too big." % ch)
--            ringtype = 2
--            ringflaga = <__mpz_struct*>omAlloc(sizeof(__mpz_struct))
--            mpz_init_set_ui(ringflaga, characteristic)
--            ringflagb = 1
--    else:
--        raise NotImplementedError("Base ring is not supported.")
- 
--    _ring = <ring*>omAlloc0Bin(sip_sring_bin)
--    if (_ring is NULL):
--        raise ValueError("Failed to allocate Singular ring.")
--    _ring.ch = characteristic
--    _ring.ringtype = ringtype
--    _ring.N = n
--    _ring.names  = _names
--
--    if is_extension:
--        rChangeCurrRing(k._ring)
--        _ring.algring = rCopy0(k._ring)
--        rComplete(_ring.algring, 1)
--        _ring.algring.pCompIndex = -1
--        _ring.P = _ring.algring.N
--        _ring.parameter = <char**>omAlloc0(sizeof(char*)*2)
--        _ring.parameter[0] = omStrDup(_ring.algring.names[0])
--
--        nmp = <lnumber*>omAlloc0Bin(rnumber_bin)
--        nmp.z= <napoly*>p_Copy(minpoly._poly, _ring.algring) # fragile?
--        nmp.s=2
--
--        _ring.minpoly=<number*>nmp
--
--    cdef nbaseblcks = len(order.blocks())
--    nblcks = nbaseblcks + order.singular_moreblocks()
--    offset = 0
-+            _info.base = <__mpz_struct*>omAlloc(sizeof(__mpz_struct))
-+            mpz_init_set_ui(_info.base, characteristic)
-+            _info.exp = 1
-+            _cf = nInitChar( n_Zn, <void *>&_info )
-+        _ring = rDefault( _cf ,nvars, _names, nblcks, _order, _block0, _block1, _wvhdl)
- 
--    _ring.wvhdl  = <int **>omAlloc0((nblcks + 2) * sizeof(int *))
--    _ring.order  = <int *>omAlloc0((nblcks + 2) * sizeof(int))
--    _ring.block0 = <int *>omAlloc0((nblcks + 2) * sizeof(int))
--    _ring.block1 = <int *>omAlloc0((nblcks + 2) * sizeof(int))
- 
--    if order.is_local():
--        _ring.OrdSgn = -1
-     else:
--        _ring.OrdSgn = 1
--
--    cdef int idx = 0
--    for i from 0 <= i < nbaseblcks:
--        s = order[i].singular_str()
--        if s[0] == 'M': # matrix order
--            _ring.order[idx] = ringorder_M
--            mtx = order[i].matrix().list()
--            wv = <int *>omAlloc0(len(mtx)*sizeof(int))
--            for j in range(len(mtx)):
--                wv[j] = int(mtx[j])
--            _ring.wvhdl[idx] = wv
--        elif s[0] == 'w' or s[0] == 'W': # weighted degree orders
--            _ring.order[idx] = order_dict.get(s[:2], ringorder_dp)
--            wts = order[i].weights()
--            wv = <int *>omAlloc0(len(wts)*sizeof(int))
--            for j in range(len(wts)):
--                wv[j] = int(wts[j])
--            _ring.wvhdl[idx] = wv
--        elif s[0] == '(' and order[i].name() == 'degneglex':  # "(a(1:n),ls(n))"
--            _ring.order[idx] = ringorder_a
--            if len(order[i]) == 0:    # may be zero for arbitrary-length orders
--                nlen = n
--            else:
--                nlen = len(order[i])
--
--            _ring.wvhdl[idx] = <int *>omAlloc0(len(order[i])*sizeof(int))
--            for j in range(nlen):  _ring.wvhdl[idx][j] = 1
--            _ring.block0[idx] = offset + 1     # same like subsequent rp block
--            _ring.block1[idx] = offset + nlen
--
--            idx += 1;                   # we need one more block here
--            _ring.order[idx] = ringorder_rp
--
--        else: # ordinary orders
--            _ring.order[idx] = order_dict.get(s, ringorder_dp)
-+        raise NotImplementedError("Base ring is not supported.")
- 
--        _ring.block0[idx] = offset + 1
--        if len(order[i]) == 0: # may be zero in some cases
--            _ring.block1[idx] = offset + n
--        else:
--            _ring.block1[idx] = offset + len(order[i])
--        offset = _ring.block1[idx]
--        idx += 1
- 
--    # TODO: if we construct a free module don't hardcode! This
--    # position determines whether we break ties at monomials first or
--    # whether we break at indices first!
--    _ring.order[nblcks] = ringorder_C
--
--    if ringtype != 0:
--        _ring.ringflaga = ringflaga
--        _ring.ringflagb = ringflagb
-+    if (_ring is NULL):
-+        raise ValueError("Failed to allocate Singular ring.")
- 
--    rComplete(_ring, 1)
-     _ring.ShortOut = 0
- 
-     rChangeCurrRing(_ring)
-@@ -322,6 +372,16 @@ cdef ring *singular_ring_new(base_ring, n, names, term_order) except NULL:
-     if wrapped_ring in ring_refcount_dict:
-         raise ValueError('newly created ring already in dictionary??')
-     ring_refcount_dict[wrapped_ring] = 1
-+
-+    rComplete(_ring, 1)
-+
-+    _ring.ShortOut = 0
-+ 
-+    if order.is_local():
-+        assert(_ring.OrdSgn == -1)
-+    if order.is_global():
-+         assert(_ring.OrdSgn == 1)
-+
-     return _ring
- 
- 
-diff --git a/src/sage/libs/singular/singular.pxd b/src/sage/libs/singular/singular.pxd
-index b02b53a..e06566e 100644
---- a/src/sage/libs/singular/singular.pxd
-+++ b/src/sage/libs/singular/singular.pxd
-@@ -17,7 +17,7 @@ from sage.rings.number_field.number_field_base cimport NumberField
- # Conversion from Singular to Sage types
- # ======================================
- 
--cdef Rational si2sa_QQ(number (*),ring (*))
-+cdef Rational si2sa_QQ(number (*), number **, ring (*))
- cdef Integer  si2sa_ZZ(number (*),ring (*))
- 
- cdef FFgivE   si2sa_GFqGivaro(number *n, ring *_ring, Cache_givaro cache)
-@@ -53,9 +53,6 @@ cdef number *sa2si(Element elem, ring * _ring)
- # Initialisation
- # ==============
- 
--cdef int overflow_check(long e, ring *_ring) except -1
-+cdef int overflow_check(unsigned long e, ring *_ring) except -1
- 
- cdef init_libsingular()
--
--
--
-diff --git a/src/sage/libs/singular/singular.pyx b/src/sage/libs/singular/singular.pyx
-index 7245090..7495325 100644
---- a/src/sage/libs/singular/singular.pyx
-+++ b/src/sage/libs/singular/singular.pyx
-@@ -5,12 +5,14 @@ AUTHOR:
- 
- - Martin Albrecht <malb at informatik.uni-bremen.de>
- """
--###############################################################################
-+
-+#*****************************************************************************
- #       Copyright (C) 2005, 2006 William Stein <wstein at gmail.com>
- #
--#  Distributed under the terms of the GNU General Public License (GPL)
--#  as published by the Free Software Foundation; either version 2 of
--#  the License, or (at your option) any later version.
-+# This program is free software: you can redistribute it and/or modify
-+# it under the terms of the GNU General Public License as published by
-+# the Free Software Foundation, either version 2 of the License, or
-+# (at your option) any later version.
- #                  http://www.gnu.org/licenses/
- ###############################################################################
- from __future__ import print_function
-@@ -24,19 +26,7 @@ cdef extern from "limits.h":
- import os
- 
- from libc.stdint cimport int64_t
--from sage.libs.singular.decl cimport intvec
--from sage.libs.singular.decl cimport SR_HDL, SR_INT, SR_TO_INT
--from sage.libs.singular.decl cimport singular_options, singular_verbose_options
--from sage.libs.singular.decl cimport On, Off, SW_USE_NTL, SW_USE_NTL_GCD_0, SW_USE_EZGCD, SW_USE_NTL_SORT, SW_USE_NTL_GCD_P
--from sage.libs.singular.decl cimport napoly, lnumber, Sy_bit, OPT_REDSB, OPT_INTSTRATEGY, OPT_REDTAIL, OPT_REDTHROUGH
--from sage.libs.singular.decl cimport nlGetNumerator, nlGetDenom, nlDelete, nlInit2gmp
--from sage.libs.singular.decl cimport naIsOne, naIsOne, naIsZero, naPar, naInit, naAdd, naMult, naDelete, naMap00
--from sage.libs.singular.decl cimport napGetCoeff, napGetExpFrom, pNext
--from sage.libs.singular.decl cimport nrzInit, nr2mMapZp, nrnMapGMP
--from sage.libs.singular.decl cimport siInit
--from sage.libs.singular.decl cimport n_Init
--from sage.libs.singular.decl cimport rChangeCurrRing, currRing
--from sage.libs.singular.decl cimport WerrorS_callback, const_char_ptr
-+from sage.libs.singular.decl cimport *
- 
- from sage.rings.rational_field import RationalField
- from sage.rings.integer_ring cimport IntegerRing_class
-@@ -52,7 +42,7 @@ from sage.rings.polynomial.multi_polynomial_libsingular cimport MPolynomial_libs
- 
- _saved_options = (int(0),0,0)
- 
--cdef Rational si2sa_QQ(number *n, ring *_ring):
-+cdef Rational si2sa_QQ(number *n, number **nn, ring *_ring):
-     """
-     TESTS::
- 
-@@ -83,26 +73,27 @@ cdef Rational si2sa_QQ(number *n, ring *_ring):
-     ##  structures aligned on 4 byte boundaries and therefor have last bit zero.
-     ##  (The second bit is reserved as tag to allow extensions of this scheme.)
-     ##  Using immediates as pointers and dereferencing them gives address errors.
