[arch-commits] Commit in sagemath/trunk (3 files)
Antonio Rojas
arojas at archlinux.org
Sat Dec 19 10:42:44 UTC 2020
Date: Saturday, December 19, 2020 @ 10:42:43
Author: arojas
Revision: 779936
Port to singular 4.2 library names
Added:
sagemath/trunk/sagemath-singular-4.2.patch
(from rev 779935, sagemath/trunk/sagemath-singular-4.1.2.patch)
Modified:
sagemath/trunk/PKGBUILD
Deleted:
sagemath/trunk/sagemath-singular-4.1.2.patch
-------------------------------+
PKGBUILD | 16
sagemath-singular-4.1.2.patch | 759 ---------------------------------
sagemath-singular-4.2.patch | 915 ++++++++++++++++++++++++++++++++++++++++
3 files changed, 921 insertions(+), 769 deletions(-)
Modified: PKGBUILD
===================================================================
--- PKGBUILD 2020-12-19 10:42:11 UTC (rev 779935)
+++ PKGBUILD 2020-12-19 10:42:43 UTC (rev 779936)
@@ -8,7 +8,7 @@
pkgbase=sagemath
pkgname=(sagemath sagemath-jupyter)
pkgver=9.2
-pkgrel=8
+pkgrel=9
pkgdesc="Open Source Mathematics Software, free alternative to Magma, Maple, Mathematica, and Matlab"
arch=(x86_64)
url="http://www.sagemath.org"
@@ -39,7 +39,7 @@
latte-count.patch
test-optional.patch
sagemath-cremona.patch
- sagemath-singular-4.1.2.patch
+ sagemath-singular-4.2.patch
sagemath-gap-4.11.patch
sagemath-flint-2.6.patch
sagemath-cypari-2.1.2.patch
@@ -50,7 +50,7 @@
'af922e1f978821a9a1f6c9a56130d71e5011c84a7aee7bf66a591bee658af30b'
'7da0dbcda15a327c21dc33853cb8f98cb86a283139f8735e3b20a71d49458a88'
'937074fa7a8a4e2aba9ea77ec622fe937985a1a9176c48460d51325ee877a4f5'
- '881186d016a6eb47b919765b9d4e6abc4560fce54e08cf42bd948ba77e16aa85'
+ 'a15446a96f2f6ddc0be37c768cbb4695e1efe6630a3479c625f4ef631aface3b'
'34f06f9776f84f6998b1350555316e0ffea76ed16e149916970f19ef750a467f'
'5d00b24c1d36b41b8ea3f07b93fc0e00b42dd84d9bc4e9b3d26e5f2cfeba6405'
'dc507eeb75eae1109273879771b4eb56172b7417e87a0693381106afd7554e04'
@@ -65,8 +65,8 @@
# Upstream patches
# use Features to detect Cremona databases https://trac.sagemath.org/ticket/25825
patch -p1 -i ../sagemath-cremona.patch
-# Fixes for singular 4.1.2 https://trac.sagemath.org/ticket/25993
- patch -p1 -i ../sagemath-singular-4.1.2.patch
+# Fixes for singular 4.2 https://trac.sagemath.org/ticket/25993
+ patch -p1 -i ../sagemath-singular-4.2.patch
# Fix segfault and tests with flint 2.6 https://trac.sagemath.org/ticket/29719
patch -p1 -i ../sagemath-flint-2.6.patch
# Fix gap.version() and doctests with GAP 4.11 https://trac.sagemath.org/ticket/29314
@@ -106,12 +106,8 @@
python setup.py install --root="$pkgdir" --optimize=1
- _pythonpath=`python -c "from sysconfig import get_path; print(get_path('platlib'))"`
# Remove sage_setup
- rm -r "$pkgdir"/$_pythonpath/sage_setup
-# Install tests
- cp -r sage/doctest/tests "$pkgdir"/$_pythonpath/sage/doctest
- cp -r sage/tests/books "$pkgdir"/$_pythonpath/sage/tests
+ rm -r "$pkgdir"/usr/lib/python*/site-packages/sage_setup
# Split jupyter kernel
rm -r "$pkgdir"/usr/share
Deleted: sagemath-singular-4.1.2.patch
===================================================================
--- sagemath-singular-4.1.2.patch 2020-12-19 10:42:11 UTC (rev 779935)
+++ sagemath-singular-4.1.2.patch 2020-12-19 10:42:43 UTC (rev 779936)
@@ -1,759 +0,0 @@
-diff --git a/src/doc/en/constructions/algebraic_geometry.rst b/src/doc/en/constructions/algebraic_geometry.rst
-index a312548..d1c9c95 100644
---- a/src/doc/en/constructions/algebraic_geometry.rst
-+++ b/src/doc/en/constructions/algebraic_geometry.rst
-@@ -139,7 +139,7 @@ Other methods
-
- sage: singular.lib("brnoeth.lib")
- sage: s = singular.ring(2,'(x,y)','lp')
-- sage: I = singular.ideal('[x^4+x, y^4+y]')
-+ sage: I = singular.ideal('x^4+x', 'y^4+y')
- sage: L = singular.closed_points(I)
- sage: # Here you have all the points :
- sage: print(L)
-@@ -325,7 +325,7 @@ Singular itself to help an understanding of how the wrapper works.
- sage: X = Curve(f); pts = X.rational_points()
- sage: D = X.divisor([ (3, pts[0]), (-1,pts[1]), (10, pts[5]) ])
- sage: X.riemann_roch_basis(D)
-- [(-x - 2*y)/(-2*x - 2*y), (-x + z)/(x + y)]
-+ [(-2*x + y)/(x + y), (-x + z)/(x + y)]
-
- - Using Singular's ``BrillNoether`` command (for details see the section
- Brill-Noether in the Singular online documentation
-diff --git a/src/sage/algebras/free_algebra.py b/src/sage/algebras/free_algebra.py
-index 7391dd9..7234f91 100644
---- a/src/sage/algebras/free_algebra.py
-+++ b/src/sage/algebras/free_algebra.py
-@@ -39,7 +39,15 @@ two-sided ideals, and thus provide ideal containment tests::
- Free Associative Unital Algebra on 3 generators (x, y, z) over Rational Field
- sage: I = F*[x*y+y*z,x^2+x*y-y*x-y^2]*F
- sage: I.groebner_basis(degbound=4)
-- Twosided Ideal (y*z*y*y - y*z*y*z + y*z*z*y - y*z*z*z, y*z*y*x + y*z*y*z + y*z*z*x + y*z*z*z, y*y*z*y - y*y*z*z + y*z*z*y - y*z*z*z, y*y*z*x + y*y*z*z + y*z*z*x + y*z*z*z, y*y*y - y*y*z + y*z*y - y*z*z, y*y*x + y*y*z + y*z*x + y*z*z, x*y + y*z, x*x - y*x - y*y - y*z) of Free Associative Unital Algebra on 3 generators (x, y, z) over Rational Field
-+ Twosided Ideal (x*y + y*z,
-+ x*x - y*x - y*y - y*z,
-+ y*y*y - y*y*z + y*z*y - y*z*z,
-+ y*y*x + y*y*z + y*z*x + y*z*z,
-+ y*y*z*y - y*y*z*z + y*z*z*y - y*z*z*z,
-+ y*z*y*y - y*z*y*z + y*z*z*y - y*z*z*z,
-+ y*y*z*x + y*y*z*z + y*z*z*x + y*z*z*z,
-+ y*z*y*x + y*z*y*z + y*z*z*x + y*z*z*z) of Free Associative Unital
-+ Algebra on 3 generators (x, y, z) over Rational Field
- sage: y*z*y*y*z*z + 2*y*z*y*z*z*x + y*z*y*z*z*z - y*z*z*y*z*x + y*z*z*z*z*x in I
- True
-
-@@ -233,7 +241,7 @@ class FreeAlgebraFactory(UniqueFactory):
- a*b^2*c^3
- """
- def create_key(self, base_ring, arg1=None, arg2=None,
-- sparse=None, order='degrevlex',
-+ sparse=None, order=None,
- names=None, name=None,
- implementation=None, degrees=None):
- """
-@@ -264,6 +272,8 @@ class FreeAlgebraFactory(UniqueFactory):
- return tuple(degrees),base_ring
- # test if we can use libSingular/letterplace
- if implementation == "letterplace":
-+ if order is None:
-+ order = 'degrevlex' if degrees is None else 'deglex'
- args = [arg for arg in (arg1, arg2) if arg is not None]
- kwds = dict(sparse=sparse, order=order, implementation="singular")
- if name is not None:
-@@ -274,7 +284,7 @@ class FreeAlgebraFactory(UniqueFactory):
- if degrees is None:
- return (PolRing,)
- from sage.all import TermOrder
-- T = PolRing.term_order() + TermOrder('lex',1)
-+ T = TermOrder(PolRing.term_order(), PolRing.ngens() + 1)
- varnames = list(PolRing.variable_names())
- newname = 'x'
- while newname in varnames:
-diff --git a/src/sage/algebras/letterplace/free_algebra_element_letterplace.pyx b/src/sage/algebras/letterplace/free_algebra_element_letterplace.pyx
-index ad863ea..d6127c9 100644
---- a/src/sage/algebras/letterplace/free_algebra_element_letterplace.pyx
-+++ b/src/sage/algebras/letterplace/free_algebra_element_letterplace.pyx
-@@ -17,6 +17,7 @@ AUTHOR:
- # https://www.gnu.org/licenses/
- # ****************************************************************************
-
-+from sage.groups.perm_gps.all import CyclicPermutationGroup
- from sage.libs.singular.function import lib, singular_function
- from sage.misc.repr import repr_lincomb
- from sage.rings.polynomial.multi_polynomial_ideal import MPolynomialIdeal
-@@ -25,7 +26,6 @@ from cpython.object cimport PyObject_RichCompare
- # Define some singular functions
- lib("freegb.lib")
- poly_reduce = singular_function("NF")
--singular_system=singular_function("system")
-
- #####################
- # Free algebra elements
-@@ -445,9 +445,10 @@ cdef class FreeAlgebraElement_letterplace(AlgebraElement):
- cdef int i
- if P.monomial_divides(s_poly,p_poly):
- return True
-+ realngens = A._commutative_ring.ngens()
-+ CG = CyclicPermutationGroup(P.ngens())
- for i from 0 <= i < p_d-s_d:
-- s_poly = singular_system("stest",s_poly,1,
-- A._degbound,A.__ngens,ring=P)
-+ s_poly = s_poly * CG[realngens]
- if P.monomial_divides(s_poly,p_poly):
- return True
- return False
-@@ -601,7 +602,9 @@ cdef class FreeAlgebraElement_letterplace(AlgebraElement):
- # we must put the polynomials into the same ring
- left._poly = A._current_ring(left._poly)