--    nom = nlGetNumerator(n, _ring)
-+    nom = nlGetNumerator(n, _ring.cf)
-     mpz_init(nom_z)
- 
-     if (SR_HDL(nom) & SR_INT): mpz_set_si(nom_z, SR_TO_INT(nom))
-     else: mpz_set(nom_z,nom.z)
- 
-     mpq_set_num(_z,nom_z)
--    nlDelete(&nom,_ring)
-+    nlDelete(&nom,_ring.cf)
-     mpz_clear(nom_z)
- 
--    denom = nlGetDenom(n, _ring)
-+    denom = nlGetDenom(n, _ring.cf)
-     mpz_init(denom_z)
- 
-     if (SR_HDL(denom) & SR_INT): mpz_set_si(denom_z, SR_TO_INT(denom))
-     else: mpz_set(denom_z,denom.z)
- 
-     mpq_set_den(_z, denom_z)
--    nlDelete(&denom,_ring)
-+    nlDelete(&denom,_ring.cf)
-     mpz_clear(denom_z)
- 
-+    nn[0] = n
-     z = Rational()
-     z.set_from_mpq(_z)
-     mpq_clear(_z)
-@@ -140,31 +131,33 @@ cdef FFgivE si2sa_GFqGivaro(number *n, ring *_ring, Cache_givaro cache):
-         sage: K(R(0))
-         0
-     """
--    cdef napoly *z
-+    cdef poly *z
-     cdef int c, e
-     cdef int a
-     cdef int ret
-     cdef int order
-+    cdef ring *cfRing = _ring.cf.extRing
- 
--    if naIsZero(n):
-+    if _ring.cf.cfIsZero(n,_ring.cf):
-         return cache._zero_element
--    elif naIsOne(n):
-+    elif _ring.cf.cfIsOne(n,_ring.cf):
-         return cache._one_element
--    z = (<lnumber*>n).z
-+
-+    z = <poly*>n
- 
-     a = cache.objectptr.indeterminate()
-     ret = cache.objectptr.zero
-     order = cache.objectptr.cardinality() - 1
- 
-     while z:
--        c = cache.objectptr.initi(c, <int64_t>napGetCoeff(z))
--        e = napGetExpFrom(z,1, _ring)
-+        c = cache.objectptr.initi(c, <int64_t>p_GetCoeff(z, cfRing))
-+        e = p_GetExp(z, 1, cfRing)
-         if e == 0:
-             ret = cache.objectptr.add(ret, c, ret)
-         else:
-             a = ( e * cache.objectptr.indeterminate() ) % order
-             ret = cache.objectptr.axpy(ret, c, a, ret)
--        z = <napoly*>pNext(<poly*>z)
-+        z = <poly*>pNext(<poly*>z)
-     return (<FFgivE>cache._zero_element)._new_c(ret)
- 
- cdef FFgf2eE si2sa_GFqNTLGF2E(number *n, ring *_ring, Cache_ntl_gf2e cache):
-@@ -179,26 +172,27 @@ cdef FFgf2eE si2sa_GFqNTLGF2E(number *n, ring *_ring, Cache_ntl_gf2e cache):
-         sage: type(f.lc())
-         <type 'sage.rings.finite_rings.element_ntl_gf2e.FiniteField_ntl_gf2eElement'>
-     """
--    cdef napoly *z
-+    cdef poly *z
-     cdef long c
-     cdef int e
-     cdef FFgf2eE a
-     cdef FFgf2eE ret
-+    cdef ring *cfRing = _ring.cf.extRing
- 
--    if naIsZero(n):
-+    if _ring.cf.cfIsZero(n,_ring.cf):
-         return cache._zero_element
--    elif naIsOne(n):
-+    elif _ring.cf.cfIsOne(n,_ring.cf):
-         return cache._one_element
--    z = (<lnumber*>n).z
- 
-+    z = <poly*>n
-     a = cache._gen
-     ret = cache._zero_element
- 
-     while z:
--        c = <long>napGetCoeff(z)
--        e = napGetExpFrom(z,1, _ring)
-+        c = <long>p_GetCoeff(z, cfRing)
-+        e = p_GetExp(z, 1, cfRing)
-         ret += c * a**e
--        z = <napoly*>pNext(<poly*>z)
-+        z = <poly*>pNext(<poly*>z)
-     return ret
- 
- cdef object si2sa_GFq_generic(number *n, ring *_ring, object base):
-@@ -222,29 +216,31 @@ cdef object si2sa_GFq_generic(number *n, ring *_ring, object base):
-         2147483646
- 
-     """
--    cdef napoly *z
-+    cdef poly *z
-     cdef long c
-     cdef int e
-     cdef object a
-     cdef object ret
-+    cdef ring *cfRing = _ring.cf.extRing
- 
--    if naIsZero(n):
-+    if _ring.cf.cfIsZero(n,_ring.cf):
-         return base.zero()
--    elif naIsOne(n):
-+    elif _ring.cf.cfIsOne(n,_ring.cf):
-         return base.one()
--    z = (<lnumber*>n).z
-+
-+    z = <poly*>n
- 
-     a = base.gen()
-     ret = base.zero()
- 
-     while z:
--        c = <long>napGetCoeff(z)
--        e = napGetExpFrom(z,1, _ring)
-+        c = <long>p_GetCoeff(z, cfRing)
-+        e = p_GetExp(z, 1, cfRing)
-         if e == 0:
-             ret = ret + c
-         elif c != 0:
-             ret = ret  + c * a**e
--        z = <napoly*>pNext(<poly*>z)
-+        z = <poly*>pNext(<poly*>z)
-     return ret
- 
- cdef object si2sa_NF(number *n, ring *_ring, object base):
-@@ -259,30 +255,40 @@ cdef object si2sa_NF(number *n, ring *_ring, object base):
-         sage: type(f.lc())
-         <type 'sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic'>
-     """
--    cdef napoly *z
-+    cdef poly *z
-     cdef number *c
-     cdef int e
-     cdef object a
-     cdef object ret
-+    cdef ring *cfRing = _ring.cf.extRing
- 
--    if naIsZero(n):
-+    if _ring.cf.cfIsZero(n,_ring.cf):
-         return base._zero_element
--    elif naIsOne(n):
-+    elif _ring.cf.cfIsOne(n,_ring.cf):
-         return base._one_element
--    z = (<lnumber*>n).z
-+
-+    z = <poly*>n
- 
-     a = base.gen()
-     ret = base(0)
- 
-     while z:
--        c = napGetCoeff(z)
--        coeff = si2sa_QQ(c, _ring)
--        e = napGetExpFrom(z,1, _ring)
-+        # p_GetCoeff returns a reference
-+        c = p_GetCoeff(z, cfRing)
-+        # si2sa_QQ might modify c
-+        coeff = si2sa_QQ(c, &c, cfRing)
-+        # so we force it back.
-+        z.coef = c
-+        #pSetCoeff0(z,c)
-+        #p_SetCoeff(z, c, cfRing)
-+        # rather than trying to let Cython and C++ automagically modify it
-+        #coeff = si2sa_QQ(p_GetCoeff(z, cfRing), cfRing)
-+        e = p_GetExp(z, 1, cfRing)
-         if e == 0:
-             ret = ret + coeff
-         elif coeff != 0:
-             ret = ret + coeff * a**e
--        z = <napoly*>pNext(<poly*>z)
-+        z = <poly*>pNext(<poly*>z)
-     return base(ret)
- 
- cdef inline object si2sa_ZZmod(number *n, ring *_ring, object base):
-@@ -322,13 +328,15 @@ cdef inline object si2sa_ZZmod(number *n, ring *_ring, object base):
-         3
-     """
-     cdef Integer ret
--    if _ring.ringtype == 1:
-+    if _ring.cf.type == n_Z2m:
-         return base(<long>n)
--    else:
-+    elif _ring.cf.type == n_Znm or _ring.cf.type == n_Zn:
-         ret = Integer()
-         ret.set_from_mpz(<mpz_ptr>n)
-         return base(ret)
- 
-+    return base(_ring.cf.cfInt(n,_ring.cf))
-+
- cdef number *sa2si_QQ(Rational r, ring *_ring):
-     """
-     TESTS::
-@@ -344,44 +352,39 @@ cdef number *sa2si_QQ(Rational r, ring *_ring):
-         12345678901234567890/23
-     """
-     if _ring != currRing: rChangeCurrRing(_ring)
--    return nlInit2gmp( mpq_numref(r.value), mpq_denref(r.value) )
-+    return nlInit2gmp( mpq_numref(r.value), mpq_denref(r.value),_ring.cf )
- 
- cdef number *sa2si_GFqGivaro(int quo, ring *_ring):
-     """
-     """
-     if _ring != currRing: rChangeCurrRing(_ring)
--    cdef number *n1
--    cdef number *n2
--    cdef number *a
--    cdef number *coeff
--    cdef number *apow1
--    cdef number *apow2
--    cdef int b = - _ring.ch
-+    cdef number *n1, *n2, *a, *coeff, *apow1, *apow2
-+    cdef int b = _ring.cf.ch
- 
--    a = naPar(1)
-+    a = _ring.cf.cfParameter(1, _ring.cf)
- 
--    apow1 = naInit(1, _ring)
--    n1 = naInit(0, _ring)
-+    apow1 = _ring.cf.cfInit(1, _ring.cf)
-+    n1 = _ring.cf.cfInit(0, _ring.cf)
- 
-     while quo!=0:
--        coeff = naInit(quo%b, _ring)
-+        coeff = _ring.cf.cfInit(quo%b, _ring.cf)
- 
--        if not naIsZero(coeff):
--            apow2 = naMult(coeff, apow1)
--            n2 = naAdd(apow2, n1)
--            naDelete(&apow2, _ring)
--            naDelete(&n1, _ring)
-+        if not _ring.cf.cfIsZero(coeff, _ring.cf):
-+            apow2 = _ring.cf.cfMult(coeff, apow1, _ring.cf)
-+            n2 = _ring.cf.cfAdd(apow2, n1, _ring.cf)
-+            _ring.cf.cfDelete(&apow2, _ring.cf)
-+            _ring.cf.cfDelete(&n1, _ring.cf)
-             n1 = n2
- 
--        apow2 = naMult(apow1, a)
--        naDelete(&apow1, _ring)
-+        apow2 = _ring.cf.cfMult(apow1, a, _ring.cf)
-+        _ring.cf.cfDelete(&apow1, _ring.cf)
-         apow1 = apow2
- 
-         quo = quo/b
--        naDelete(&coeff, _ring)
-+        _ring.cf.cfDelete(&coeff, _ring.cf)
- 
--    naDelete(&apow1, _ring)
--    naDelete(&a, _ring)
-+    _ring.cf.cfDelete(&apow1, _ring.cf)
-+    _ring.cf.cfDelete(&a, _ring.cf)
-     return n1
- 
- cdef number *sa2si_GFqNTLGF2E(FFgf2eE elem, ring *_ring):
-@@ -398,30 +401,30 @@ cdef number *sa2si_GFqNTLGF2E(FFgf2eE elem, ring *_ring):
-     cdef GF2X_c rep = GF2E_rep(elem.x)
- 
-     if GF2X_deg(rep) >= 1:
--        n1 = naInit(0, _ring)
--        a = naPar(1)
--        apow1 = naInit(1, _ring)
-+        n1 = _ring.cf.cfInit(0, _ring.cf)
-+        a = _ring.cf.cfParameter(1,_ring.cf)
-+        apow1 = _ring.cf.cfInit(1, _ring.cf)
- 
-         for i from 0 <= i <= GF2X_deg(rep):
--            coeff = naInit(GF2_conv_to_long(GF2X_coeff(rep,i)), _ring)
-+            coeff = _ring.cf.cfInit(GF2_conv_to_long(GF2X_coeff(rep,i)), _ring.cf)
- 
--            if not naIsZero(coeff):
--                apow2 = naMult(coeff, apow1)
--                n2 = naAdd(apow2, n1)
--                naDelete(&apow2, _ring)
--                naDelete(&n1, _ring);
-+            if not _ring.cf.cfIsZero(coeff,_ring.cf):
-+                apow2 = _ring.cf.cfMult(coeff, apow1,_ring.cf)
-+                n2 = _ring.cf.cfAdd(apow2, n1,_ring.cf)
-+                _ring.cf.cfDelete(&apow2, _ring.cf)
-+                _ring.cf.cfDelete(&n1, _ring.cf);
-                 n1 = n2
- 
--            apow2 = naMult(apow1, a)
--            naDelete(&apow1, _ring)
-+            apow2 = _ring.cf.cfMult(apow1, a,_ring.cf)
-+            _ring.cf.cfDelete(&apow1, _ring.cf)
-             apow1 = apow2
- 
--            naDelete(&coeff, _ring)
-+            _ring.cf.cfDelete(&coeff, _ring.cf)
- 
--        naDelete(&apow1, _ring)
--        naDelete(&a, _ring)
-+        _ring.cf.cfDelete(&apow1, _ring.cf)
-+        _ring.cf.cfDelete(&a, _ring.cf)
-     else:
--        n1 = naInit(GF2_conv_to_long(GF2X_coeff(rep,0)), _ring)
-+        n1 = _ring.cf.cfInit(GF2_conv_to_long(GF2X_coeff(rep,0)), _ring.cf)
- 
-     return n1
- 
-@@ -439,30 +442,30 @@ cdef number *sa2si_GFq_generic(object elem, ring *_ring):
- 
-     if _ring != currRing: rChangeCurrRing(_ring)
-     if elem.degree() > 0:
--        n1 = naInit(0, _ring)
--        a = naPar(1)
--        apow1 = naInit(1, _ring)
-+        n1 = _ring.cf.cfInit(0, _ring.cf)
-+        a = _ring.cf.cfParameter(1,_ring.cf)
-+        apow1 = _ring.cf.cfInit(1, _ring.cf)
- 
-         for i from 0 <= i <= elem.degree():
--            coeff = naInit(int(elem[i]), _ring)
-+            coeff = _ring.cf.cfInit(int(elem[i]), _ring.cf)
- 
--            if not naIsZero(coeff):
--                apow2 = naMult(coeff, apow1)
--                n2 = naAdd(apow2, n1)
--                naDelete(&apow2, _ring)
--                naDelete(&n1, _ring);
-+            if not _ring.cf.cfIsZero(coeff,_ring.cf):
-+                apow2 = _ring.cf.cfMult(coeff, apow1,_ring.cf)
-+                n2 = _ring.cf.cfAdd(apow2, n1,_ring.cf)
-+                _ring.cf.cfDelete(&apow2, _ring.cf)
-+                _ring.cf.cfDelete(&n1, _ring.cf);
-                 n1 = n2
- 
--            apow2 = naMult(apow1, a)
--            naDelete(&apow1, _ring)
-+            apow2 = _ring.cf.cfMult(apow1, a,_ring.cf)
-+            _ring.cf.cfDelete(&apow1, _ring.cf)
-             apow1 = apow2
- 
--            naDelete(&coeff, _ring)
-+            _ring.cf.cfDelete(&coeff, _ring.cf)
- 
--        naDelete(&apow1, _ring)
--        naDelete(&a, _ring)
-+        _ring.cf.cfDelete(&apow1, _ring.cf)
-+        _ring.cf.cfDelete(&a, _ring.cf)
-     else:
--        n1 = naInit(int(elem), _ring)
-+        n1 = _ring.cf.cfInit(int(elem), _ring.cf)
- 
-     return n1
- 
-@@ -477,32 +480,58 @@ cdef number *sa2si_NF(object elem, ring *_ring):
-     cdef number *naCoeff
-     cdef number *apow1
-     cdef number *apow2
-+
-+    cdef nMapFunc nMapFuncPtr = NULL;
-+
-+    nMapFuncPtr =  naSetMap(_ring.cf, currRing.cf) # choose correct mapping function
-+
-+    if (nMapFuncPtr is NULL):
-+        raise RuntimeError, "Failed to determine nMapFuncPtr"
-+
-     elem = list(elem)
- 
-     if _ring != currRing: rChangeCurrRing(_ring)
--    n1 = naInit(0, _ring)
--    a = naPar(1)
--    apow1 = naInit(1, _ring)
--
-+    n1 = _ring.cf.cfInit(0, _ring.cf)
-+    a = _ring.cf.cfParameter(1,_ring.cf)
-+    apow1 = _ring.cf.cfInit(1, _ring.cf)
-+
-+    cdef char *_name
-+
-+    # the result of nlInit2gmp() is in a plain polynomial ring over QQ (not an extension ring!),
-+    # so we hace to get/create one :
-+    #
-+    # todo: reuse qqr/ get an existing Singular polynomial ring over Q.
-+    varname = "a"
-+    _name = omStrDup(varname)
-+    cdef char **_ext_names
-+    _ext_names = <char**>omAlloc0(sizeof(char*))
-+    _ext_names[0] = omStrDup(_name)
-+    qqr = rDefault( 0, 1, _ext_names);
-+    rComplete(qqr,1)
-+    qqr.ShortOut = 0
-+    
-+
-+    nMapFuncPtr =  naSetMap( qqr.cf , _ring.cf ) # choose correct mapping function
-+    cdef poly *_p
-     for i from 0 <= i < len(elem):
--        nlCoeff = nlInit2gmp( mpq_numref((<Rational>elem[i]).value), mpq_denref((<Rational>elem[i]).value) )
--        naCoeff = naMap00(nlCoeff)
--        nlDelete(&nlCoeff, _ring)
-+        nlCoeff = nlInit2gmp( mpq_numref((<Rational>elem[i]).value), mpq_denref((<Rational>elem[i]).value),  qqr.cf )
-+        naCoeff = nMapFuncPtr(nlCoeff, qqr.cf , _ring.cf )
-+        nlDelete(&nlCoeff, _ring.cf)
- 
-         # faster would be to assign the coefficient directly
--        apow2 = naMult(naCoeff, apow1)
--        n2 = naAdd(apow2, n1)
--        naDelete(&apow2, _ring)
--        naDelete(&n1, _ring);
--        naDelete(&naCoeff, _ring)
-+        apow2 = _ring.cf.cfMult(naCoeff, apow1,_ring.cf)
-+        n2 = _ring.cf.cfAdd(apow2, n1,_ring.cf)
-+        _ring.cf.cfDelete(&apow2, _ring.cf)
-+        _ring.cf.cfDelete(&n1, _ring.cf);
-+        _ring.cf.cfDelete(&naCoeff, _ring.cf)
-         n1 = n2
- 
--        apow2 = naMult(apow1, a)
--        naDelete(&apow1, _ring)
-+        apow2 = _ring.cf.cfMult(apow1, a,_ring.cf)
-+        _ring.cf.cfDelete(&apow1, _ring.cf)
-         apow1 = apow2
- 
--    naDelete(&apow1, _ring)
--    naDelete(&a, _ring)
-+    _ring.cf.cfDelete(&apow1, _ring.cf)
-+    _ring.cf.cfDelete(&a, _ring.cf)
- 
-     return n1
- 
-@@ -521,7 +550,7 @@ cdef number *sa2si_ZZ(Integer d, ring *_ring):
-         12345678901234567890
-     """
-     if _ring != currRing: rChangeCurrRing(_ring)
--    cdef number *n = nrzInit(0, _ring)
-+    cdef number *n = nrzInit(0, _ring.cf)
-     mpz_set(<mpz_ptr>n, d.value)
-     return <number*>n
- 
-@@ -563,20 +592,49 @@ cdef inline number *sa2si_ZZmod(IntegerMod_abstract d, ring *_ring):
-     """
-     nr2mModul = d.parent().characteristic()
-     if _ring != currRing: rChangeCurrRing(_ring)
--    cdef int _d
--    if _ring.ringtype == 1:
-+
-+    cdef number *nn
-+
-+    cdef int64_t _d
-+    cdef char *_name
-+    cdef char **_ext_names
-+    varname = "a"
-+
-+    cdef nMapFunc nMapFuncPtr = NULL;
-+
-+    if _ring.cf.type == n_Z2m:
-         _d = long(d)
--        return nr2mMapZp(<number *>_d)
--    else:
-+        return nr2mMapZp(<number *>_d, currRing.cf, _ring.cf)
-+    elif _ring.cf.type == n_Zn or _ring.cf.type == n_Znm:
-         lift = d.lift()
--        return nrnMapGMP(<number *>((<Integer>lift).value))
-+
-+        # if I understand nrnMapGMP/nMapFuncPtr correctly we need first
-+        # a source value in ZZr
-+        # create ZZr, a plain polynomial ring over ZZ with one variable.
-+        #
-+        # todo (later): reuse ZZr
-+        _name = omStrDup(varname)
-+        _ext_names = <char**>omAlloc0(sizeof(char*))
-+        _ext_names[0] = omStrDup(_name)
-+        _cf = nInitChar( n_Z, NULL) # integer coefficient ring
-+        ZZr = rDefault (_cf ,1, _ext_names)
-+        rComplete(ZZr,1)
-+        ZZr.ShortOut = 0
-+
-+        nn = nrzInit(0, ZZr.cf)
-+        mpz_set(<mpz_ptr>nn, (<Integer>lift).value)
-+        nMapFuncPtr  = nrnSetMap( ZZr.cf, _ring.cf)
-+
-+        return nMapFuncPtr(nn, ZZr.cf, _ring.cf)
-+    else:
-+        raise ValueError
- 
- cdef object si2sa(number *n, ring *_ring, object base):
-     if isinstance(base, FiniteField_prime_modn):
--        return base(_ring.cf.n_Int(n, _ring))
-+        return base(_ring.cf.cfInt(n, _ring.cf))
- 
-     elif isinstance(base, RationalField):
--        return si2sa_QQ(n,_ring)
-+        return si2sa_QQ(n,&n,_ring)
- 
-     elif isinstance(base, IntegerRing_class):
-         return si2sa_ZZ(n,_ring)
-@@ -594,8 +652,8 @@ cdef object si2sa(number *n, ring *_ring, object base):
-         return si2sa_NF(n, _ring, base)
- 
-     elif isinstance(base, IntegerModRing_generic):
--        if _ring.ringtype == 0:
--            return base(_ring.cf.n_Int(n, _ring))
-+        if _ring.cf.type == n_unknown:
-+            return base(_ring.cf.cfInt(n, _ring.cf))
-         return si2sa_ZZmod(n, _ring, base)
- 
-     else:
-@@ -624,7 +682,7 @@ cdef number *sa2si(Element elem, ring * _ring):
-     elif isinstance(elem._parent, NumberField) and elem._parent.is_absolute():
-         return sa2si_NF(elem, _ring)
-     elif isinstance(elem._parent, IntegerModRing_generic):
--        if _ring.ringtype == 0:
-+        if _ring.cf.type == n_unknown:
-             return n_Init(int(elem),_ring)
-         return sa2si_ZZmod(elem, _ring)
-     else:
-@@ -654,45 +712,36 @@ cdef extern from "dlfcn.h":
-     cdef long RTLD_LAZY
-     cdef long RTLD_GLOBAL
- 
--cdef int overflow_check(long e, ring *_ring) except -1:
-+cdef int overflow_check(unsigned long e, ring *_ring) except -1:
-     """
--    Raises an ``OverflowError`` if e is > max degree per variable,
--    or if it is not acceptable for Singular as exponent of the
--    given ring.
-+    Raise an ``OverflowError`` if e is > max degree per variable.
- 
-     INPUT:
- 
--    - ``e`` - some integer representing a degree.
--    - ``_ring`` - a pointer to some ring.
-+    - ``e`` -- some integer representing a degree.
- 
--    TESTS:
-+    - ``_ring`` -- a pointer to some ring.
- 
--    Whether an overflow occurs or not, partially depends
--    on the number of variables in the ring. See :trac:`11856`::
-+    Whether an overflow occurs or not partially depends
-+    on the number of variables in the ring. See trac ticket
-+    :trac:`11856`. With Singular 4, it is by default optimized
-+    for at least 4 variables on 64-bit and 2 variables on 32-bit,
-+    which in both cases makes a maximal default exponent of
-+    2^16-1.
- 
--        sage: P.<x,y,z> = QQ[]
--        sage: y^2^30
--        Traceback (most recent call last):
--        ...
--        OverflowError: Exponent overflow (1073741824).
--        sage: P.<x,y> = QQ[]
--        sage: y^2^30
--        y^1073741824                                   # 64-bit
--        Traceback (most recent call last):             # 32-bit
--        ...                                            # 32-bit
--        OverflowError: Exponent overflow (1073741824). # 32-bit
-+    EXAMPLES::
- 
--        sage: x^2^30*x^2^30
-+        sage: P.<x,y> = QQ[]
-+        sage: y^(2^16-1)
-+        y^65535
-+        sage: y^2^16
-         Traceback (most recent call last):
-         ...