- right._poly = A._current_ring(right._poly)
-- rshift = singular_system("stest",right._poly,left._poly.degree(),A._degbound,A.__ngens, ring=A._current_ring)
-+ realngens = A._commutative_ring.ngens()
-+ CG = CyclicPermutationGroup(A._current_ring.ngens())
-+ rshift = right._poly * CG[left._poly.degree() * realngens]
- return FreeAlgebraElement_letterplace(A,left._poly*rshift, check=False)
-
- def __pow__(FreeAlgebraElement_letterplace self, int n, k):
-@@ -627,10 +630,11 @@ cdef class FreeAlgebraElement_letterplace(AlgebraElement):
- self._poly = A._current_ring(self._poly)
- cdef int d = self._poly.degree()
- q = p = self._poly
-+ realngens = A._commutative_ring.ngens()
- cdef int i
-+ CG = CyclicPermutationGroup(A._current_ring.ngens())
- for i from 0<i<n:
-- q = singular_system("stest",q,d,A._degbound,A.__ngens,
-- ring=A._current_ring)
-+ q = q * CG[d * realngens]
- p *= q
- return FreeAlgebraElement_letterplace(A, p, check=False)
-
-diff --git a/src/sage/algebras/letterplace/free_algebra_letterplace.pxd b/src/sage/algebras/letterplace/free_algebra_letterplace.pxd
-index 7e5f2bb..d1d162c 100644
---- a/src/sage/algebras/letterplace/free_algebra_letterplace.pxd
-+++ b/src/sage/algebras/letterplace/free_algebra_letterplace.pxd
-@@ -13,8 +13,15 @@ from sage.rings.ring cimport Algebra
- from sage.structure.element cimport AlgebraElement, ModuleElement, RingElement, Element
- from sage.rings.polynomial.multi_polynomial_libsingular cimport MPolynomialRing_libsingular, MPolynomial_libsingular
- from sage.algebras.letterplace.free_algebra_element_letterplace cimport FreeAlgebraElement_letterplace
-+from sage.libs.singular.decl cimport ring
-
-
-+cdef class FreeAlgebra_letterplace_libsingular():
-+ cdef ring* _lp_ring
-+ cdef MPolynomialRing_libsingular _commutative_ring
-+ cdef MPolynomialRing_libsingular _lp_ring_internal
-+ cdef object __ngens
-+
- cdef class FreeAlgebra_letterplace(Algebra):
- cdef MPolynomialRing_libsingular _commutative_ring
- cdef MPolynomialRing_libsingular _current_ring
-diff --git a/src/sage/algebras/letterplace/free_algebra_letterplace.pyx b/src/sage/algebras/letterplace/free_algebra_letterplace.pyx
-index a9d09ad..714284e 100644
---- a/src/sage/algebras/letterplace/free_algebra_letterplace.pyx
-+++ b/src/sage/algebras/letterplace/free_algebra_letterplace.pyx
-@@ -37,7 +37,15 @@ The preceding containment test is based on the computation of Groebner
- bases with degree bound::
-
- sage: I.groebner_basis(degbound=4)
-- Twosided Ideal (y*z*y*y - y*z*y*z + y*z*z*y - y*z*z*z, y*z*y*x + y*z*y*z + y*z*z*x + y*z*z*z, y*y*z*y - y*y*z*z + y*z*z*y - y*z*z*z, y*y*z*x + y*y*z*z + y*z*z*x + y*z*z*z, y*y*y - y*y*z + y*z*y - y*z*z, y*y*x + y*y*z + y*z*x + y*z*z, x*y + y*z, x*x - y*x - y*y - y*z) of Free Associative Unital Algebra on 3 generators (x, y, z) over Rational Field
-+ Twosided Ideal (x*y + y*z,
-+ x*x - y*x - y*y - y*z,
-+ y*y*y - y*y*z + y*z*y - y*z*z,
-+ y*y*x + y*y*z + y*z*x + y*z*z,
-+ y*y*z*y - y*y*z*z + y*z*z*y - y*z*z*z,
-+ y*z*y*y - y*z*y*z + y*z*z*y - y*z*z*z,
-+ y*y*z*x + y*y*z*z + y*z*z*x + y*z*z*z,
-+ y*z*y*x + y*z*y*z + y*z*z*x + y*z*z*z) of Free Associative Unital
-+ Algebra on 3 generators (x, y, z) over Rational Field
-
- When reducing an element by `I`, the original generators are chosen::
-
-@@ -67,7 +75,13 @@ different normal form::
- Lexicographic term order
- sage: J = L*[a*b+b*c,a^2+a*b-b*c-c^2]*L
- sage: J.groebner_basis(4)
-- Twosided Ideal (2*b*c*b - b*c*c + c*c*b, a*c*c - 2*b*c*a - 2*b*c*c - c*c*a, a*b + b*c, a*a - 2*b*c - c*c) of Free Associative Unital Algebra on 3 generators (a, b, c) over Rational Field
-+ Twosided Ideal (2*b*c*b - b*c*c + c*c*b,
-+ a*b + b*c,
-+ -a*c*c + 2*b*c*a + 2*b*c*c + c*c*a,
-+ a*c*c*b - 2*b*c*c*b + b*c*c*c,
-+ a*a - 2*b*c - c*c,
-+ a*c*c*a - 2*b*c*c*a - 4*b*c*c*c - c*c*c*c) of Free Associative Unital
-+ Algebra on 3 generators (a, b, c) over Rational Field
- sage: (b*c*b*b).normal_form(J)
- 1/2*b*c*c*b - 1/2*c*c*b*b
-
-@@ -105,15 +119,16 @@ TESTS::
- from sage.misc.misc_c import prod
- from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
- from sage.libs.singular.function import lib, singular_function
--from sage.rings.polynomial.term_order import TermOrder
-+from sage.libs.singular.function cimport RingWrap
-+from sage.libs.singular.ring cimport singular_ring_delete, singular_ring_reference
- from sage.categories.algebras import Algebras
- from sage.rings.noncommutative_ideals import IdealMonoid_nc
-+from sage.rings.polynomial.plural cimport new_CRing
-
- #####################
- # Define some singular functions
- lib("freegb.lib")
--poly_reduce = singular_function("NF")
--singular_system=singular_function("system")
-+freeAlgebra = singular_function("freeAlgebra")
-
- # unfortunately we can not set Singular attributes for MPolynomialRing_libsingular
- # Hence, we must constantly work around Letterplace's sanity checks,
-@@ -242,7 +257,7 @@ cdef class FreeAlgebra_letterplace(Algebra):
- sage: F.<a,b,c> = FreeAlgebra(K, implementation='letterplace')
- sage: TestSuite(F).run()
- """
-- if not isinstance(R,MPolynomialRing_libsingular):
-+ if not isinstance(R, MPolynomialRing_libsingular):
- raise TypeError("A letterplace algebra must be provided by a polynomial ring of type %s" % MPolynomialRing_libsingular)
- self.__ngens = R.ngens()
- if degrees is None:
-@@ -260,7 +275,9 @@ cdef class FreeAlgebra_letterplace(Algebra):
- if degrees is None:
- self._degrees = tuple([int(1)]*self.__ngens)
- else:
-- if (not isinstance(degrees,(tuple,list))) or len(degrees)!=self.__ngens-1 or any(i <= 0 for i in degrees):
-+ if (not isinstance(degrees, (tuple, list))) \
-+ or len(degrees) != self.__ngens - self._nb_slackvars \
-+ or any(i <= 0 for i in degrees):
- raise TypeError("The generator degrees must be given by a list or tuple of %d positive integers" % (self.__ngens-1))
- self._degrees = tuple([int(i) for i in degrees])
- self.set_degbound(max(self._degrees))
-@@ -666,7 +683,7 @@ cdef class FreeAlgebra_letterplace(Algebra):
- Sage, since it does the reductions in a different order
- compared to Singular. Therefore, we call the original Singular
- reduction method, and prevent a warning message by asserting
-- that `G` is a Groebner basis.
-+ that `G` is a Groebner basis. ::
-
- sage: from sage.libs.singular.function import singular_function
- sage: poly_reduce = singular_function("NF")
-@@ -682,8 +699,10 @@ cdef class FreeAlgebra_letterplace(Algebra):
- ngens = self.__ngens
- degbound = self._degbound
- cdef list G = [C(x._poly) for x in g]
-+ from sage.groups.perm_gps.all import CyclicPermutationGroup
-+ CG = CyclicPermutationGroup(C.ngens())
- for y in G:
-- out.extend([y]+[singular_system("stest",y,n+1,degbound,ngens,ring=C) for n in xrange(d-y.degree())])
-+ out.extend([y]+[y * CG[ngens*(n+1)] for n in xrange(d-y.degree())])
- return C.ideal(out)
-
- ###########################
-@@ -879,3 +898,28 @@ cdef class FreeAlgebra_letterplace(Algebra):
- PNames[P.ngens(): len(PNames): P.ngens()+1] = list(Names[self.ngens(): len(Names): self.ngens()+1])[:P.degbound()]
- x = Ppoly.hom([Gens[Names.index(asdf)] for asdf in PNames])(x.letterplace_polynomial())
- return FreeAlgebraElement_letterplace(self,self._current_ring(x))
-+
-+cdef class FreeAlgebra_letterplace_libsingular():
-+ """
-+ Internally used wrapper around a Singular Letterplace polynomial ring.
-+ """
-+
-+ def __cinit__(self, MPolynomialRing_libsingular commutative_ring,
-+ int degbound):
-+ cdef RingWrap rw = freeAlgebra(commutative_ring, degbound)
-+ self._lp_ring = singular_ring_reference(rw._ring)
-+ # `_lp_ring` viewed as `MPolynomialRing_libsingular` with additional
-+ # letterplace attributes set (for internal use only)
-+ self._lp_ring_internal = new_CRing(rw, commutative_ring.base_ring())
-+ self._commutative_ring = commutative_ring
-+
-+ def __init__(self, commutative_ring, degbound):
-+ self.__ngens = commutative_ring.ngens() * degbound
-+
-+ def __dealloc__(self):
-+ r"""
-+ Carefully deallocate the ring, without changing ``currRing``
-+ (since this method can be at unpredictable times due to garbage
-+ collection).