--        OverflowError: Exponent overflow (2147483648). # 64-bit
--        OverflowError: Exponent overflow (1073741824). # 32-bit
--
-+        OverflowError: exponent overflow (65536)
-     """
--    # 2^31 (pPower takes ints)
--    if unlikely(e >= _ring.bitmask or e >= 2**31):
--        raise OverflowError("Exponent overflow (%d)."%(e))
--    return 0
-+    if unlikely(e > _ring.bitmask):
-+        raise OverflowError("exponent overflow (%d)"%(e))
-+
- 
- cdef init_libsingular():
-     """
-@@ -712,18 +761,26 @@ cdef init_libsingular():
- 
-     cdef void *handle = NULL
- 
--    for extension in ["so", "dylib", "dll"]:
--        lib = os.environ['SAGE_LOCAL']+"/lib/libsingular."+extension
--        if os.path.exists(lib):
--            handle = dlopen(lib, RTLD_GLOBAL|RTLD_LAZY)
--            if not handle:
--                err = dlerror()
--                if err:
--                    print(err)
--            break
-+    import os
-+    from sage.env import SAGE_LOCAL 
-+    UNAME = os.uname()[0]
-+    if UNAME[:6] == "CYGWIN":
-+        extension = "dll"
-+    elif UNAME == "Darwin":
-+        extension = "dylib"
-+    else:
-+        extension = "so"
-+
-+    # library name changed from libsingular to libSingular btw 3.x and 4.x
-+    lib = SAGE_LOCAL+"/lib/libSingular."+extension
-+
-+    if not os.path.exists(lib):
-+        raise ImportError("cannot locate Singular library ({})".format(lib))
- 
--    if handle == NULL:
--        raise ImportError("cannot load libSINGULAR library")
-+    handle = dlopen(lib, RTLD_GLOBAL|RTLD_LAZY)   
-+    if not handle:
-+        err = dlerror()
-+        raise ImportError("cannot load Singular library ({})".format(err))
- 
-     # load SINGULAR
-     siInit(lib)
-@@ -737,9 +794,7 @@ cdef init_libsingular():
-     _saved_options = (int(singular_options), 0, 0)
-     _saved_verbose_options = int(singular_verbose_options)
- 
--    On(SW_USE_NTL)
--    On(SW_USE_NTL_GCD_0)
--    On(SW_USE_NTL_GCD_P)
-+    #On(SW_USE_NTL)
-     On(SW_USE_EZGCD)
-     Off(SW_USE_NTL_SORT)
- 
-diff --git a/src/sage/misc/cython.py b/src/sage/misc/cython.py
-index 2348c4b..8abb91c 100644
---- a/src/sage/misc/cython.py
-+++ b/src/sage/misc/cython.py
-@@ -310,7 +310,7 @@ def cython(filename, verbose=False, compile_message=False,
-         sage: code = [
-         ....: "#clang C++",
-         ....: "#cinclude %s/include/singular %s/include/factory"%(SAGE_LOCAL, SAGE_LOCAL),
--        ....: "#clib m readline singular givaro ntl gmpxx gmp",
-+        ....: "#clib m readline Singular givaro ntl gmpxx gmp",
-         ....: "from sage.rings.polynomial.multi_polynomial_libsingular cimport MPolynomial_libsingular",
-         ....: "from sage.libs.singular.polynomial cimport singular_polynomial_pow",
-         ....: "def test(MPolynomial_libsingular p):",
-diff --git a/src/sage/rings/multi_power_series_ring_element.py b/src/sage/rings/multi_power_series_ring_element.py
-index 6388859..142f38b 100644
---- a/src/sage/rings/multi_power_series_ring_element.py
-+++ b/src/sage/rings/multi_power_series_ring_element.py
-@@ -1690,9 +1690,9 @@ class MPowerSeries(PowerSeries):
-             sage: aa.is_gen()
-             False
-             sage: aa.integral(aa)
--            -2*a^2
-+            3*a^2
-             sage: aa.integral(a)
--            -2*a^2
-+            3*a^2
-         """
-         P = self.parent()
-         R = P.base_ring()
-diff --git a/src/sage/rings/polynomial/multi_polynomial_ideal.py b/src/sage/rings/polynomial/multi_polynomial_ideal.py
-index 816c448..53df08a 100644
---- a/src/sage/rings/polynomial/multi_polynomial_ideal.py
-+++ b/src/sage/rings/polynomial/multi_polynomial_ideal.py
-@@ -90,8 +90,8 @@ Or we can work with `\ZZ/17\ZZ` directly::
- 
-     sage: a^2 + b^2 == 0
-     True
--    sage: a^3 - b^2
--    -a*b^2 - b^2
-+    sage: a^3 - b^2 == -a*b^2 - b^2 == 16*a*b^2 + 16*b^2
-+    True
-     sage: (a+b)^17
-     a*b^16 + b^17
-     sage: S(17) == 0
-@@ -187,10 +187,10 @@ when the system has no solutions over the rationals.
-         sage: I.change_ring(P.change_ring( GF(11777 ))).groebner_basis()
-         [x + 5633, y - 3007, z - 2626]
- 
--    The Groebner basis modulo any product of the prime factors is also non-trivial. ::
-+    The Groebner basis modulo any product of the prime factors is also non-trivial::
- 
-         sage: I.change_ring(P.change_ring( IntegerModRing(2*7) )).groebner_basis()
--        [x + y + z, y^2 + 3*y, y*z + 11*y + 4, 2*y + 6, z^2 + 3, 2*z + 10]
-+        [x + 3*y + 11*z, y^2 + 3*y, y*z + 11*y + 4, 2*y + 6, z^2 + 3, 2*z + 10]
- 
-     Modulo any other prime the Groebner basis is trivial so there are
-     no other solutions. For example::
-@@ -712,10 +712,10 @@ class MPolynomialIdeal_singular_repr(
-             sage: p = z^2 + 1; q = z^3 + 2
-             sage: I = (p*q^2, y-z^2)*R
-             sage: pd = I.complete_primary_decomposition(); pd
--            [(Ideal (z^6 + 4*z^3 + 4, y - z^2) of Multivariate Polynomial Ring in x, y, z over Rational Field,
--              Ideal (z^3 + 2, y - z^2) of Multivariate Polynomial Ring in x, y, z over Rational Field),
--             (Ideal (z^2 + 1, y + 1) of Multivariate Polynomial Ring in x, y, z over Rational Field,
--              Ideal (z^2 + 1, y + 1) of Multivariate Polynomial Ring in x, y, z over Rational Field)]
-+            [(Ideal (z^2 + 1, y + 1) of Multivariate Polynomial Ring in x, y, z over Rational Field,
-+              Ideal (z^2 + 1, y + 1) of Multivariate Polynomial Ring in x, y, z over Rational Field),
-+             (Ideal (z^6 + 4*z^3 + 4, y - z^2) of Multivariate Polynomial Ring in x, y, z over Rational Field,
-+              Ideal (z^3 + 2, y - z^2) of Multivariate Polynomial Ring in x, y, z over Rational Field)]
- 
-             sage: I.primary_decomposition_complete(algorithm = 'gtz')
-             [(Ideal (z^6 + 4*z^3 + 4, y - z^2) of Multivariate Polynomial Ring in x, y, z over Rational Field,
-@@ -832,8 +832,8 @@ class MPolynomialIdeal_singular_repr(
-             sage: p = z^2 + 1; q = z^3 + 2
-             sage: I = (p*q^2, y-z^2)*R
-             sage: pd = I.primary_decomposition(); pd
--            [Ideal (z^6 + 4*z^3 + 4, y - z^2) of Multivariate Polynomial Ring in x, y, z over Rational Field,
--             Ideal (z^2 + 1, y + 1) of Multivariate Polynomial Ring in x, y, z over Rational Field]
-+            [Ideal (z^2 + 1, y + 1) of Multivariate Polynomial Ring in x, y, z over Rational Field,
-+             Ideal (z^6 + 4*z^3 + 4, y - z^2) of Multivariate Polynomial Ring in x, y, z over Rational Field]
- 
-         ::
- 
-@@ -904,8 +904,8 @@ class MPolynomialIdeal_singular_repr(
-             sage: p = z^2 + 1; q = z^3 + 2
-             sage: I = (p*q^2, y-z^2)*R
-             sage: pd = I.associated_primes(); pd
--            [Ideal (z^3 + 2, y - z^2) of Multivariate Polynomial Ring in x, y, z over Rational Field,
--             Ideal (z^2 + 1, y + 1) of Multivariate Polynomial Ring in x, y, z over Rational Field]
-+            [Ideal (z^2 + 1, y + 1) of Multivariate Polynomial Ring in x, y, z over Rational Field,
-+             Ideal (z^3 + 2, y - z^2) of Multivariate Polynomial Ring in x, y, z over Rational Field]
- 
-         ALGORITHM:
- 
-@@ -3623,9 +3623,12 @@ class MPolynomialIdeal( MPolynomialIdeal_singular_repr, \
-             sage: P.<a,b,c> = PolynomialRing(ZZ,3)
-             sage: I = P * (a + 2*b + 2*c - 1, a^2 - a + 2*b^2 + 2*c^2, 2*a*b + 2*b*c - b)
-             sage: I.groebner_basis()
--            [b^3 - 23*b*c^2 + 3*b^2 + 5*b*c, 2*b*c^2 - 6*c^3 - b^2 - b*c + 2*c^2,
--             42*c^3 + 5*b^2 + 4*b*c - 14*c^2, 2*b^2 + 6*b*c + 6*c^2 - b - 2*c,
--             10*b*c + 12*c^2 - b - 4*c, a + 2*b + 2*c - 1]
-+            [b^3 - 181*b*c^2 + 222*c^3 - 26*b*c - 146*c^2 + 19*b + 24*c,
-+             2*b*c^2 - 48*c^3 + 3*b*c + 22*c^2 - 2*b - 2*c,
-+             42*c^3 + 45*b^2 + 54*b*c + 22*c^2 - 13*b - 12*c,
-+             2*b^2 + 6*b*c + 6*c^2 - b - 2*c,
-+             10*b*c + 12*c^2 - b - 4*c,
-+             a + 2*b + 2*c - 1]
- 
-         ::
- 
-@@ -3642,7 +3645,7 @@ class MPolynomialIdeal( MPolynomialIdeal_singular_repr, \
-             sage: I = P * (a + 2*b + 2*c - 1, a^2 - a + 2*b^2 + 2*c^2, 2*a*b + 2*b*c - b)
-             sage: I.groebner_basis()
-             [b*c^2 + 992*b*c + 712*c^2 + 332*b + 96*c,
--             2*c^3 + 589*b*c + 862*c^2 + 762*b + 268*c,
-+             2*c^3 + 214*b*c + 862*c^2 + 762*b + 268*c,
-              b^2 + 438*b*c + 281*b,
-              5*b*c + 156*c^2 + 112*b + 948*c,
-              50*c^2 + 600*b + 650*c, a + 2*b + 2*c + 999, 125*b]
-@@ -3652,7 +3655,6 @@ class MPolynomialIdeal( MPolynomialIdeal_singular_repr, \
-             sage: R.<x,y,z> = PolynomialRing(Zmod(2233497349584))
-             sage: I = R.ideal([z*(x-3*y), 3^2*x^2-y*z, z^2+y^2])
-             sage: I.groebner_basis()
--            verbose 0 (...: multi_polynomial_ideal.py, groebner_basis) Warning: falling back to very slow toy implementation.
-             [2*z^4, y*z^2 + 81*z^3, 248166372176*z^3, 9*x^2 - y*z, y^2 + z^2, x*z +
-             2233497349581*y*z, 248166372176*y*z]
- 
-diff --git a/src/sage/rings/polynomial/multi_polynomial_ideal_libsingular.pyx b/src/sage/rings/polynomial/multi_polynomial_ideal_libsingular.pyx
-index b66653c..902283d 100644
---- a/src/sage/rings/polynomial/multi_polynomial_ideal_libsingular.pyx
-+++ b/src/sage/rings/polynomial/multi_polynomial_ideal_libsingular.pyx
-@@ -52,11 +52,12 @@ Two examples from the Mathematica documentation (done in Sage):
- include "cysignals/signals.pxi"
- 
- from sage.libs.singular.decl cimport tHomog, number, IDELEMS, p_Copy, rChangeCurrRing
--from sage.libs.singular.decl cimport idInit, id_Delete, currRing, currQuotient, Sy_bit, OPT_REDSB
--from sage.libs.singular.decl cimport scKBase, poly, testHomog, idSkipZeroes, idRankFreeModule, kStd
-+from sage.libs.singular.decl cimport idInit, id_Delete, currRing, Sy_bit, OPT_REDSB
-+from sage.libs.singular.decl cimport scKBase, poly, testHomog, idSkipZeroes, id_RankFreeModule, kStd
- from sage.libs.singular.decl cimport OPT_REDTAIL, singular_options, kInterRed, t_rep_gb, p_GetCoeff
- from sage.libs.singular.decl cimport pp_Mult_nn, p_Delete, n_Delete
- from sage.libs.singular.decl cimport rIsPluralRing
-+from sage.libs.singular.decl cimport n_unknown,  n_Zp,  n_Q,   n_R,   n_GF,  n_long_R,  n_algExt,n_transExt,n_long_C,   n_Z,   n_Zn,  n_Znm,  n_Z2m,  n_CF
- 
- from sage.rings.polynomial.multi_polynomial_libsingular cimport new_MP
- from sage.rings.polynomial.plural cimport new_NCP
-@@ -174,7 +175,7 @@ def kbase_libsingular(I):
- 
-     cdef ideal *i = sage_ideal_to_singular_ideal(I)
-     cdef ring *r = currRing
--    cdef ideal *q = currQuotient
-+    cdef ideal *q = currRing.qideal
- 
-     cdef ideal *result
-     singular_options = singular_options | Sy_bit(OPT_REDSB)
-@@ -244,7 +245,7 @@ def slimgb_libsingular(I):
-         id_Delete(&i, r)
-         raise TypeError("ordering must be global for slimgb")
- 
--    if i.rank < idRankFreeModule(i, r):
-+    if i.rank < id_RankFreeModule(i, r):
-         id_Delete(&i, r)
-         raise TypeError
- 
-@@ -274,12 +275,12 @@ def interred_libsingular(I):
-         sage: P.<x,y,z> = PolynomialRing(ZZ)
-         sage: I = ideal( x^2 - 3*y, y^3 - x*y, z^3 - x, x^4 - y*z + 1 )
-         sage: I.interreduced_basis()
--        [y^3 - x*y, z^3 - x, x^2 - 3*y, 9*y^2 - y*z + 1]
-+        [y*z^2 - 81*x*y - 9*y - z, z^3 - x, x^2 - 3*y, 9*y^2 - y*z + 1]
- 
-         sage: P.<x,y,z> = PolynomialRing(QQ)
-         sage: I = ideal( x^2 - 3*y, y^3 - x*y, z^3 - x, x^4 - y*z + 1 )
-         sage: I.interreduced_basis()
--        [y*z^2 - 81*x*y - 9*y - z, z^3 - x, x^2 - 3*y, y^2 - 1/9*y*z + 1/9]
-+        [y*z^2 - 81*x*y - 9*y - z, z^3 - x, x^2 - 3*y, 9*y^2 - y*z + 1]
-     """
-     global singular_options
- 
-@@ -296,7 +297,7 @@ def interred_libsingular(I):
-             return Sequence([], check=False, immutable=True)
-     except AttributeError:
-         pass
--            
-+
-     i = sage_ideal_to_singular_ideal(I)
-     r = currRing
- 
-@@ -309,12 +310,12 @@ def interred_libsingular(I):
- 
- 
-     # divide head by coefficients
--    if r.ringtype == 0:
-+    if r.cf.type == n_unknown:
-         for j from 0 <= j < IDELEMS(result):
-             p = result.m[j]
-             if p:
-                 n = p_GetCoeff(p,r)
--                n = r.cf.nInvers(n)
-+                n = r.cf.cfInvers(n,r.cf)
-             result.m[j] = pp_Mult_nn(p, n, r)
-             p_Delete(&p,r)
-             n_Delete(&n,r)
-@@ -325,5 +326,3 @@ def interred_libsingular(I):
- 
-     id_Delete(&result,r)
-     return res
--
--
-diff --git a/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx b/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx
-index 4210fd4..81f64bb 100644
---- a/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx
-+++ b/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx
-@@ -170,19 +170,20 @@ include "cysignals/signals.pxi"
- 
- # singular types
- from sage.libs.singular.decl cimport ring, poly, ideal, intvec, number, currRing
-+from sage.libs.singular.decl cimport n_unknown,  n_Zp,  n_Q,   n_R,   n_GF,  n_long_R,  n_algExt,n_transExt,n_long_C,   n_Z,   n_Zn,  n_Znm,  n_Z2m,  n_CF
- 
- # singular functions
- from sage.libs.singular.decl cimport (
--    errorreported, libfac_interruptflag,
-+    errorreported,
-     p_ISet, rChangeCurrRing, p_Copy, p_Init, p_SetCoeff, p_Setm, p_SetExp, p_Add_q,
-     p_NSet, p_GetCoeff, p_Delete, p_GetExp, pNext, rRingVar, omAlloc0, omStrDup,
-     omFree, pDivide, p_SetCoeff0, n_Init, p_DivisibleBy, pLcm, p_LmDivisibleBy,
-     pDivide, p_IsConstant, p_ExpVectorEqual, p_String, p_LmInit, n_Copy,
--    p_IsUnit, pInvers, p_Head, idInit, fast_map, id_Delete,
--    pIsHomogeneous, pHomogen, p_Totaldegree, singclap_pdivide, singclap_factorize,
-+    p_IsUnit, pInvers, p_Head, idInit, fast_map_common_subexp, id_Delete,
-+    p_IsHomogeneous, pHomogen, p_Totaldegree,pLDeg1_Totaldegree, singclap_pdivide, singclap_factorize,
-     idLift, IDELEMS, On, Off, SW_USE_CHINREM_GCD, SW_USE_EZGCD,
-     p_LmIsConstant, pTakeOutComp1, singclap_gcd, pp_Mult_qq, p_GetMaxExp,
--    pLength, kNF, singclap_isSqrFree, p_Neg, p_Minus_mm_Mult_qq, p_Plus_mm_Mult_qq,
-+    pLength, kNF, p_Neg, p_Minus_mm_Mult_qq, p_Plus_mm_Mult_qq,
-     pDiff, singclap_resultant, p_Normalize,
-     prCopyR, prCopyR_NoSort )
- 
-@@ -219,10 +220,12 @@ from sage.rings.integer cimport Integer
- from sage.rings.finite_rings.integer_mod_ring import is_IntegerModRing
- from sage.rings.number_field.number_field_base cimport NumberField
- 
--from sage.arith.all import gcd
-+from sage.rings.arith import gcd
- from sage.structure.element import coerce_binop
- 
- from sage.structure.parent cimport Parent
-+from sage.structure.parent_base cimport ParentWithBase
-+from sage.structure.parent_gens cimport ParentWithGens
- from sage.structure.category_object cimport CategoryObject
- 
- from sage.structure.element cimport EuclideanDomainElement
-@@ -586,6 +589,7 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_generic):
-         Coercion from SINGULAR elements::
- 
-             sage: P._singular_()
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 0
-             //   number of vars : 3
-             //        block   1 : ordering dp
-@@ -806,7 +810,7 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_generic):
-             if element.parent() is base_ring:
-                 # shortcut for GF(p)
-                 if isinstance(base_ring, FiniteField_prime_modn):
--                    _p = p_ISet(int(element) % _ring.ch, _ring)
-+                    _p = p_ISet(int(element) % _ring.cf.ch, _ring)
-                 else:
-                     _n = sa2si(element,_ring)
-                     _p = p_NSet(_n, _ring)
-@@ -830,7 +834,7 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_generic):
- 
-         elif isinstance(element, int) or isinstance(element, long):
-             if isinstance(base_ring, FiniteField_prime_modn):
--                _p = p_ISet(element % _ring.ch, _ring)
-+                _p = p_ISet(element % _ring.cf.ch, _ring)
-             else:
-                 _n = sa2si(base_ring(element), _ring)
-                 _p = p_NSet(_n, _ring)
-@@ -977,7 +981,6 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_generic):
- 
-         if is_Macaulay2Element(element):
-             return self(element.external_string())
--
-         try:
-             return self(str(element))
-         except TypeError:
-@@ -1174,6 +1177,7 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_generic):
- 
-             sage: P.<x,y,z> = QQ[]
-             sage: P._singular_()
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 0
-             //   number of vars : 3
-             //        block   1 : ordering dp
-@@ -1189,6 +1193,7 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_generic):
-             sage: k.<a> = GF(3^3)
-             sage: P.<x,y,z> = PolynomialRing(k,3)
-             sage: P._singular_()
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 3
-             //   1 parameter    : a
-             //   minpoly        : (a^3-a+1)
-@@ -1206,6 +1211,7 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_generic):
-         TESTS:
-             sage: P.<x> = QQ[]
-             sage: P._singular_()
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 0
-             //   number of vars : 1
-             //        block   1 : ordering lp
-@@ -1245,6 +1251,7 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_generic):
- 
-             sage: P.<x,y,z> = QQ[]
-             sage: P._singular_init_()
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 0
-             //   number of vars : 3
-             //        block   1 : ordering dp
-@@ -1259,6 +1266,7 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_generic):
-             sage: w = var('w')
-             sage: R.<x,y> = PolynomialRing(NumberField(w^2+1,'s'))
-             sage: singular(R)
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 0
-             //   1 parameter    : s
-             //   minpoly        : (s^2+1)
-@@ -1269,6 +1277,7 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_generic):
- 
-             sage: R = PolynomialRing(GF(2**8,'a'),10,'x', order='invlex')
-             sage: singular(R)
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 2
-             //   1 parameter    : a
-             //   minpoly        : (a^8+a^4+a^3+a^2+1)
-@@ -1279,6 +1288,7 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_generic):
- 
-             sage: R = PolynomialRing(GF(127),2,'x', order='invlex')
-             sage: singular(R)
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 127
-             //   number of vars : 2
-             //        block   1 : ordering rp
-@@ -1287,6 +1297,7 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_generic):
- 
-             sage: R = PolynomialRing(QQ,2,'x', order='invlex')
-             sage: singular(R)
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 0
-             //   number of vars : 2
-             //        block   1 : ordering rp
-@@ -1295,6 +1306,7 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_generic):
- 
-             sage: R = PolynomialRing(QQ,2,'x', order='degneglex')
-             sage: singular(R)
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 0
-             //   number of vars : 2
-             //        block   1 : ordering a
-@@ -1306,6 +1318,7 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_generic):
- 
-             sage: R = PolynomialRing(QQ,'x')
-             sage: singular(R)
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 0
-             //   number of vars : 1
-             //        block   1 : ordering lp
-@@ -1314,6 +1327,7 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_generic):
- 
-             sage: R = PolynomialRing(GF(127),'x')
-             sage: singular(R)
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 127
-             //   number of vars : 1
-             //        block   1 : ordering lp
-@@ -1322,7 +1336,8 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_generic):
- 
-             sage: R = ZZ['x,y']
-             sage: singular(R)
--            //   coeff. ring is : Integers
-+            polynomial ring, over a domain, global ordering
-+            //   coeff. ring is : integer
-             //   number of vars : 2
-             //        block   1 : ordering dp
-             //                  : names    x y
-@@ -1330,6 +1345,7 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_generic):
- 
-             sage: R = IntegerModRing(1024)['x,y']
-             sage: singular(R)
-+            polynomial ring, over a ring (with zero-divisors), global ordering
-             //   coeff. ring is : Z/2^10
-             //   number of vars : 2
-             //        block   1 : ordering dp
-@@ -1338,7 +1354,8 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_generic):
- 
-             sage: R = IntegerModRing(15)['x,y']
-             sage: singular(R)
--            //   coeff. ring is : Z/15
-+            polynomial ring, over a ring (with zero-divisors), global ordering
-+            //   coeff. ring is : ZZ/15
-             //   number of vars : 2
-             //        block   1 : ordering dp
-             //                  : names    x y
-@@ -1348,6 +1365,7 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_generic):
- 
-             sage: P.<x> = QQ[]
-             sage: P._singular_init_()
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 0
-             //   number of vars : 1
-             //        block   1 : ordering lp
-@@ -1370,14 +1388,14 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_generic):
-             # singular converts to bits from base_10 in mpr_complex.cc by:
-             #  size_t bits = 1 + (size_t) ((float)digits * 3.5);
-             precision = base_ring.precision()
--            digits = sage.arith.all.ceil((2*precision - 2)/7.0)
-+            digits = sage.rings.arith.ceil((2*precision - 2)/7.0)
-             self.__singular = singular.ring("(real,%d,0)"%digits, _vars, order=order)
- 
-         elif is_ComplexField(base_ring):
-             # singular converts to bits from base_10 in mpr_complex.cc by:
-             #  size_t bits = 1 + (size_t) ((float)digits * 3.5);
-             precision = base_ring.precision()
--            digits = sage.arith.all.ceil((2*precision - 2)/7.0)
-+            digits = sage.rings.arith.ceil((2*precision - 2)/7.0)
-             self.__singular = singular.ring("(complex,%d,0,I)"%digits, _vars,  order=order)
- 
-         elif base_ring.is_prime_field():
-@@ -1615,8 +1633,7 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_generic):
-             9/4
- 
-             sage: P.monomial_quotient(x,y) # Note the wrong result
--            x*y^1048575*z^1048575 # 64-bit
--            x*y^65535*z^65535 # 32-bit
-+            x*y^65535*z^65535
- 
-             sage: P.monomial_quotient(x,P(1))
-             x
-@@ -1645,8 +1662,8 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_generic):
-         if r!=currRing: rChangeCurrRing(r)  # pDivide
-         res = pDivide(f._poly, g._poly)
-         if coeff:
--            if r.ringtype == 0 or r.cf.nDivBy(p_GetCoeff(f._poly, r), p_GetCoeff(g._poly, r)):
--                n = r.cf.nDiv( p_GetCoeff(f._poly, r) , p_GetCoeff(g._poly, r))
-+            if r.cf.type == n_unknown or r.cf.cfDivBy(p_GetCoeff(f._poly, r), p_GetCoeff(g._poly, r), r.cf):
-+                n = r.cf.cfDiv( p_GetCoeff(f._poly, r) , p_GetCoeff(g._poly, r), r.cf)
-                 p_SetCoeff0(res, n, r)
-             else:
-                 raise ArithmeticError("Cannot divide these coefficients.")