-+ """
-+ singular_ring_delete(self._lp_ring)
-diff --git a/src/sage/algebras/letterplace/letterplace_ideal.pyx b/src/sage/algebras/letterplace/letterplace_ideal.pyx
-index d7214d1..5b8cf48 100644
---- a/src/sage/algebras/letterplace/letterplace_ideal.pyx
-+++ b/src/sage/algebras/letterplace/letterplace_ideal.pyx
-@@ -18,7 +18,11 @@ One can compute Groebner bases out to a finite degree, can compute normal
- forms and can test containment in the ideal::
-
- sage: I.groebner_basis(degbound=3)
-- Twosided Ideal (y*y*y - y*y*z + y*z*y - y*z*z, y*y*x + y*y*z + y*z*x + y*z*z, x*y + y*z, x*x - y*x - y*y - y*z) of Free Associative Unital Algebra on 3 generators (x, y, z) over Rational Field
-+ Twosided Ideal (x*y + y*z,
-+ x*x - y*x - y*y - y*z,
-+ y*y*y - y*y*z + y*z*y - y*z*z,
-+ y*y*x + y*y*z + y*z*x + y*z*z) of Free Associative Unital Algebra
-+ on 3 generators (x, y, z) over Rational Field
- sage: (x*y*z*y*x).normal_form(I)
- y*z*z*y*z + y*z*z*z*x + y*z*z*z*z
- sage: x*y*z*y*x - (x*y*z*y*x).normal_form(I) in I
-@@ -42,14 +46,14 @@ AUTHOR:
-
- from sage.rings.noncommutative_ideals import Ideal_nc
- from sage.libs.singular.function import lib, singular_function
--from sage.algebras.letterplace.free_algebra_letterplace cimport FreeAlgebra_letterplace
-+from sage.algebras.letterplace.free_algebra_letterplace cimport FreeAlgebra_letterplace, FreeAlgebra_letterplace_libsingular
- from sage.algebras.letterplace.free_algebra_element_letterplace cimport FreeAlgebraElement_letterplace
- from sage.rings.infinity import Infinity
-
- #####################
- # Define some singular functions
- lib("freegb.lib")
--singular_system=singular_function("system")
-+singular_twostd=singular_function("twostd")
- poly_reduce=singular_function("NF")
-
- class LetterplaceIdeal(Ideal_nc):
-@@ -69,14 +73,22 @@ class LetterplaceIdeal(Ideal_nc):
- sage: I.groebner_basis(2)
- Twosided Ideal (x*y + y*z, x*x - y*x - y*y - y*z) of Free Associative Unital Algebra on 3 generators (x, y, z) over Rational Field
- sage: I.groebner_basis(4)
-- Twosided Ideal (y*z*y*y - y*z*y*z + y*z*z*y - y*z*z*z, y*z*y*x + y*z*y*z + y*z*z*x + y*z*z*z, y*y*z*y - y*y*z*z + y*z*z*y - y*z*z*z, y*y*z*x + y*y*z*z + y*z*z*x + y*z*z*z, y*y*y - y*y*z + y*z*y - y*z*z, y*y*x + y*y*z + y*z*x + y*z*z, x*y + y*z, x*x - y*x - y*y - y*z) of Free Associative Unital Algebra on 3 generators (x, y, z) over Rational Field
-+ Twosided Ideal (x*y + y*z,
-+ x*x - y*x - y*y - y*z,
-+ y*y*y - y*y*z + y*z*y - y*z*z,
-+ y*y*x + y*y*z + y*z*x + y*z*z,
-+ y*y*z*y - y*y*z*z + y*z*z*y - y*z*z*z,
-+ y*z*y*y - y*z*y*z + y*z*z*y - y*z*z*z,
-+ y*y*z*x + y*y*z*z + y*z*z*x + y*z*z*z,
-+ y*z*y*x + y*z*y*z + y*z*z*x + y*z*z*z) of Free Associative Unital
-+ Algebra on 3 generators (x, y, z) over Rational Field
-
- Groebner bases are cached. If one has computed a Groebner basis
- out to a high degree then it will also be returned if a Groebner
- basis with a lower degree bound is requested::
-
-- sage: I.groebner_basis(2)
-- Twosided Ideal (y*z*y*y - y*z*y*z + y*z*z*y - y*z*z*z, y*z*y*x + y*z*y*z + y*z*z*x + y*z*z*z, y*y*z*y - y*y*z*z + y*z*z*y - y*z*z*z, y*y*z*x + y*y*z*z + y*z*z*x + y*z*z*z, y*y*y - y*y*z + y*z*y - y*z*z, y*y*x + y*y*z + y*z*x + y*z*z, x*y + y*z, x*x - y*x - y*y - y*z) of Free Associative Unital Algebra on 3 generators (x, y, z) over Rational Field
-+ sage: I.groebner_basis(2) is I.groebner_basis(4)
-+ True
-
- Of course, the normal form of any element has to satisfy the following::
-
-@@ -116,8 +128,11 @@ class LetterplaceIdeal(Ideal_nc):
- sage: F.<x,y,z> = FreeAlgebra(QQ, implementation='letterplace',degrees=[1,2,3])
- sage: I = F*[x*y+z-y*x,x*y*z-x^6+y^3]*F
- sage: I.groebner_basis(Infinity)
-- Twosided Ideal (x*z*z - y*x*x*z - y*x*y*y + y*x*z*x + y*y*y*x + z*x*z + z*y*y - z*z*x,
-- x*y - y*x + z,
-+ Twosided Ideal (x*y - y*x + z,
-+ x*x*x*x*x*x - y*x*z - y*y*y + z*z,
-+ x*z*z - y*x*x*z + y*x*z*x + y*y*z + y*z*y + z*x*z + z*y*y - z*z*x,
-+ x*x*x*x*x*z + x*x*x*x*z*x + x*x*x*z*x*x + x*x*z*x*x*x + x*z*x*x*x*x +
-+ y*x*z*y - y*y*x*z + y*z*z + z*x*x*x*x*x - z*z*y,
- x*x*x*x*z*y*y + x*x*x*z*y*y*x - x*x*x*z*y*z - x*x*z*y*x*z + x*x*z*y*y*x*x +
- x*x*z*y*y*y - x*x*z*y*z*x - x*z*y*x*x*z - x*z*y*x*z*x +
- x*z*y*y*x*x*x + 2*x*z*y*y*y*x - 2*x*z*y*y*z - x*z*y*z*x*x -
-@@ -135,10 +150,7 @@ class LetterplaceIdeal(Ideal_nc):
- z*y*y*y*y - 3*z*y*y*z*x - z*y*z*x*x*x - 2*z*y*z*y*x +
- 2*z*y*z*z - z*z*x*x*x*x*x + 4*z*z*x*x*z + 4*z*z*x*z*x -
- 4*z*z*y*x*x*x - 3*z*z*y*y*x + 4*z*z*y*z + 4*z*z*z*x*x +
-- 2*z*z*z*y,
-- x*x*x*x*x*z + x*x*x*x*z*x + x*x*x*z*x*x + x*x*z*x*x*x + x*z*x*x*x*x +
-- y*x*z*y - y*y*x*z + y*z*z + z*x*x*x*x*x - z*z*y,
-- x*x*x*x*x*x - y*x*z - y*y*y + z*z)
-+ 2*z*z*z*y)
- of Free Associative Unital Algebra on 3 generators (x, y, z) over Rational Field
-
- Again, we can compute normal forms::
-@@ -226,7 +238,15 @@ class LetterplaceIdeal(Ideal_nc):
- sage: I.groebner_basis() # not tested
- Twosided Ideal (y*y*y - y*y*z + y*z*y - y*z*z, y*y*x + y*y*z + y*z*x + y*z*z, x*y + y*z, x*x - y*x - y*y - y*z) of Free Associative Unital Algebra on 3 generators (x, y, z) over Rational Field
- sage: I.groebner_basis(4)
-- Twosided Ideal (y*z*y*y - y*z*y*z + y*z*z*y - y*z*z*z, y*z*y*x + y*z*y*z + y*z*z*x + y*z*z*z, y*y*z*y - y*y*z*z + y*z*z*y - y*z*z*z, y*y*z*x + y*y*z*z + y*z*z*x + y*z*z*z, y*y*y - y*y*z + y*z*y - y*z*z, y*y*x + y*y*z + y*z*x + y*z*z, x*y + y*z, x*x - y*x - y*y - y*z) of Free Associative Unital Algebra on 3 generators (x, y, z) over Rational Field
-+ Twosided Ideal (x*y + y*z,
-+ x*x - y*x - y*y - y*z,
-+ y*y*y - y*y*z + y*z*y - y*z*z,
-+ y*y*x + y*y*z + y*z*x + y*z*z,
-+ y*y*z*y - y*y*z*z + y*z*z*y - y*z*z*z,
-+ y*z*y*y - y*z*y*z + y*z*z*y - y*z*z*z,
-+ y*y*z*x + y*y*z*z + y*z*z*x + y*z*z*z,
-+ y*z*y*x + y*z*y*z + y*z*z*x + y*z*z*z) of Free Associative
-+ Unital Algebra on 3 generators (x, y, z) over Rational Field
- sage: I.groebner_basis(2) is I.groebner_basis(4)
- True
- sage: G = I.groebner_basis(4)
-@@ -238,7 +258,14 @@ class LetterplaceIdeal(Ideal_nc):
-
- sage: I = F*[x*y-y*x,x*z-z*x,y*z-z*y,x^2*y-z^3,x*y^2+z*x^2]*F
- sage: I.groebner_basis(Infinity)
-- Twosided Ideal (z*z*z*y*y + z*z*z*z*x, z*x*x*x + z*z*z*y, y*z - z*y, y*y*x + z*x*x, y*x*x - z*z*z, x*z - z*x, x*y - y*x) of Free Associative Unital Algebra on 3 generators (x, y, z) over Rational Field
-+ Twosided Ideal (-y*z + z*y,
-+ -x*z + z*x,
-+ -x*y + y*x,
-+ x*x*z + x*y*y,
-+ x*x*y - z*z*z,
-+ x*x*x*z + y*z*z*z,
-+ x*z*z*z*z + y*y*z*z*z) of Free Associative Unital Algebra
-+ on 3 generators (x, y, z) over Rational Field
-
- Since the commutators of the generators are contained in the ideal,
- we can verify the above result by a computation in a polynomial ring
-@@ -276,9 +303,32 @@ class LetterplaceIdeal(Ideal_nc):
- libsingular_options['redSB'] = True
- A.set_degbound(degbound)
- P = A._current_ring
-- out = [FreeAlgebraElement_letterplace(A,X,check=False) for X in
-- singular_system("freegb",P.ideal([x._poly for x in self.__GB.gens()]),
-- degbound,A.__ngens, ring = P)]
-+
-+ # note that degbound might be smaller than A._degbound due to caching,
-+ # but degbound must be large enough to map all generators to the
-+ # letterplace ring L
-+ if degbound < A._degbound:
-+ max_deg = max([x._poly.degree() for x in self.__GB.gens()])
-+ if degbound < max_deg:
-+ degbound = max_deg
-+
-+ # The following is a workaround for calling Singular's new Letterplace
-+ # API (see :trac:`25993`). We construct a temporary polynomial ring L
-+ # with letterplace attributes set as required by the API. As L has
-+ # duplicate variable names, we need to handle this ring carefully; in
-+ # particular, we cannot coerce to and from L, so we use homomorphisms
-+ # for the conversion.