-@@ -2277,10 +2294,10 @@ cdef class MPolynomial_libsingular(sage.rings.polynomial.multi_polynomial.MPolyn
-             9/4*x^2 - 1/4*y^2 - y - 1
- 
-             sage: P.<x,y> = PolynomialRing(QQ,order='lex')
--            sage: (x^2^30) * x^2^30
-+            sage: (x^2^15) * x^2^15
-             Traceback (most recent call last):
-             ...
--            OverflowError: Exponent overflow (...).
-+            OverflowError: exponent overflow (...)
-         """
-         # all currently implemented rings are commutative
-         cdef poly *_p
-@@ -2391,10 +2408,10 @@ cdef class MPolynomial_libsingular(sage.rings.polynomial.multi_polynomial.MPolyn
-             TypeError: non-integral exponents not supported
- 
-             sage: P.<x,y> = PolynomialRing(QQ,order='lex')
--            sage: (x+y^2^30)^10
-+            sage: (x+y^2^15)^10
-             Traceback (most recent call last):
-             ....
--            OverflowError: Exponent overflow (...).
-+            OverflowError: exponent overflow (...)
-         """
-         if type(exp) is not Integer:
-             try:
-@@ -2541,7 +2558,7 @@ cdef class MPolynomial_libsingular(sage.rings.polynomial.multi_polynomial.MPolyn
-         argument ``std_grading=True``.
- 
-             sage: tord = TermOrder(matrix([3,0,1,1,1,0,1,0,0]))
--            sage: R.<x,y,z> = PolynomialRing(QQ,'x',3,order=tord)
-+            sage: R.<x,y,z> = PolynomialRing(QQ,3,order=tord)
-             sage: (x^3*y+x*z^4).degree()
-             9
-             sage: (x^3*y+x*z^4).degree(std_grading=True)
-@@ -2650,10 +2667,10 @@ cdef class MPolynomial_libsingular(sage.rings.polynomial.multi_polynomial.MPolyn
- 
-         With a matrix term ordering, the grading changes.
-         To evaluate the total degree using the standard grading,
--        use the optional argument``std_grading=True``.
-+        use the optional argument``std_grading=True``::
- 
-             sage: tord=TermOrder(matrix([3,0,1,1,1,0,1,0,0]))
--            sage: R.<x,y,z> = PolynomialRing(QQ,'x',3,order=tord)
-+            sage: R.<x,y,z> = PolynomialRing(QQ,3,order=tord)
-             sage: (x^2*y).total_degree()
-             6
-             sage: (x^2*y).total_degree(std_grading=True)
-@@ -3114,7 +3131,7 @@ cdef class MPolynomial_libsingular(sage.rings.polynomial.multi_polynomial.MPolyn
-         """
-         cdef ring *_ring = self._parent_ring
-         if(_ring != currRing): rChangeCurrRing(_ring)
--        return bool(pIsHomogeneous(self._poly))
-+        return bool(p_IsHomogeneous(self._poly,_ring))
- 
-     cpdef _homogenize(self, int var):
-         """
-@@ -3184,7 +3201,7 @@ cdef class MPolynomial_libsingular(sage.rings.polynomial.multi_polynomial.MPolyn
-         _p = p_Head(self._poly, _ring)
-         _n = p_GetCoeff(_p, _ring)
- 
--        ret = bool((not self._poly.next) and _ring.cf.nIsOne(_n))
-+        ret = bool((not self._poly.next) and _ring.cf.cfIsOne(_n,_ring.cf))
- 
-         p_Delete(&_p, _ring)
-         return ret
-@@ -3274,17 +3291,16 @@ cdef class MPolynomial_libsingular(sage.rings.polynomial.multi_polynomial.MPolyn
-         We are catching overflows::
- 
-             sage: R.<x,y> = QQ[]
--            sage: n=1000; f = x^n
-+            sage: n=100; f = x^n
-             sage: try:
-             ....:   f.subs(x = x^n)
-             ....:   print("no overflow")
-             ....: except OverflowError:
--            ....:   print("overflow")
--            overflow    # 32-bit
--            x^1000000   # 64-bit
--            no overflow # 64-bit
-+            ....:   print "overflow"
-+            x^10000
-+            no overflow
- 
--            sage: n=100000;
-+            sage: n=1000;
-             sage: try:
-             ....:   f = x^n
-             ....:   f.subs(x = x^n)
-@@ -3360,7 +3376,7 @@ cdef class MPolynomial_libsingular(sage.rings.polynomial.multi_polynomial.MPolyn
-                     if  degree > _ring.bitmask:
-                         id_Delete(&to_id, _ring)
-                         p_Delete(&_p, _ring)
--                        raise OverflowError("Exponent overflow (%d)."%(degree))
-+                        raise OverflowError("exponent overflow (%d)"%(degree))
-                     to_id.m[mi-1] = p_Copy(_f, _ring)
- 
-                 if _p == NULL:
-@@ -3398,7 +3414,7 @@ cdef class MPolynomial_libsingular(sage.rings.polynomial.multi_polynomial.MPolyn
-                     if degree > _ring.bitmask:
-                         id_Delete(&to_id, _ring)
-                         p_Delete(&_p, _ring)
--                        raise OverflowError("Exponent overflow (%d)."%(degree))
-+                        raise OverflowError("exponent overflow (%d)"%(degree))
-                     need_map = 1
- 
-                 if _p == NULL:
-@@ -3417,7 +3433,7 @@ cdef class MPolynomial_libsingular(sage.rings.polynomial.multi_polynomial.MPolyn
-                 from_id.m[0] = _p
- 
-                 rChangeCurrRing(_ring)
--                res_id = fast_map(from_id, _ring, to_id, _ring)
-+                res_id = fast_map_common_subexp(from_id, _ring, to_id, _ring)
-                 _p = res_id.m[0]
- 
-                 from_id.m[0] = NULL
-@@ -3595,7 +3611,10 @@ cdef class MPolynomial_libsingular(sage.rings.polynomial.multi_polynomial.MPolyn
-             Univariate Polynomial Ring in x over Rational Field
-         """
-         cdef poly *p = self._poly
-+        cdef poly *p2 = self._poly
-         cdef ring *r = self._parent_ring
-+        cdef long pTotDegMax
-+
-         k = self.base_ring()
- 
-         if not self.is_univariate():
-@@ -3609,12 +3628,20 @@ cdef class MPolynomial_libsingular(sage.rings.polynomial.multi_polynomial.MPolyn
-                 R = self.base_ring()[str(self.variables()[0])]
- 
-         zero = k(0)
--        coefficients = [zero] * (self.degree() + 1)
- 
-         if(r != currRing): rChangeCurrRing(r)
- 
-+        pTotDegMax = -1
-+        while p2:
-+            pTotDegMax = max(pTotDegMax, p_Totaldegree(p2, r))
-+            p2 = pNext(p2)
-+
-+        coefficients = [zero] * (pTotDegMax + 1)
-         while p:
--            coefficients[p_Totaldegree(p, r)] = si2sa(p_GetCoeff(p, r), r, k)
-+            pTotDeg = p_Totaldegree(p, r)
-+            if ( pTotDeg >= len(coefficients)  or  pTotDeg < 0 ):
-+                raise IndexError("list index("+str(pTotDeg)+" out of range(0-"+str(len(coefficients))+")")
-+            coefficients[pTotDeg] = si2sa(p_GetCoeff(p, r), r, k)
-             p = pNext(p)
- 
-         return R(coefficients)
-@@ -3931,8 +3958,8 @@ cdef class MPolynomial_libsingular(sage.rings.polynomial.multi_polynomial.MPolyn
-         _self = <MPolynomial_libsingular>self
-         _right = <MPolynomial_libsingular>right
- 
--        if r.ringtype != 0:
--            if r.ringtype == 4:
-+        if r.cf.type != n_unknown:
-+            if r.cf.type == n_Z:
-                 P = parent.change_ring(RationalField())
-                 f = P(self)//P(right)
-                 CM = list(f)
-@@ -3948,13 +3975,14 @@ cdef class MPolynomial_libsingular(sage.rings.polynomial.multi_polynomial.MPolyn
-                         quo = p_Add_q(quo, temp, r)
-                     p = pNext(p)
-                 return new_MP(parent, quo)
--            raise NotImplementedError("Division of multivariate polynomials over non fields by non-monomials not implemented.")
-+            if r.cf.type == n_Znm or r.cf.type == n_Zn or r.cf.type == n_Z2m :
-+                raise NotImplementedError("Division of multivariate polynomials over non fields by non-monomials not implemented.")
- 
-         cdef int count = singular_polynomial_length_bounded(_self._poly,15)
-         if count >= 15:  # note that _right._poly must be of shorter length than self._poly for us to care about this call
-             sig_on()
-         if r!=currRing: rChangeCurrRing(r)   # singclap_pdivide
--        quo = singclap_pdivide( _self._poly, _right._poly )
-+        quo = singclap_pdivide( _self._poly, _right._poly, r )
-         if count >= 15:
-             sig_off()
-         f = new_MP(parent, quo)
-@@ -4230,7 +4258,7 @@ cdef class MPolynomial_libsingular(sage.rings.polynomial.multi_polynomial.MPolyn
-         iv = NULL
-         sig_on()
-         if _ring!=currRing: rChangeCurrRing(_ring)   # singclap_factorize
--        I = singclap_factorize ( ptemp, &iv , 0)
-+        I = singclap_factorize ( ptemp, &iv , 0, _ring)
-         sig_off()
- 
-         ivv = iv.ivGetVec()
-@@ -4290,10 +4318,10 @@ cdef class MPolynomial_libsingular(sage.rings.polynomial.multi_polynomial.MPolyn
-             ValueError: polynomial is not in the ideal
-             sage: foo = I.complete_primary_decomposition() # indirect doctest
-             sage: foo[0][0]
--            Ideal (x2 - 1, x1 - 1) of Multivariate Polynomial Ring in x1, x2 over Rational Field
-+            Ideal (x1 + 1, x2^2 - 3) of Multivariate Polynomial Ring in x1, x2 over Rational Field
- 
-         """
--        global errorreported, libfac_interruptflag
-+        global errorreported
-         if not self._parent._base.is_field():
-             raise NotImplementedError("Lifting of multivariate polynomials over non-fields is not implemented.")
- 
-@@ -4327,10 +4355,9 @@ cdef class MPolynomial_libsingular(sage.rings.polynomial.multi_polynomial.MPolyn
- 
-         if r!=currRing: rChangeCurrRing(r)  # idLift
-         res = idLift(_I, fI, NULL, 0, 0, 0)
--        if errorreported != 0 or libfac_interruptflag != 0:
-+        if errorreported != 0 :
-             errorcode = errorreported
-             errorreported = 0
--            libfac_interruptflag = 0
-             if errorcode == 1:
-                 raise ValueError("polynomial is not in the ideal")
-             raise RuntimeError
-@@ -4561,14 +4588,17 @@ cdef class MPolynomial_libsingular(sage.rings.polynomial.multi_polynomial.MPolyn
-         else:
-             raise TypeError("algorithm %s not supported" % algorithm)
- 
--        if _ring.ringtype != 0:
--            if _ring.ringtype == 4:
-+        if _ring.cf.type != n_unknown:
-+            if _ring.cf.type == n_Z:
-                 P = self._parent.change_ring(RationalField())
-                 res = P(self).gcd(P(right))
-                 coef = sage.rings.integer.GCD_list(self.coefficients() + right.coefficients())
-                 return self._parent(coef*res)
- 
--            raise NotImplementedError("GCD over rings not implemented.")
-+            #TODO:
-+            if _ring.cf.type == n_Znm or _ring.cf.type == n_Zn or _ring.cf.type == n_Z2m :
-+                raise NotImplementedError("GCD over rings not implemented.")
-+            #raise NotImplementedError("GCD over rings not implemented.")
- 
-         if self._parent._base.is_finite() and self._parent._base.characteristic() > 1<<29:
-             raise NotImplementedError("GCD of multivariate polynomials over prime fields with characteristic > 2^29 is not implemented.")
-@@ -4586,7 +4616,7 @@ cdef class MPolynomial_libsingular(sage.rings.polynomial.multi_polynomial.MPolyn
-         if count >= 20:
-             sig_on()
-         if _ring!=currRing: rChangeCurrRing(_ring)  # singclap_gcd
--        _res = singclap_gcd(p_Copy(self._poly, _ring), p_Copy(_right._poly, _ring))
-+        _res = singclap_gcd(p_Copy(self._poly, _ring), p_Copy(_right._poly, _ring), _ring )
-         if count >= 20:
-             sig_off()
- 
-@@ -4632,14 +4662,15 @@ cdef class MPolynomial_libsingular(sage.rings.polynomial.multi_polynomial.MPolyn
-         cdef MPolynomial_libsingular _g
-         if _ring!=currRing: rChangeCurrRing(_ring)
- 
--        if _ring.ringtype != 0:
--            if _ring.ringtype == 4:
-+        if _ring.cf.type != n_unknown:
-+            if _ring.cf.type == n_Z:
-                 P = self.parent().change_ring(RationalField())
-                 py_gcd = P(self).gcd(P(g))
-                 py_prod = P(self*g)
-                 return self.parent(py_prod//py_gcd)
-             else:
--                raise TypeError("LCM over non-integral domains not available.")
-+                if _ring.cf.type == n_Znm or _ring.cf.type == n_Zn or _ring.cf.type == n_Z2m :
-+                    raise TypeError("LCM over non-integral domains not available.")
- 
-         if self._parent is not g._parent:
-             _g = self._parent._coerce_c(g)
-@@ -4654,9 +4685,9 @@ cdef class MPolynomial_libsingular(sage.rings.polynomial.multi_polynomial.MPolyn
-         if count >= 20:
-             sig_on()
-         if _ring!=currRing: rChangeCurrRing(_ring)  # singclap_gcd
--        gcd = singclap_gcd(p_Copy(self._poly, _ring), p_Copy(_g._poly, _ring))
-+        gcd = singclap_gcd(p_Copy(self._poly, _ring), p_Copy(_g._poly, _ring), _ring )
-         prod = pp_Mult_qq(self._poly, _g._poly, _ring)
--        ret = singclap_pdivide(prod , gcd )
-+        ret = singclap_pdivide(prod , gcd , _ring)
-         p_Delete(&prod, _ring)
-         p_Delete(&gcd, _ring)
-         if count >= 20:
-@@ -4677,13 +4708,8 @@ cdef class MPolynomial_libsingular(sage.rings.polynomial.multi_polynomial.MPolyn
-             sage: h.is_squarefree()
-             False
-         """
--        cdef ring *_ring = self._parent_ring
--
--        if self._parent._base.is_finite() and self._parent._base.characteristic() > 1<<29:
--            raise NotImplementedError("is_squarefree of multivariate polynomials over prime fields with characteristic > 2^29 is not implemented.")
--
--        if(_ring != currRing): rChangeCurrRing(_ring)
--        return bool(singclap_isSqrFree(self._poly))
-+        # TODO:  Use Singular (4.x) intrinsics.  (Temporary solution from #17254.)
-+        return all([ e == 1 for (f, e) in self.factor() ])
- 
-     @coerce_binop
-     def quo_rem(self, MPolynomial_libsingular right):
-@@ -4740,7 +4766,7 @@ cdef class MPolynomial_libsingular(sage.rings.polynomial.multi_polynomial.MPolyn
-         if count >= 15:  # note that _right._poly must be of shorter length than self._poly for us to care about this call
-             sig_on()
-         if r!=currRing: rChangeCurrRing(r)   # singclap_pdivide
--        quo = singclap_pdivide( self._poly, right._poly )
-+        quo = singclap_pdivide( self._poly, right._poly, r )
-         rem = p_Add_q(p_Copy(self._poly, r), p_Neg(pp_Mult_qq(right._poly, quo, r), r), r)
-         if count >= 15:
-             sig_off()
-@@ -5181,7 +5207,7 @@ cdef class MPolynomial_libsingular(sage.rings.polynomial.multi_polynomial.MPolyn
-         if count >= 20:
-             sig_on()
-         if _ring != currRing: rChangeCurrRing(_ring)   # singclap_resultant
--        rt =  singclap_resultant(p_Copy(self._poly, _ring), p_Copy(other._poly, _ring),p_Copy((<MPolynomial_libsingular>variable)._poly, _ring))
-+        rt =  singclap_resultant(p_Copy(self._poly, _ring), p_Copy(other._poly, _ring), p_Copy((<MPolynomial_libsingular>variable)._poly , _ring ), _ring)
-         if count >= 20:
-             sig_off()
-         return new_MP(self._parent, rt)
-diff --git a/src/sage/rings/polynomial/multi_polynomial_ring_generic.pyx b/src/sage/rings/polynomial/multi_polynomial_ring_generic.pyx
-index d4ff6fd..3abece4 100644
---- a/src/sage/rings/polynomial/multi_polynomial_ring_generic.pyx
-+++ b/src/sage/rings/polynomial/multi_polynomial_ring_generic.pyx
-@@ -850,7 +850,7 @@ cdef class MPolynomialRing_generic(sage.rings.ring.CommutativeRing):
- 
-             sage: R.<x> = PolynomialRing(Integers(3), 1)
-             sage: R.random_element()
--            -x^2 + x
-+            2*x^2 + x
- 
-         To produce a dense polynomial, pick ``terms=Infinity``::
- 
-diff --git a/src/sage/rings/polynomial/pbori.pyx b/src/sage/rings/polynomial/pbori.pyx
-index 54e00d9..13b6cdb 100644
---- a/src/sage/rings/polynomial/pbori.pyx
-+++ b/src/sage/rings/polynomial/pbori.pyx
-@@ -1370,6 +1370,7 @@ cdef class BooleanPolynomialRing(MPolynomialRing_generic):
- 
-             sage: B.<x,y> = BooleanPolynomialRing(2)
-             sage: B._singular_() # indirect doctest
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 2
-             //   number of vars : 2
-             //        block   1 : ordering lp
-diff --git a/src/sage/rings/polynomial/plural.pxd b/src/sage/rings/polynomial/plural.pxd
-index eec63df..0f0b659 100644
---- a/src/sage/rings/polynomial/plural.pxd
-+++ b/src/sage/rings/polynomial/plural.pxd
-@@ -5,6 +5,10 @@ from sage.structure.parent cimport Parent
- from sage.libs.singular.function cimport RingWrap
- from sage.rings.polynomial.multi_polynomial_libsingular cimport MPolynomialRing_libsingular
- 
-+from sage.libs.singular.decl cimport wFunctionalBuch
-+
-+from sage.libs.singular.decl cimport p_Totaldegree
-+
- cdef extern from *:
-     ctypedef long Py_hash_t
- 
-diff --git a/src/sage/rings/polynomial/plural.pyx b/src/sage/rings/polynomial/plural.pyx
-index bba5da7..83d632a 100644
---- a/src/sage/rings/polynomial/plural.pyx
-+++ b/src/sage/rings/polynomial/plural.pyx
-@@ -110,14 +110,16 @@ from sage.categories.algebras import Algebras
- 
- # singular rings
- 
-+from sage.libs.singular.ring cimport singular_ring_new, singular_ring_delete, wrap_ring, singular_ring_reference
-+
-+from sage.libs.singular.singular cimport si2sa, sa2si, overflow_check
-+
-+
- from sage.libs.singular.function cimport RingWrap
- 
- from sage.libs.singular.polynomial cimport (singular_polynomial_call, singular_polynomial_cmp, singular_polynomial_add, singular_polynomial_sub, singular_polynomial_neg, singular_polynomial_pow, singular_polynomial_mul, singular_polynomial_rmul, singular_polynomial_deg, singular_polynomial_str_with_changed_varnames, singular_polynomial_latex, singular_polynomial_str, singular_polynomial_div_coeff)
- 
- import sage.libs.singular.ring
--from sage.libs.singular.ring cimport singular_ring_new, singular_ring_delete, wrap_ring, singular_ring_reference
--
--from sage.libs.singular.singular cimport si2sa, sa2si, overflow_check
- 
- from sage.rings.finite_rings.finite_field_prime_modn import FiniteField_prime_modn
- from sage.rings.integer cimport Integer
-@@ -485,7 +487,7 @@ cdef class NCPolynomialRing_plural(Ring):
-             if  <Parent>element.parent() is base_ring:
-                 # shortcut for GF(p)
-                 if isinstance(base_ring, FiniteField_prime_modn):
--                    _p = p_ISet(int(element) % _ring.ch, _ring)
-+                    _p = p_ISet(int(element) % _ring.cf.ch, _ring)
-                 else:
-                     _n = sa2si(element,_ring)
-                     _p = p_NSet(_n, _ring)
-@@ -506,7 +508,7 @@ cdef class NCPolynomialRing_plural(Ring):
-         # Accepting int
-         elif isinstance(element, int):
-             if isinstance(base_ring, FiniteField_prime_modn):
--                _p = p_ISet(int(element) % _ring.ch,_ring)
-+                _p = p_ISet(int(element) % _ring.cf.ch,_ring)
-             else:
-                 _n = sa2si(base_ring(element),_ring)
-                 _p = p_NSet(_n, _ring)
-@@ -991,8 +993,8 @@ cdef class NCPolynomialRing_plural(Ring):
- 
-         res = pDivide(f._poly,g._poly)
-         if coeff:
--            if r.ringtype == 0 or r.cf.nDivBy(p_GetCoeff(f._poly, r), p_GetCoeff(g._poly, r)):
--                n = r.cf.nDiv( p_GetCoeff(f._poly, r) , p_GetCoeff(g._poly, r))
-+            if (r.cf.type == n_unknown) or r.cf.cfDivBy(p_GetCoeff(f._poly, r), p_GetCoeff(g._poly, r), r.cf):
-+                n = r.cf.cfDiv( p_GetCoeff(f._poly, r) , p_GetCoeff(g._poly, r), r.cf)
-                 p_SetCoeff0(res, n, r)
-             else:
-                 raise ArithmeticError("Cannot divide these coefficients.")
-@@ -1371,8 +1373,6 @@ cdef class NCPolynomial_plural(RingElement):
-         if self._parent is not None and (<NCPolynomialRing_plural>self._parent)._ring != NULL and self._poly != NULL:
-             p_Delete(&self._poly, (<NCPolynomialRing_plural>self._parent)._ring)
- 
--#    def __call__(self, *x, **kwds): # ?
--
-     def __reduce__(self):
-         """
-         TEST::
-@@ -1550,10 +1550,10 @@ cdef class NCPolynomial_plural(RingElement):
-             sage: P = A.g_algebra(relations={y*x:-x*y + z},  order='lex')
-             sage: P.inject_variables()
-             Defining x, z, y
--            sage: (x^2^30) * x^2^30
-+            sage: (x^2^15) * x^2^15
-             Traceback (most recent call last):
-             ...
--            OverflowError: Exponent overflow (...).
-+            OverflowError: exponent overflow (65536)
-         """
-         # all currently implemented rings are commutative
-         cdef poly *_p
-@@ -1620,10 +1620,10 @@ cdef class NCPolynomial_plural(RingElement):
-             sage: P = A.g_algebra(relations={y*x:-x*y + z},  order='lex')
-             sage: P.inject_variables()
-             Defining x, z, y
--            sage: (x+y^2^30)^10
-+            sage: (x+y^2^15)^10
-             Traceback (most recent call last):
-             ....
--            OverflowError: Exponent overflow (...).