-+
-+ cdef FreeAlgebra_letterplace_libsingular lp_ring = \
-+ FreeAlgebra_letterplace_libsingular(A._commutative_ring, degbound)
-+ L = lp_ring._lp_ring_internal
-+ to_L = P.hom(L.gens(), L, check=False)
-+ from_L = L.hom(P.gens(), P, check=False)
-+ I = L.ideal([to_L(x._poly) for x in self.__GB.gens()])
-+ gb = singular_twostd(I)
-+ out = [FreeAlgebraElement_letterplace(A, from_L(X), check=False)
-+ for X in gb]
-+
- libsingular_options['redTail'] = bck[0]
- libsingular_options['redSB'] = bck[1]
- self.__GB = A.ideal(out,side='twosided',coerce=False)
-diff --git a/src/sage/combinat/root_system/hecke_algebra_representation.py b/src/sage/combinat/root_system/hecke_algebra_representation.py
-index 51f4113..ba42ed1 100644
---- a/src/sage/combinat/root_system/hecke_algebra_representation.py
-+++ b/src/sage/combinat/root_system/hecke_algebra_representation.py
-@@ -746,7 +746,7 @@ class HeckeAlgebraRepresentation(WithEqualityById, SageObject):
- -2121 + 212,
- (q2/(q1-q2))*2121 + (q2/(-q1+q2))*121 + (q2/(-q1+q2))*212 - 12 + ((-q2)/(-q1+q2))*21 + 2,
- ((-q2^2)/(-q1^2+q1*q2-q2^2))*2121 - 121 + (q2^2/(-q1^2+q1*q2-q2^2))*212 + 21,
-- ((q1^2+q2^2)/(-q1^2+q1*q2-q2^2))*2121 + ((-q1^2-q2^2)/(-q1^2+q1*q2-q2^2))*121 + ((-q2^2)/(-q1^2+q1*q2-q2^2))*212 + (q2^2/(-q1^2+q1*q2-q2^2))*12 - 21 + 1,
-+ ((-q1^2-q2^2)/(q1^2-q1*q2+q2^2))*2121 + ((-q1^2-q2^2)/(-q1^2+q1*q2-q2^2))*121 + ((-q2^2)/(-q1^2+q1*q2-q2^2))*212 + (q2^2/(-q1^2+q1*q2-q2^2))*12 - 21 + 1,
- 2121,
- (q2/(-q1+q2))*2121 + ((-q2)/(-q1+q2))*121 - 212 + 12,
- -2121 + 121]
-diff --git a/src/sage/combinat/root_system/non_symmetric_macdonald_polynomials.py b/src/sage/combinat/root_system/non_symmetric_macdonald_polynomials.py
-index 3537772..ee8ddec 100644
---- a/src/sage/combinat/root_system/non_symmetric_macdonald_polynomials.py
-+++ b/src/sage/combinat/root_system/non_symmetric_macdonald_polynomials.py
-@@ -555,8 +555,7 @@ class NonSymmetricMacdonaldPolynomials(CherednikOperatorsEigenvectors):
- B[(1, 0, 0)]
-
- sage: E[-omega[1]]
-- B[(-1, 0, 0)] + ((-q*q1^6-q*q1^5*q2-q1*q2^5-q2^6)/(-q^3*q1^6-q^2*q1^5*q2-q*q1*q2^5-q2^6))*B[(1, 0, 0)] + ((-q1-q2)/(-q*q1-q2))*B[(0, -1, 0)]
-- + ((q1+q2)/(q*q1+q2))*B[(0, 1, 0)] + ((-q1-q2)/(-q*q1-q2))*B[(0, 0, -1)] + ((-q1-q2)/(-q*q1-q2))*B[(0, 0, 1)]
-+ B[(-1, 0, 0)] + ((q*q1^6+q*q1^5*q2+q1*q2^5+q2^6)/(q^3*q1^6+q^2*q1^5*q2+q*q1*q2^5+q2^6))*B[(1, 0, 0)] + ((q1+q2)/(q*q1+q2))*B[(0, -1, 0)] + ((q1+q2)/(q*q1+q2))*B[(0, 1, 0)] + ((q1+q2)/(q*q1+q2))*B[(0, 0, -1)] + ((q1+q2)/(q*q1+q2))*B[(0, 0, 1)]
-
- sage: E[omega[2]]
- ((-q1*q2^3-q2^4)/(q*q1^4-q2^4))*B[(1, 0, 0)] + B[(0, 1, 0)]
-@@ -567,14 +566,7 @@ class NonSymmetricMacdonaldPolynomials(CherednikOperatorsEigenvectors):
- + ((-q1*q2-q2^2)/(q*q1^2-q2^2))*B[(0, 0, -1)] + ((q1*q2+q2^2)/(-q*q1^2+q2^2))*B[(0, 0, 1)]
-
- sage: E[-omega[1]-omega[2]]
-- ((-q^3*q1^6-q^3*q1^5*q2-2*q^2*q1^6-3*q^2*q1^5*q2+q^2*q1^4*q2^2+2*q^2*q1^3*q2^3+q*q1^5*q2+2*q*q1^4*q2^2-q*q1^3*q2^3-2*q*q1^2*q2^4+q*q1*q2^5+q*q2^6-q1^3*q2^3-q1^2*q2^4+2*q1*q2^5+2*q2^6)/(-q^4*q1^6-q^3*q1^5*q2+q^3*q1^4*q2^2-q*q1^2*q2^4+q*q1*q2^5+q2^6))*B[(0, 0, 0)] + B[(-1, -1, 0)]
-- + ((q*q1^4+q*q1^3*q2+q1*q2^3+q2^4)/(q^3*q1^4+q^2*q1^3*q2+q*q1*q2^3+q2^4))*B[(-1, 1, 0)] + ((q1+q2)/(q*q1+q2))*B[(-1, 0, -1)] + ((-q1-q2)/(-q*q1-q2))*B[(-1, 0, 1)]
-- + ((q*q1^4+q*q1^3*q2+q1*q2^3+q2^4)/(q^3*q1^4+q^2*q1^3*q2+q*q1*q2^3+q2^4))*B[(1, -1, 0)]
-- + ((-q^2*q1^6-q^2*q1^5*q2-q*q1^5*q2+q*q1^3*q2^3+q1^5*q2+q1^4*q2^2-q1^3*q2^3-q1^2*q2^4+q1*q2^5+q2^6)/(-q^4*q1^6-q^3*q1^5*q2+q^3*q1^4*q2^2-q*q1^2*q2^4+q*q1*q2^5+q2^6))*B[(1, 1, 0)]
-- + ((-q*q1^4-2*q*q1^3*q2-q*q1^2*q2^2+q1^3*q2+q1^2*q2^2-q1*q2^3-q2^4)/(-q^3*q1^4-q^2*q1^3*q2-q*q1*q2^3-q2^4))*B[(1, 0, -1)]
-- + ((-q*q1^4-2*q*q1^3*q2-q*q1^2*q2^2+q1^3*q2+q1^2*q2^2-q1*q2^3-q2^4)/(-q^3*q1^4-q^2*q1^3*q2-q*q1*q2^3-q2^4))*B[(1, 0, 1)] + ((q1+q2)/(q*q1+q2))*B[(0, -1, -1)]
-- + ((-q1-q2)/(-q*q1-q2))*B[(0, -1, 1)] + ((q*q1^4+2*q*q1^3*q2+q*q1^2*q2^2-q1^3*q2-q1^2*q2^2+q1*q2^3+q2^4)/(q^3*q1^4+q^2*q1^3*q2+q*q1*q2^3+q2^4))*B[(0, 1, -1)]
-- + ((q*q1^4+2*q*q1^3*q2+q*q1^2*q2^2-q1^3*q2-q1^2*q2^2+q1*q2^3+q2^4)/(q^3*q1^4+q^2*q1^3*q2+q*q1*q2^3+q2^4))*B[(0, 1, 1)]
-+ ((q^3*q1^6+q^3*q1^5*q2+2*q^2*q1^6+3*q^2*q1^5*q2-q^2*q1^4*q2^2-2*q^2*q1^3*q2^3-q*q1^5*q2-2*q*q1^4*q2^2+q*q1^3*q2^3+2*q*q1^2*q2^4-q*q1*q2^5-q*q2^6+q1^3*q2^3+q1^2*q2^4-2*q1*q2^5-2*q2^6)/(q^4*q1^6+q^3*q1^5*q2-q^3*q1^4*q2^2+q*q1^2*q2^4-q*q1*q2^5-q2^6))*B[(0, 0, 0)] + B[(-1, -1, 0)] + ((q*q1^4+q*q1^3*q2+q1*q2^3+q2^4)/(q^3*q1^4+q^2*q1^3*q2+q*q1*q2^3+q2^4))*B[(-1, 1, 0)] + ((q1+q2)/(q*q1+q2))*B[(-1, 0, -1)] + ((-q1-q2)/(-q*q1-q2))*B[(-1, 0, 1)] + ((q*q1^4+q*q1^3*q2+q1*q2^3+q2^4)/(q^3*q1^4+q^2*q1^3*q2+q*q1*q2^3+q2^4))*B[(1, -1, 0)] + ((q^2*q1^6+q^2*q1^5*q2+q*q1^5*q2-q*q1^3*q2^3-q1^5*q2-q1^4*q2^2+q1^3*q2^3+q1^2*q2^4-q1*q2^5-q2^6)/(q^4*q1^6+q^3*q1^5*q2-q^3*q1^4*q2^2+q*q1^2*q2^4-q*q1*q2^5-q2^6))*B[(1, 1, 0)] + ((q*q1^4+2*q*q1^3*q2+q*q1^2*q2^2-q1^3*q2-q1^2*q2^2+q1*q2^3+q2^4)/(q^3*q1^4+q^2*q1^3*q2+q*q1*q2^3+q2^4))*B[(1, 0, -1)] + ((q*q1^4+2*q*q1^3*q2+q*q1^2*q2^2-q1^3*q2-q1^2*q2^2+q1*q2^3+q2^4)/(q^3*q1^4+q^2*q1^3*q2+q*q1*q2^3+q2^4))*B[(1, 0, 1)] + ((q1+q2)/(q*q1+q2))*B[(0, -1, -1)] + ((q1
+q2)/(q*q1+q2))*B[(0, -1, 1)] + ((q*q1^4+2*q*q1^3*q2+q*q1^2*q2^2-q1^3*q2-q1^2*q2^2+q1*q2^3+q2^4)/(q^3*q1^4+q^2*q1^3*q2+q*q1*q2^3+q2^4))*B[(0, 1, -1)] + ((q*q1^4+2*q*q1^3*q2+q*q1^2*q2^2-q1^3*q2-q1^2*q2^2+q1*q2^3+q2^4)/(q^3*q1^4+q^2*q1^3*q2+q*q1*q2^3+q2^4))*B[(0, 1, 1)]