-+            OverflowError: exponent overflow (327680)
-         """
-         if type(exp) is not Integer:
-             try:
-@@ -2327,7 +2327,7 @@ cdef class NCPolynomial_plural(RingElement):
-         """
-         cdef ring *_ring = (<NCPolynomialRing_plural>self._parent)._ring
-         if(_ring != currRing): rChangeCurrRing(_ring)
--        return bool(pIsHomogeneous(self._poly))
-+        return bool(p_IsHomogeneous(self._poly,_ring))
- 
- 
-     def is_monomial(self):
-@@ -2365,7 +2365,7 @@ cdef class NCPolynomial_plural(RingElement):
-         _p = p_Head(self._poly, _ring)
-         _n = p_GetCoeff(_p, _ring)
- 
--        ret = bool((not self._poly.next) and _ring.cf.nIsOne(_n))
-+        ret = bool((not self._poly.next) and _ring.cf.cfIsOne(_n,_ring.cf))
- 
-         p_Delete(&_p, _ring)
-         return ret
-diff --git a/src/sage/rings/polynomial/polynomial_quotient_ring.py b/src/sage/rings/polynomial/polynomial_quotient_ring.py
-index 01c8c84..1c8003f 100644
---- a/src/sage/rings/polynomial/polynomial_quotient_ring.py
-+++ b/src/sage/rings/polynomial/polynomial_quotient_ring.py
-@@ -599,6 +599,7 @@ class PolynomialQuotientRing_generic(CommutativeRing):
-             sage: P.<x> = QQ[]
-             sage: Q = P.quo([(x^2+1)])
-             sage: singular(Q)        # indirect doctest
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 0
-             //   number of vars : 1
-             //        block   1 : ordering lp
-diff --git a/src/sage/rings/polynomial/polynomial_singular_interface.py b/src/sage/rings/polynomial/polynomial_singular_interface.py
-index 4784673..43bad63 100644
---- a/src/sage/rings/polynomial/polynomial_singular_interface.py
-+++ b/src/sage/rings/polynomial/polynomial_singular_interface.py
-@@ -80,6 +80,7 @@ class PolynomialRing_singular_repr:
- 
-             sage: R.<x,y> = PolynomialRing(CC,'x',2)
-             sage: singular(R)
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 0 (complex:15 digits, additional 0 digits)
-             //   1 parameter    : I
-             //   minpoly        : (I^2+1)
-@@ -89,7 +90,8 @@ class PolynomialRing_singular_repr:
-             //        block   2 : ordering C
-             sage: R.<x,y> = PolynomialRing(RealField(100),'x',2)
-             sage: singular(R)
--            //   characteristic : 0 (real:29 digits, additional 0 digits)
-+            polynomial ring, over a field, global ordering
-+            //   characteristic : 0 (real)
-             //   number of vars : 2
-             //        block   1 : ordering dp
-             //                  : names    x y
-@@ -98,6 +100,7 @@ class PolynomialRing_singular_repr:
-             sage: w = var('w')
-             sage: R.<x> = PolynomialRing(NumberField(w^2+1,'s'))
-             sage: singular(R)
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 0
-             //   1 parameter    : s
-             //   minpoly        : (s^2+1)
-@@ -108,6 +111,7 @@ class PolynomialRing_singular_repr:
- 
-             sage: R = PolynomialRing(GF(127),1,'x')
-             sage: singular(R)
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 127
-             //   number of vars : 1
-             //        block   1 : ordering lp
-@@ -116,6 +120,7 @@ class PolynomialRing_singular_repr:
- 
-             sage: R = PolynomialRing(QQ,1,'x')
-             sage: singular(R)
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 0
-             //   number of vars : 1
-             //        block   1 : ordering lp
-@@ -124,6 +129,7 @@ class PolynomialRing_singular_repr:
- 
-             sage: R = PolynomialRing(QQ,'x')
-             sage: singular(R)
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 0
-             //   number of vars : 1
-             //        block   1 : ordering lp
-@@ -132,6 +138,7 @@ class PolynomialRing_singular_repr:
- 
-             sage: R = PolynomialRing(GF(127),'x')
-             sage: singular(R)
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 127
-             //   number of vars : 1
-             //        block   1 : ordering lp
-@@ -140,6 +147,7 @@ class PolynomialRing_singular_repr:
- 
-             sage: R = Frac(ZZ['a,b'])['x,y']
-             sage: singular(R)
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 0
-             //   2 parameter    : a b
-             //   minpoly        : 0
-@@ -151,6 +159,7 @@ class PolynomialRing_singular_repr:
- 
-             sage: R = IntegerModRing(1024)['x,y']
-             sage: singular(R)
-+            polynomial ring, over a ring (with zero-divisors), global ordering
-             //   coeff. ring is : Z/2^10
-             //   number of vars : 2
-             //        block   1 : ordering dp
-@@ -159,7 +168,8 @@ class PolynomialRing_singular_repr:
- 
-             sage: R = IntegerModRing(15)['x,y']
-             sage: singular(R)
--            //   coeff. ring is : Z/15
-+            polynomial ring, over a ring (with zero-divisors), global ordering
-+            //   coeff. ring is : ZZ/15
-             //   number of vars : 2
-             //        block   1 : ordering dp
-             //                  : names    x y
-@@ -167,7 +177,8 @@ class PolynomialRing_singular_repr:
- 
-             sage: R = ZZ['x,y']
-             sage: singular(R)
--            //   coeff. ring is : Integers
-+            polynomial ring, over a domain, global ordering
-+            //   coeff. ring is : integer
-             //   number of vars : 2
-             //        block   1 : ordering dp
-             //                  : names    x y
-@@ -178,6 +189,7 @@ class PolynomialRing_singular_repr:
-             sage: K = R.fraction_field()
-             sage: S = K['y']
-             sage: singular(S)
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 5
-             //   1 parameter    : x
-             //   minpoly        : 0
-@@ -221,6 +233,7 @@ class PolynomialRing_singular_repr:
-         EXAMPLES::
- 
-             sage: PolynomialRing(QQ,'u_ba')._singular_init_()
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 0
-             //   number of vars : 1
-             //        block   1 : ordering lp
-diff --git a/src/sage/rings/polynomial/term_order.py b/src/sage/rings/polynomial/term_order.py
-index 17345c0..46bc69a 100644
---- a/src/sage/rings/polynomial/term_order.py
-+++ b/src/sage/rings/polynomial/term_order.py
-@@ -1665,6 +1665,7 @@ class TermOrder(SageObject):
-             sage: T.singular_str()
-             '(lp(3),Dp(5),lp(2))'
-             sage: P._singular_()
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 127
-             //   number of vars : 10
-             //        block   1 : ordering lp
-@@ -1692,6 +1693,7 @@ class TermOrder(SageObject):
-             sage: T.singular_str()
-             '(a(1:2),ls(2),a(1:2),ls(2))'
-             sage: P._singular_()
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 0
-             //   number of vars : 4
-             //        block   1 : ordering a
-diff --git a/src/sage/rings/quotient_ring.py b/src/sage/rings/quotient_ring.py
-index 4c2ea8d..da9083a 100644
---- a/src/sage/rings/quotient_ring.py
-+++ b/src/sage/rings/quotient_ring.py
-@@ -1174,6 +1174,7 @@ class QuotientRing_nc(ring.Ring, sage.structure.parent_gens.ParentWithGens):
-             sage: R.<x,y> = PolynomialRing(QQ)
-             sage: S = R.quotient_ring(x^2+y^2)
-             sage: S._singular_()
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 0
-             //   number of vars : 2
-             //        block   1 : ordering dp
-diff --git a/src/sage/rings/quotient_ring_element.py b/src/sage/rings/quotient_ring_element.py
-index 20a1a2d..8e59d6d 100644
---- a/src/sage/rings/quotient_ring_element.py
-+++ b/src/sage/rings/quotient_ring_element.py
-@@ -785,6 +785,7 @@ class QuotientRingElement(RingElement):
-             sage: I = sage.rings.ideal.FieldIdeal(P)
-             sage: Q = P.quo(I)
-             sage: Q._singular_()
-+            polynomial ring, over a field, global ordering
-             //   characteristic : 2
-             //   number of vars : 2
-             //        block   1 : ordering dp
-diff --git a/src/sage/schemes/curves/affine_curve.py b/src/sage/schemes/curves/affine_curve.py
-index 40235a1..72c520d 100644
---- a/src/sage/schemes/curves/affine_curve.py
-+++ b/src/sage/schemes/curves/affine_curve.py
-@@ -729,9 +729,9 @@ class AffineCurve(Curve_generic, AlgebraicScheme_subscheme_affine):
-             (Affine Plane Curve over Number Field in a0 with defining polynomial y^4 - 4*y^2 + 16 defined by
-             24*x^2*ss1^3 + 24*ss1^3 + (a0^3 - 8*a0),
-              Affine Plane Curve over Number Field in a0 with defining polynomial y^4 - 4*y^2 + 16 defined by
--             24*s1^2*ss0 + (a0^3 - 8*a0)*ss0^2 + (6*a0^3)*s1,
-+             24*s1^2*ss0 + (a0^3 - 8*a0)*ss0^2 + (-6*a0^3)*s1,
-              Affine Plane Curve over Number Field in a0 with defining polynomial y^4 - 4*y^2 + 16 defined by
--             8*y^2*s0^4 + (-4*a0^3)*y*s0^3 - 32*s0^2 + (a0^3 - 8*a0)*y)
-+             8*y^2*s0^4 + (4*a0^3)*y*s0^3 - 32*s0^2 + (a0^3 - 8*a0)*y)
- 
-         ::
- 
-@@ -1471,7 +1471,7 @@ class AffinePlaneCurve(AffineCurve):
-               To:   Affine Plane Curve over Number Field in a with defining
-             polynomial a^2 + 7 defined by x^2 + y^2 + 7
-               Defn: Defined on coordinates by sending (t) to
--                    (((7*a)*t^2 + (a))/(-7*t^2 + 1), (-14*t)/(-7*t^2 + 1))
-+                    ((-7*t^2 + 7)/((-a)*t^2 + (-a)), 14*t/((-a)*t^2 + (-a)))
-         """
-         para = self.projective_closure(i=0).rational_parameterization().defining_polynomials()
-         # these polynomials are homogeneous in two indeterminants, so dehomogenize wrt one of the variables
-diff --git a/src/sage/schemes/curves/projective_curve.py b/src/sage/schemes/curves/projective_curve.py
-index f666231..e62a177 100644
---- a/src/sage/schemes/curves/projective_curve.py
-+++ b/src/sage/schemes/curves/projective_curve.py
-@@ -1537,7 +1537,7 @@ class ProjectivePlaneCurve(ProjectiveCurve):
-               To:   Projective Plane Curve over Number Field in a with defining
-               polynomial a^2 + 1 defined by x^2 + y^2 + z^2
-               Defn: Defined on coordinates by sending (s : t) to
--                    (s^2 - t^2 : (a)*s^2 + (a)*t^2 : -2*s*t)
-+                    ((-a)*s^2 + (-a)*t^2 : s^2 - t^2 : 2*s*t)
-         """
-         if self.genus() != 0:
-             raise TypeError("this curve must have geometric genus zero")
-diff --git a/src/sage/structure/element.pyx b/src/sage/structure/element.pyx
-index 6eaf3ec..1cc469c 100644
---- a/src/sage/structure/element.pyx
-+++ b/src/sage/structure/element.pyx
-@@ -2391,15 +2391,14 @@ cdef class RingElement(ModuleElement):
-             ...
-             OverflowError: Exponent overflow (2147483648).
- 
--        Another example from :trac:`2956`; this should overflow on x32
--        and succeed on x64::
-+        Another example from :trac:`2956` which always overflows
-+        with Singular 4::
- 
-             sage: K.<x,y> = ZZ[]
-             sage: (x^12345)^54321
--            x^670592745                                   # 64-bit
--            Traceback (most recent call last):            # 32-bit
--            ...                                           # 32-bit
--            OverflowError: Exponent overflow (670592745). # 32-bit
-+            Traceback (most recent call last):
-+            ...
-+            OverflowError: exponent overflow (670592745)
- 
-         """
-         if dummy is not None:
-diff --git a/src/sage/tests/french_book/mpoly.py b/src/sage/tests/french_book/mpoly.py
-index 430b9a3..19975ac 100644
---- a/src/sage/tests/french_book/mpoly.py
-+++ b/src/sage/tests/french_book/mpoly.py
-@@ -163,7 +163,7 @@ Sage example in ./mpoly.tex, line 432::
-   [Ideal (z^17 - 1, y - 2*z^10, x - 3*z^3) of Multivariate
-   Polynomial Ring in x, y, z over Rational Field]
-   sage: J.transformed_basis()
--  [z^17 - 1, -2*z^10 + y, -3*z^3 + x]
-+  [z^17 - 1, -2*z^10 + y, -3/4*y^2 + x]
- 
- Sage example in ./mpoly.tex, line 534::



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