-
- sage: E[omega[1]-omega[2]]
- ((q^3*q1^7+q^3*q1^6*q2-q*q1*q2^6-q*q2^7)/(q^3*q1^7-q^2*q1^5*q2^2+q*q1^2*q2^5-q2^7))*B[(0, 0, 0)] + B[(1, -1, 0)]
-@@ -812,7 +804,7 @@ class NonSymmetricMacdonaldPolynomials(CherednikOperatorsEigenvectors):
- ((-q*q1*q2^3-q*q2^4)/(q^2*q1^4-q2^4))*B[(0, 0)] + B[(1, 0)]
-
- sage: E[2*omega[2]] # long time # not checked against Bogdan's notes, but a good self-consistency test
-- ((-q^12*q1^6-q^12*q1^5*q2+2*q^10*q1^5*q2+5*q^10*q1^4*q2^2+3*q^10*q1^3*q2^3+2*q^8*q1^5*q2+4*q^8*q1^4*q2^2+q^8*q1^3*q2^3-q^8*q1^2*q2^4+q^8*q1*q2^5+q^8*q2^6-q^6*q1^3*q2^3+q^6*q1^2*q2^4+4*q^6*q1*q2^5+2*q^6*q2^6+q^4*q1^3*q2^3+3*q^4*q1^2*q2^4+4*q^4*q1*q2^5+2*q^4*q2^6)/(-q^12*q1^6-q^10*q1^5*q2-q^8*q1^3*q2^3+q^6*q1^4*q2^2-q^6*q1^2*q2^4+q^4*q1^3*q2^3+q^2*q1*q2^5+q2^6))*B[(0, 0)] + ((q^7*q1^2*q2+2*q^7*q1*q2^2+q^7*q2^3+q^5*q1^2*q2+2*q^5*q1*q2^2+q^5*q2^3)/(-q^8*q1^3-q^6*q1^2*q2+q^2*q1*q2^2+q2^3))*B[(-1, 0)] + ((q^6*q1*q2+q^6*q2^2)/(-q^6*q1^2+q2^2))*B[(-1, -1)] + ((q^6*q1^2*q2+2*q^6*q1*q2^2+q^6*q2^3+q^4*q1^2*q2+2*q^4*q1*q2^2+q^4*q2^3)/(-q^8*q1^3-q^6*q1^2*q2+q^2*q1*q2^2+q2^3))*B[(-1, 1)] + ((q^3*q1*q2+q^3*q2^2)/(-q^6*q1^2+q2^2))*B[(-1, 2)] + ((-q^7*q1^3-q^7*q1^2*q2+q^7*q1*q2^2+q^7*q2^3+2*q^5*q1^2*q2+4*q^5*q1*q2^2+2*q^5*q2^3+2*q^3*q1^2*q2+4*q^3*q1*q2^2+2*q^3*q2^3)/(-q^8*q1^3-q^6*q1^2*q2+q^2*q1*q2^2+q2^3))*B[(1, 0)] + ((-q^6*q1^2*q2-2*q^6*q1*q2^2-q^6*q2^3-q^4*q1^2*q2-2*q^4*q1*q2^2-q^4*q2^3
)/(q^8*q1^3+q^6*q1^2*q2-q^2*q1*q2^2-q2^3))*B[(1, -1)] + ((q^8*q1^3+q^8*q1^2*q2+q^6*q1^3+q^6*q1^2*q2-q^6*q1*q2^2-q^6*q2^3-2*q^4*q1^2*q2-4*q^4*q1*q2^2-2*q^4*q2^3-q^2*q1^2*q2-3*q^2*q1*q2^2-2*q^2*q2^3)/(q^8*q1^3+q^6*q1^2*q2-q^2*q1*q2^2-q2^3))*B[(1, 1)] + ((-q^5*q1^2-q^5*q1*q2+q^3*q1*q2+q^3*q2^2+q*q1*q2+q*q2^2)/(-q^6*q1^2+q2^2))*B[(1, 2)] + ((-q^6*q1^2-q^6*q1*q2+q^4*q1*q2+q^4*q2^2+q^2*q1*q2+q^2*q2^2)/(-q^6*q1^2+q2^2))*B[(2, 0)] + ((q^3*q1*q2+q^3*q2^2)/(-q^6*q1^2+q2^2))*B[(2, -1)] + ((-q^5*q1^2-q^5*q1*q2+q^3*q1*q2+q^3*q2^2+q*q1*q2+q*q2^2)/(-q^6*q1^2+q2^2))*B[(2, 1)] + B[(2, 2)] + ((-q^7*q1^2*q2-2*q^7*q1*q2^2-q^7*q2^3-q^5*q1^2*q2-2*q^5*q1*q2^2-q^5*q2^3)/(q^8*q1^3+q^6*q1^2*q2-q^2*q1*q2^2-q2^3))*B[(0, -1)] + ((q^7*q1^3+q^7*q1^2*q2-q^7*q1*q2^2-q^7*q2^3-2*q^5*q1^2*q2-4*q^5*q1*q2^2-2*q^5*q2^3-2*q^3*q1^2*q2-4*q^3*q1*q2^2-2*q^3*q2^3)/(q^8*q1^3+q^6*q1^2*q2-q^2*q1*q2^2-q2^3))*B[(0, 1)] + ((-q^6*q1^2-q^6*q1*q2+q^4*q1*q2+q^4*q2^2+q^2*q1*q2+q^2*q2^2)/(-q^6*q1^2+q2^2))*B[(0, 2)]
-+ ((-q^12*q1^6-q^12*q1^5*q2+2*q^10*q1^5*q2+5*q^10*q1^4*q2^2+3*q^10*q1^3*q2^3+2*q^8*q1^5*q2+4*q^8*q1^4*q2^2+q^8*q1^3*q2^3-q^8*q1^2*q2^4+q^8*q1*q2^5+q^8*q2^6-q^6*q1^3*q2^3+q^6*q1^2*q2^4+4*q^6*q1*q2^5+2*q^6*q2^6+q^4*q1^3*q2^3+3*q^4*q1^2*q2^4+4*q^4*q1*q2^5+2*q^4*q2^6)/(-q^12*q1^6-q^10*q1^5*q2-q^8*q1^3*q2^3+q^6*q1^4*q2^2-q^6*q1^2*q2^4+q^4*q1^3*q2^3+q^2*q1*q2^5+q2^6))*B[(0, 0)] + ((q^7*q1^2*q2+2*q^7*q1*q2^2+q^7*q2^3+q^5*q1^2*q2+2*q^5*q1*q2^2+q^5*q2^3)/(-q^8*q1^3-q^6*q1^2*q2+q^2*q1*q2^2+q2^3))*B[(-1, 0)] + ((-q^6*q1*q2-q^6*q2^2)/(q^6*q1^2-q2^2))*B[(-1, -1)] + ((q^6*q1^2*q2+2*q^6*q1*q2^2+q^6*q2^3+q^4*q1^2*q2+2*q^4*q1*q2^2+q^4*q2^3)/(-q^8*q1^3-q^6*q1^2*q2+q^2*q1*q2^2+q2^3))*B[(-1, 1)] + ((-q^3*q1*q2-q^3*q2^2)/(q^6*q1^2-q2^2))*B[(-1, 2)] + ((q^7*q1^3+q^7*q1^2*q2-q^7*q1*q2^2-q^7*q2^3-2*q^5*q1^2*q2-4*q^5*q1*q2^2-2*q^5*q2^3-2*q^3*q1^2*q2-4*q^3*q1*q2^2-2*q^3*q2^3)/(q^8*q1^3+q^6*q1^2*q2-q^2*q1*q2^2-q2^3))*B[(1, 0)] + ((q^6*q1^2*q2+2*q^6*q1*q2^2+q^6*q2^3+q^4*q1^2*q2+2*q^4*q1*q2^2+q^4*q2^3)/(
-q^8*q1^3-q^6*q1^2*q2+q^2*q1*q2^2+q2^3))*B[(1, -1)] + ((q^8*q1^3+q^8*q1^2*q2+q^6*q1^3+q^6*q1^2*q2-q^6*q1*q2^2-q^6*q2^3-2*q^4*q1^2*q2-4*q^4*q1*q2^2-2*q^4*q2^3-q^2*q1^2*q2-3*q^2*q1*q2^2-2*q^2*q2^3)/(q^8*q1^3+q^6*q1^2*q2-q^2*q1*q2^2-q2^3))*B[(1, 1)] + ((q^5*q1^2+q^5*q1*q2-q^3*q1*q2-q^3*q2^2-q*q1*q2-q*q2^2)/(q^6*q1^2-q2^2))*B[(1, 2)] + ((-q^6*q1^2-q^6*q1*q2+q^4*q1*q2+q^4*q2^2+q^2*q1*q2+q^2*q2^2)/(-q^6*q1^2+q2^2))*B[(2, 0)] + ((-q^3*q1*q2-q^3*q2^2)/(q^6*q1^2-q2^2))*B[(2, -1)] + ((-q^5*q1^2-q^5*q1*q2+q^3*q1*q2+q^3*q2^2+q*q1*q2+q*q2^2)/(-q^6*q1^2+q2^2))*B[(2, 1)] + B[(2, 2)] + ((q^7*q1^2*q2+2*q^7*q1*q2^2+q^7*q2^3+q^5*q1^2*q2+2*q^5*q1*q2^2+q^5*q2^3)/(-q^8*q1^3-q^6*q1^2*q2+q^2*q1*q2^2+q2^3))*B[(0, -1)] + ((q^7*q1^3+q^7*q1^2*q2-q^7*q1*q2^2-q^7*q2^3-2*q^5*q1^2*q2-4*q^5*q1*q2^2-2*q^5*q2^3-2*q^3*q1^2*q2-4*q^3*q1*q2^2-2*q^3*q2^3)/(q^8*q1^3+q^6*q1^2*q2-q^2*q1*q2^2-q2^3))*B[(0, 1)] + ((q^6*q1^2+q^6*q1*q2-q^4*q1*q2-q^4*q2^2-q^2*q1*q2-q^2*q2^2)/(q^6*q1^2-q2^2))*B[(0, 2)]
- sage: E.recursion(2*omega[2])
- [0, 1, 0, 2, 1, 0, 2, 1, 0]
-
-@@ -997,7 +989,7 @@ class NonSymmetricMacdonaldPolynomials(CherednikOperatorsEigenvectors):
- sage: L0 = E.keys()
- sage: omega = L0.fundamental_weights()
- sage: E[2*omega[2]]
-- ((q*q1+q*q2)/(q*q1+q2))*B[(1, 2, 1)] + ((q*q1+q*q2)/(q*q1+q2))*B[(2, 1, 1)] + B[(2, 2, 0)]
-+ ((-q*q1-q*q2)/(-q*q1-q2))*B[(1, 2, 1)] + ((-q*q1-q*q2)/(-q*q1-q2))*B[(2, 1, 1)] + B[(2, 2, 0)]
- sage: for d in range(4): # long time (9s)
- ....: for weight in IntegerVectors(d,3).map(list).map(L0):
- ....: eigenvalues = E.eigenvalues(E[L0(weight)])
-diff --git a/src/sage/combinat/sf/macdonald.py b/src/sage/combinat/sf/macdonald.py
-index e664e21..cc525b4 100644
---- a/src/sage/combinat/sf/macdonald.py
-+++ b/src/sage/combinat/sf/macdonald.py
-@@ -483,7 +483,7 @@ class Macdonald(UniqueRepresentation):
- sage: Ht = Sym.macdonald().Ht()
- sage: s = Sym.schur()
- sage: Ht(s([2,1]))
-- ((-q)/(-q*t^2+t^3+q^2-q*t))*McdHt[1, 1, 1] + ((q^2+q*t+t^2)/(-q^2*t^2+q^3+t^3-q*t))*McdHt[2, 1] + (t/(-q^3+q^2*t+q*t-t^2))*McdHt[3]
-+ (q/(q*t^2-t^3-q^2+q*t))*McdHt[1, 1, 1] + ((-q^2-q*t-t^2)/(q^2*t^2-q^3-t^3+q*t))*McdHt[2, 1] + (t/(-q^3+q^2*t+q*t-t^2))*McdHt[3]
- sage: Ht(s([2]))
- ((-q)/(-q+t))*McdHt[1, 1] + (t/(-q+t))*McdHt[2]
- """
-@@ -901,7 +901,7 @@ class MacdonaldPolynomials_generic(sfa.SymmetricFunctionAlgebra_generic):
- sage: Q._multiply(Q[1],Q[2])
- McdQ[2, 1] + ((q^2*t-q^2+q*t-q+t-1)/(q^2*t-1))*McdQ[3]
- sage: Ht._multiply(Ht[1],Ht[2])
-- ((-q^2+1)/(-q^2+t))*McdHt[2, 1] + ((-t+1)/(q^2-t))*McdHt[3]
-+ ((q^2-1)/(q^2-t))*McdHt[2, 1] + ((t-1)/(-q^2+t))*McdHt[3]
- """
- return self( self._s(left)*self._s(right) )
-
-diff --git a/src/sage/interfaces/singular.py b/src/sage/interfaces/singular.py
-index 88a33b0..a7cf5ea 100644
---- a/src/sage/interfaces/singular.py
-+++ b/src/sage/interfaces/singular.py
-@@ -191,13 +191,21 @@ The 1x1 and 2x2 minors::
- 6*y+2*x^3-6*x^2*y,
- 6*x^2*y-6*x*y^2,
- 6*x^2*y-6*x*y^2,
-- 6*x+6*x*y^2-2*y^3
-+ 6*x+6*x*y^2-2*y^3,
-+ 0,
-+ 0,
-+ 0,
-+ 0
- sage: H.minor(2)
- 12*y+4*x^3-12*x^2*y,
- 12*x^2*y-12*x*y^2,
- 12*x^2*y-12*x*y^2,
- 12*x+12*x*y^2-4*y^3,
-- -36*x*y-12*x^4+36*x^3*y-36*x*y^3+12*y^4+24*x^4*y^2-32*x^3*y^3+24*x^2*y^4
-+ -36*x*y-12*x^4+36*x^3*y-36*x*y^3+12*y^4+24*x^4*y^2-32*x^3*y^3+24*x^2*y^4,
-+ 0,
-+ 0,
-+ 0,
-+ 0
-
- ::
-
-diff --git a/src/sage/libs/singular/function.pyx b/src/sage/libs/singular/function.pyx
-index 0fea70a..26c74d0 100644
---- a/src/sage/libs/singular/function.pyx
-+++ b/src/sage/libs/singular/function.pyx
-@@ -1257,7 +1257,7 @@ cdef class SingularFunction(SageObject):
- Traceback (most recent call last):
- ...
- RuntimeError: error in Singular function call 'size':
-- Wrong number of arguments (got 2 arguments, arity code is 300)
-+ Wrong number of arguments (got 2 arguments, arity code is 302)
- sage: size('foobar', ring=P)
- 6
-
-@@ -1308,7 +1308,7 @@ cdef class SingularFunction(SageObject):
- ...
- RuntimeError: error in Singular function call 'triangL':
- The input is no groebner basis.
-- leaving triang.lib::triangL
-+ leaving triang.lib::triangL (0)
-
- Flush any stray output -- see :trac:`28622`::
-
-@@ -1671,17 +1671,17 @@ def singular_function(name):
- Traceback (most recent call last):
- ...
- RuntimeError: error in Singular function call 'factorize':
-- Wrong number of arguments (got 0 arguments, arity code is 303)
-+ Wrong number of arguments (got 0 arguments, arity code is 305)
- sage: factorize(f, 1, 2)
- Traceback (most recent call last):
- ...
- RuntimeError: error in Singular function call 'factorize':
-- Wrong number of arguments (got 3 arguments, arity code is 303)
-+ Wrong number of arguments (got 3 arguments, arity code is 305)
- sage: factorize(f, 1, 2, 3)
- Traceback (most recent call last):
- ...
- RuntimeError: error in Singular function call 'factorize':
-- Wrong number of arguments (got 4 arguments, arity code is 303)
-+ Wrong number of arguments (got 4 arguments, arity code is 305)
-
- The Singular function ``list`` can be called with any number of
- arguments::
-diff --git a/src/sage/rings/asymptotic/asymptotics_multivariate_generating_functions.py b/src/sage/rings/asymptotic/asymptotics_multivariate_generating_functions.py
-index 8b9367e..ef04d4f 100644
---- a/src/sage/rings/asymptotic/asymptotics_multivariate_generating_functions.py
-+++ b/src/sage/rings/asymptotic/asymptotics_multivariate_generating_functions.py
-@@ -1579,7 +1579,7 @@ class FractionWithFactoredDenominator(RingElement):
- (1, [(x*y + x + y - 1, 2)])
- sage: alpha = [4, 3]
- sage: decomp = F.asymptotic_decomposition(alpha); decomp
-- (0, []) + (-3/2*r*(1/y + 1) - 1/2/y - 1/2, [(x*y + x + y - 1, 1)])
-+ (0, []) + (-2*r*(1/x + 1) - 1/2/x - 1/2, [(x*y + x + y - 1, 1)])
- sage: F1 = decomp[1]
- sage: p = {y: 1/3, x: 1/2}
- sage: asy = F1.asymptotics(p, alpha, 2, verbose=True)
-@@ -1613,7 +1613,7 @@ class FractionWithFactoredDenominator(RingElement):
- sage: alpha = [3, 3, 2]
- sage: decomp = F.asymptotic_decomposition(alpha); decomp
- (0, []) +
-- (-16*r*(3/y - 4/z) - 16/y + 32/z,
-+ (16*r*(3/x - 2/z) + 16/x - 16/z,
- [(x + 2*y + z - 4, 1), (2*x + y + z - 4, 1)])
- sage: F1 = decomp[1]
- sage: p = {x: 1, y: 1, z: 1}
-diff --git a/src/sage/rings/polynomial/multi_polynomial_element.py b/src/sage/rings/polynomial/multi_polynomial_element.py
-index d86833f..3742439 100644
---- a/src/sage/rings/polynomial/multi_polynomial_element.py
-+++ b/src/sage/rings/polynomial/multi_polynomial_element.py
-@@ -2231,7 +2231,7 @@ def degree_lowest_rational_function(r, x):
- ::
-
- sage: r = f/g; r
-- (-b*c^2 + 2)/(a*b^3*c^6 - 2*a*c)
-+ (-2*b*c^2 - 1)/(2*a*b^3*c^6 + a*c)
- sage: degree_lowest_rational_function(r,a)
- -1
- sage: degree_lowest_rational_function(r,b)
-diff --git a/src/sage/rings/polynomial/multi_polynomial_ideal.py b/src/sage/rings/polynomial/multi_polynomial_ideal.py
-index f025b3a..94e130d 100644
---- a/src/sage/rings/polynomial/multi_polynomial_ideal.py
-+++ b/src/sage/rings/polynomial/multi_polynomial_ideal.py
-@@ -154,7 +154,7 @@ when the system has no solutions over the rationals.
- which is not 1. ::
-
- sage: I.groebner_basis()
-- [x + 130433*y + 59079*z, y^2 + 3*y + 17220, y*z + 5*y + 14504, 2*y + 158864, z^2 + 17223, 2*z + 41856, 164878]
-+ [x + y + 57119*z + 4, y^2 + 3*y + 17220, y*z + y + 26532, 2*y + 158864, z^2 + 17223, 2*z + 41856, 164878]
-
- Now for each prime `p` dividing this integer 164878, the Groebner
- basis of I modulo `p` will be non-trivial and will thus give a
-@@ -1567,8 +1567,8 @@ class MPolynomialIdeal_singular_repr(
- sage: I2 = y*R
- sage: I3 = (x, y)*R
- sage: I4 = (x^2 + x*y*z, y^2 - z^3*y, z^3 + y^5*x*z)*R
-- sage: I1.intersection(I2, I3, I4)
-- Ideal (x*y*z^20 - x*y*z^3, x*y^2 - x*y*z^3, x^2*y + x*y*z^4) of Multivariate Polynomial Ring in x, y, z over Rational Field
-+ sage: I1.intersection(I2, I3, I4).groebner_basis()
-+ [x^2*y + x*y*z^4, x*y^2 - x*y*z^3, x*y*z^20 - x*y*z^3]
-
- The ideals must share the same ring::
-
-@@ -4008,7 +4008,7 @@ class MPolynomialIdeal( MPolynomialIdeal_singular_repr, \
-
- sage: J.groebner_basis.set_cache(gb)
- sage: ideal(J.transformed_basis()).change_ring(P).interreduced_basis() # testing trac 21884
-- [a - 60*c^3 + 158/7*c^2 + 8/7*c - 1, b + 30*c^3 - 79/7*c^2 + 3/7*c, c^4 - 10/21*c^3 + 1/84*c^2 + 1/84*c]
-+ ...[a - 60*c^3 + 158/7*c^2 + 8/7*c - 1, b + 30*c^3 - 79/7*c^2 + 3/7*c, c^4 - 10/21*c^3 + 1/84*c^2 + 1/84*c]
-
- Giac's gbasis over `\QQ` can benefit from a probabilistic lifting and
- multi threaded operations::
-@@ -4111,9 +4111,9 @@ 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 - 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,
-+ [b^3 + b*c^2 + 12*c^3 + b^2 + b*c - 4*c^2,
-+ 2*b*c^2 - 6*c^3 - b^2 - b*c + 2*c^2,
-+ 42*c^3 + b^2 + 2*b*c - 14*c^2 + b,
- 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]
-diff --git a/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx b/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx
-index 1758424..553d22d 100644
---- a/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx
-+++ b/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx
-@@ -1349,7 +1349,7 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_base):
- sage: R = IntegerModRing(15)['x,y']
- sage: singular(R)
- polynomial ring, over a ring (with zero-divisors), global ordering
-- // coefficients: ZZ/bigint(15)
-+ // coefficients: ZZ/...(15)
- // number of vars : 2
- // block 1 : ordering dp
- // : names x y
-diff --git a/src/sage/rings/polynomial/plural.pyx b/src/sage/rings/polynomial/plural.pyx
-index c2792ae..aa2ef59 100644
---- a/src/sage/rings/polynomial/plural.pyx
-+++ b/src/sage/rings/polynomial/plural.pyx
-@@ -390,28 +390,30 @@ cdef class NCPolynomialRing_plural(Ring):
- TESTS:
-
- This example caused a segmentation fault with a previous version
-- of this method::
-+ of this method. This doctest still results in a segmentation fault
-+ occasionally which is difficult to isolate, so this test is partially
-+ disabled (:trac:`29528`)::
-
- sage: import gc
- sage: from sage.rings.polynomial.plural import NCPolynomialRing_plural
- sage: from sage.algebras.free_algebra import FreeAlgebra
- sage: A1.<x,y,z> = FreeAlgebra(QQ, 3)
- sage: R1 = A1.g_algebra({y*x:x*y-z, z*x:x*z+2*x, z*y:y*z-2*y}, order=TermOrder('degrevlex', 2))
-- sage: A2.<x,y,z> = FreeAlgebra(GF(5), 3)
-- sage: R2 = A2.g_algebra({y*x:x*y-z, z*x:x*z+2*x, z*y:y*z-2*y}, order=TermOrder('degrevlex', 2))
-- sage: A3.<x,y,z> = FreeAlgebra(GF(11), 3)
-- sage: R3 = A3.g_algebra({y*x:x*y-z, z*x:x*z+2*x, z*y:y*z-2*y}, order=TermOrder('degrevlex', 2))
-- sage: A4.<x,y,z> = FreeAlgebra(GF(13), 3)
-- sage: R4 = A4.g_algebra({y*x:x*y-z, z*x:x*z+2*x, z*y:y*z-2*y}, order=TermOrder('degrevlex', 2))
-+ sage: A2.<x,y,z> = FreeAlgebra(GF(5), 3) # not tested
-+ sage: R2 = A2.g_algebra({y*x:x*y-z, z*x:x*z+2*x, z*y:y*z-2*y}, order=TermOrder('degrevlex', 2)) # not tested
-+ sage: A3.<x,y,z> = FreeAlgebra(GF(11), 3) # not tested
-+ sage: R3 = A3.g_algebra({y*x:x*y-z, z*x:x*z+2*x, z*y:y*z-2*y}, order=TermOrder('degrevlex', 2)) # not tested
-+ sage: A4.<x,y,z> = FreeAlgebra(GF(13), 3) # not tested
-+ sage: R4 = A4.g_algebra({y*x:x*y-z, z*x:x*z+2*x, z*y:y*z-2*y}, order=TermOrder('degrevlex', 2)) # not tested
- sage: _ = gc.collect()
- sage: foo = R1.gen(0)
- sage: del foo
- sage: del R1
- sage: _ = gc.collect()
-- sage: del R2
-- sage: _ = gc.collect()
-- sage: del R3
-- sage: _ = gc.collect()
-+ sage: del R2 # not tested
-+ sage: _ = gc.collect() # not tested
-+ sage: del R3 # not tested
-+ sage: _ = gc.collect() # not tested
- """
- singular_ring_delete(self._ring)
-
-@@ -2886,7 +2888,8 @@ cpdef MPolynomialRing_libsingular new_CRing(RingWrap rw, base_ring):
- self.__ngens = rw.ngens()
- self.__term_order = TermOrder(rw.ordering_string(), force=True)
-
-- ParentWithGens.__init__(self, base_ring, rw.var_names())
-+ ParentWithGens.__init__(self, base_ring, tuple(rw.var_names()),
-+ normalize=False)
- # self._populate_coercion_lists_() # ???
-
- #MPolynomialRing_generic.__init__(self, base_ring, n, names, order)
-diff --git a/src/sage/rings/polynomial/polynomial_singular_interface.py b/src/sage/rings/polynomial/polynomial_singular_interface.py
-index 74b8b82..beee5ad 100644
---- a/src/sage/rings/polynomial/polynomial_singular_interface.py
-+++ b/src/sage/rings/polynomial/polynomial_singular_interface.py
-@@ -165,7 +165,7 @@ class PolynomialRing_singular_repr:
- sage: R = IntegerModRing(15)['x,y']
- sage: singular(R)
- polynomial ring, over a ring (with zero-divisors), global ordering
-- // coefficients: ZZ/bigint(15)
-+ // coefficients: ZZ/...(15)
- // number of vars : 2
- // block 1 : ordering dp
- // : names x y
-diff --git a/src/sage/schemes/curves/projective_curve.py b/src/sage/schemes/curves/projective_curve.py
-index 1091c29..4f5936e 100644
---- a/src/sage/schemes/curves/projective_curve.py
-+++ b/src/sage/schemes/curves/projective_curve.py
-@@ -2001,7 +2001,7 @@ class ProjectivePlaneCurve_finite_field(ProjectivePlaneCurve_field):
- sage: C = Curve(f); pts = C.rational_points()
- sage: D = C.divisor([ (3, pts[0]), (-1,pts[1]), (10, pts[5]) ])
- sage: C.riemann_roch_basis(D)
-- [(-x - 2*y)/(-2*x - 2*y), (-x + z)/(x + y)]
-+ [(-2*x + y)/(x + y), (-x + z)/(x + y)]
-
- .. NOTE::
-
Copied: sagemath/trunk/sagemath-singular-4.2.patch (from rev 779935, sagemath/trunk/sagemath-singular-4.1.2.patch)
===================================================================
--- sagemath-singular-4.2.patch (rev 0)
+++ sagemath-singular-4.2.patch 2020-12-19 10:42:43 UTC (rev 779936)
@@ -0,0 +1,915 @@
+diff --git a/src/doc/en/constructions/algebraic_geometry.rst b/src/doc/en/constructions/algebraic_geometry.rst
+index a312548..d1c9c95 100644
+--- a/src/doc/en/constructions/algebraic_geometry.rst
++++ b/src/doc/en/constructions/algebraic_geometry.rst
+@@ -139,7 +139,7 @@ Other methods
+
+ sage: singular.lib("brnoeth.lib")
+ sage: s = singular.ring(2,'(x,y)','lp')
+- sage: I = singular.ideal('[x^4+x, y^4+y]')
++ sage: I = singular.ideal('x^4+x', 'y^4+y')
+ sage: L = singular.closed_points(I)
+ sage: # Here you have all the points :
+ sage: print(L)
+@@ -325,7 +325,7 @@ Singular itself to help an understanding of how the wrapper works.
+ sage: X = Curve(f); pts = X.rational_points()
+ sage: D = X.divisor([ (3, pts[0]), (-1,pts[1]), (10, pts[5]) ])
+ sage: X.riemann_roch_basis(D)
+- [(-x - 2*y)/(-2*x - 2*y), (-x + z)/(x + y)]
++ [(-2*x + y)/(x + y), (-x + z)/(x + y)]
+
+ - Using Singular's ``BrillNoether`` command (for details see the section
+ Brill-Noether in the Singular online documentation
+diff --git a/src/sage/algebras/free_algebra.py b/src/sage/algebras/free_algebra.py
+index 7391dd9..7234f91 100644
+--- a/src/sage/algebras/free_algebra.py
++++ b/src/sage/algebras/free_algebra.py
+@@ -39,7 +39,15 @@ two-sided ideals, and thus provide ideal containment tests::
+ Free Associative Unital Algebra on 3 generators (x, y, z) over Rational Field
+ sage: I = F*[x*y+y*z,x^2+x*y-y*x-y^2]*F
+ sage: I.groebner_basis(degbound=4)
+- Twosided Ideal (y*z*y*y - y*z*y*z + y*z*z*y - y*z*z*z, y*z*y*x + y*z*y*z + y*z*z*x + y*z*z*z, y*y*z*y - y*y*z*z + y*z*z*y - y*z*z*z, y*y*z*x + y*y*z*z + y*z*z*x + y*z*z*z, y*y*y - y*y*z + y*z*y - y*z*z, y*y*x + y*y*z + y*z*x + y*z*z, x*y + y*z, x*x - y*x - y*y - y*z) of Free Associative Unital Algebra on 3 generators (x, y, z) over Rational Field
++ Twosided Ideal (x*y + y*z,
++ x*x - y*x - y*y - y*z,
++ y*y*y - y*y*z + y*z*y - y*z*z,
++ y*y*x + y*y*z + y*z*x + y*z*z,
++ y*y*z*y - y*y*z*z + y*z*z*y - y*z*z*z,
++ y*z*y*y - y*z*y*z + y*z*z*y - y*z*z*z,
++ y*y*z*x + y*y*z*z + y*z*z*x + y*z*z*z,
++ y*z*y*x + y*z*y*z + y*z*z*x + y*z*z*z) of Free Associative Unital
++ Algebra on 3 generators (x, y, z) over Rational Field
+ sage: y*z*y*y*z*z + 2*y*z*y*z*z*x + y*z*y*z*z*z - y*z*z*y*z*x + y*z*z*z*z*x in I
+ True
+
+@@ -233,7 +241,7 @@ class FreeAlgebraFactory(UniqueFactory):
+ a*b^2*c^3
+ """
+ def create_key(self, base_ring, arg1=None, arg2=None,
+- sparse=None, order='degrevlex',
++ sparse=None, order=None,
+ names=None, name=None,
+ implementation=None, degrees=None):
+ """
+@@ -264,6 +272,8 @@ class FreeAlgebraFactory(UniqueFactory):
+ return tuple(degrees),base_ring
+ # test if we can use libSingular/letterplace
+ if implementation == "letterplace":
++ if order is None:
++ order = 'degrevlex' if degrees is None else 'deglex'
+ args = [arg for arg in (arg1, arg2) if arg is not None]
+ kwds = dict(sparse=sparse, order=order, implementation="singular")
+ if name is not None:
+@@ -274,7 +284,7 @@ class FreeAlgebraFactory(UniqueFactory):
+ if degrees is None:
+ return (PolRing,)
+ from sage.all import TermOrder
+- T = PolRing.term_order() + TermOrder('lex',1)
++ T = TermOrder(PolRing.term_order(), PolRing.ngens() + 1)
+ varnames = list(PolRing.variable_names())
+ newname = 'x'
+ while newname in varnames:
+diff --git a/src/sage/algebras/letterplace/free_algebra_element_letterplace.pyx b/src/sage/algebras/letterplace/free_algebra_element_letterplace.pyx
+index ad863ea..d6127c9 100644
+--- a/src/sage/algebras/letterplace/free_algebra_element_letterplace.pyx
++++ b/src/sage/algebras/letterplace/free_algebra_element_letterplace.pyx
+@@ -17,6 +17,7 @@ AUTHOR:
+ # https://www.gnu.org/licenses/
+ # ****************************************************************************
+
++from sage.groups.perm_gps.all import CyclicPermutationGroup
+ from sage.libs.singular.function import lib, singular_function
+ from sage.misc.repr import repr_lincomb
+ from sage.rings.polynomial.multi_polynomial_ideal import MPolynomialIdeal
+@@ -25,7 +26,6 @@ from cpython.object cimport PyObject_RichCompare
+ # Define some singular functions
+ lib("freegb.lib")
+ poly_reduce = singular_function("NF")
+-singular_system=singular_function("system")
+
+ #####################
+ # Free algebra elements
+@@ -445,9 +445,10 @@ cdef class FreeAlgebraElement_letterplace(AlgebraElement):
+ cdef int i
+ if P.monomial_divides(s_poly,p_poly):
+ return True
++ realngens = A._commutative_ring.ngens()
++ CG = CyclicPermutationGroup(P.ngens())
+ for i from 0 <= i < p_d-s_d:
+- s_poly = singular_system("stest",s_poly,1,
+- A._degbound,A.__ngens,ring=P)
++ s_poly = s_poly * CG[realngens]
+ if P.monomial_divides(s_poly,p_poly):
+ return True
+ return False
+@@ -601,7 +602,9 @@ cdef class FreeAlgebraElement_letterplace(AlgebraElement):
+ # we must put the polynomials into the same ring
+ left._poly = A._current_ring(left._poly)
+ right._poly = A._current_ring(right._poly)
+- rshift = singular_system("stest",right._poly,left._poly.degree(),A._degbound,A.__ngens, ring=A._current_ring)
++ realngens = A._commutative_ring.ngens()
++ CG = CyclicPermutationGroup(A._current_ring.ngens())
++ rshift = right._poly * CG[left._poly.degree() * realngens]
+ return FreeAlgebraElement_letterplace(A,left._poly*rshift, check=False)
+
+ def __pow__(FreeAlgebraElement_letterplace self, int n, k):
+@@ -627,10 +630,11 @@ cdef class FreeAlgebraElement_letterplace(AlgebraElement):
+ self._poly = A._current_ring(self._poly)
+ cdef int d = self._poly.degree()
+ q = p = self._poly
++ realngens = A._commutative_ring.ngens()
+ cdef int i
++ CG = CyclicPermutationGroup(A._current_ring.ngens())
+ for i from 0<i<n:
+- q = singular_system("stest",q,d,A._degbound,A.__ngens,
+- ring=A._current_ring)
++ q = q * CG[d * realngens]
+ p *= q
+ return FreeAlgebraElement_letterplace(A, p, check=False)
+
+diff --git a/src/sage/algebras/letterplace/free_algebra_letterplace.pxd b/src/sage/algebras/letterplace/free_algebra_letterplace.pxd
+index 7e5f2bb..d1d162c 100644
+--- a/src/sage/algebras/letterplace/free_algebra_letterplace.pxd
++++ b/src/sage/algebras/letterplace/free_algebra_letterplace.pxd
+@@ -13,8 +13,15 @@ from sage.rings.ring cimport Algebra
+ from sage.structure.element cimport AlgebraElement, ModuleElement, RingElement, Element
+ from sage.rings.polynomial.multi_polynomial_libsingular cimport MPolynomialRing_libsingular, MPolynomial_libsingular
+ from sage.algebras.letterplace.free_algebra_element_letterplace cimport FreeAlgebraElement_letterplace
++from sage.libs.singular.decl cimport ring
+
+
++cdef class FreeAlgebra_letterplace_libsingular():
++ cdef ring* _lp_ring
++ cdef MPolynomialRing_libsingular _commutative_ring
++ cdef MPolynomialRing_libsingular _lp_ring_internal
++ cdef object __ngens
++
+ cdef class FreeAlgebra_letterplace(Algebra):
+ cdef MPolynomialRing_libsingular _commutative_ring
+ cdef MPolynomialRing_libsingular _current_ring
+diff --git a/src/sage/algebras/letterplace/free_algebra_letterplace.pyx b/src/sage/algebras/letterplace/free_algebra_letterplace.pyx
+index a9d09ad..714284e 100644
+--- a/src/sage/algebras/letterplace/free_algebra_letterplace.pyx
++++ b/src/sage/algebras/letterplace/free_algebra_letterplace.pyx
+@@ -37,7 +37,15 @@ The preceding containment test is based on the computation of Groebner
+ bases with degree bound::
+
+ sage: I.groebner_basis(degbound=4)
+- Twosided Ideal (y*z*y*y - y*z*y*z + y*z*z*y - y*z*z*z, y*z*y*x + y*z*y*z + y*z*z*x + y*z*z*z, y*y*z*y - y*y*z*z + y*z*z*y - y*z*z*z, y*y*z*x + y*y*z*z + y*z*z*x + y*z*z*z, y*y*y - y*y*z + y*z*y - y*z*z, y*y*x + y*y*z + y*z*x + y*z*z, x*y + y*z, x*x - y*x - y*y - y*z) of Free Associative Unital Algebra on 3 generators (x, y, z) over Rational Field
++ Twosided Ideal (x*y + y*z,
++ x*x - y*x - y*y - y*z,
++ y*y*y - y*y*z + y*z*y - y*z*z,
++ y*y*x + y*y*z + y*z*x + y*z*z,
++ y*y*z*y - y*y*z*z + y*z*z*y - y*z*z*z,
++ y*z*y*y - y*z*y*z + y*z*z*y - y*z*z*z,
++ y*y*z*x + y*y*z*z + y*z*z*x + y*z*z*z,
++ y*z*y*x + y*z*y*z + y*z*z*x + y*z*z*z) of Free Associative Unital
++ Algebra on 3 generators (x, y, z) over Rational Field
+
+ When reducing an element by `I`, the original generators are chosen::
+
+@@ -67,7 +75,13 @@ different normal form::
+ Lexicographic term order
+ sage: J = L*[a*b+b*c,a^2+a*b-b*c-c^2]*L
+ sage: J.groebner_basis(4)
+- Twosided Ideal (2*b*c*b - b*c*c + c*c*b, a*c*c - 2*b*c*a - 2*b*c*c - c*c*a, a*b + b*c, a*a - 2*b*c - c*c) of Free Associative Unital Algebra on 3 generators (a, b, c) over Rational Field
++ Twosided Ideal (2*b*c*b - b*c*c + c*c*b,
++ a*b + b*c,
++ -a*c*c + 2*b*c*a + 2*b*c*c + c*c*a,
++ a*c*c*b - 2*b*c*c*b + b*c*c*c,
++ a*a - 2*b*c - c*c,
++ a*c*c*a - 2*b*c*c*a - 4*b*c*c*c - c*c*c*c) of Free Associative Unital
++ Algebra on 3 generators (a, b, c) over Rational Field
+ sage: (b*c*b*b).normal_form(J)
+ 1/2*b*c*c*b - 1/2*c*c*b*b
+
+@@ -105,15 +119,16 @@ TESTS::
+ from sage.misc.misc_c import prod
+ from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
+ from sage.libs.singular.function import lib, singular_function
+-from sage.rings.polynomial.term_order import TermOrder
++from sage.libs.singular.function cimport RingWrap
++from sage.libs.singular.ring cimport singular_ring_delete, singular_ring_reference
+ from sage.categories.algebras import Algebras
+ from sage.rings.noncommutative_ideals import IdealMonoid_nc
++from sage.rings.polynomial.plural cimport new_CRing
+
+ #####################
+ # Define some singular functions
+ lib("freegb.lib")
+-poly_reduce = singular_function("NF")
+-singular_system=singular_function("system")
++freeAlgebra = singular_function("freeAlgebra")
+
+ # unfortunately we can not set Singular attributes for MPolynomialRing_libsingular
+ # Hence, we must constantly work around Letterplace's sanity checks,
+@@ -242,7 +257,7 @@ cdef class FreeAlgebra_letterplace(Algebra):
+ sage: F.<a,b,c> = FreeAlgebra(K, implementation='letterplace')
+ sage: TestSuite(F).run()
+ """
+- if not isinstance(R,MPolynomialRing_libsingular):
++ if not isinstance(R, MPolynomialRing_libsingular):
+ raise TypeError("A letterplace algebra must be provided by a polynomial ring of type %s" % MPolynomialRing_libsingular)
+ self.__ngens = R.ngens()
+ if degrees is None:
+@@ -260,7 +275,9 @@ cdef class FreeAlgebra_letterplace(Algebra):
+ if degrees is None:
+ self._degrees = tuple([int(1)]*self.__ngens)
+ else:
+- if (not isinstance(degrees,(tuple,list))) or len(degrees)!=self.__ngens-1 or any(i <= 0 for i in degrees):
++ if (not isinstance(degrees, (tuple, list))) \
++ or len(degrees) != self.__ngens - self._nb_slackvars \
++ or any(i <= 0 for i in degrees):
+ raise TypeError("The generator degrees must be given by a list or tuple of %d positive integers" % (self.__ngens-1))
+ self._degrees = tuple([int(i) for i in degrees])
+ self.set_degbound(max(self._degrees))
+@@ -666,7 +683,7 @@ cdef class FreeAlgebra_letterplace(Algebra):
+ Sage, since it does the reductions in a different order
+ compared to Singular. Therefore, we call the original Singular
+ reduction method, and prevent a warning message by asserting
+- that `G` is a Groebner basis.
++ that `G` is a Groebner basis. ::
+
+ sage: from sage.libs.singular.function import singular_function
+ sage: poly_reduce = singular_function("NF")
+@@ -682,8 +699,10 @@ cdef class FreeAlgebra_letterplace(Algebra):
+ ngens = self.__ngens
+ degbound = self._degbound
+ cdef list G = [C(x._poly) for x in g]
++ from sage.groups.perm_gps.all import CyclicPermutationGroup
++ CG = CyclicPermutationGroup(C.ngens())
+ for y in G:
+- out.extend([y]+[singular_system("stest",y,n+1,degbound,ngens,ring=C) for n in xrange(d-y.degree())])
++ out.extend([y]+[y * CG[ngens*(n+1)] for n in xrange(d-y.degree())])
+ return C.ideal(out)
+
+ ###########################
+@@ -879,3 +898,28 @@ cdef class FreeAlgebra_letterplace(Algebra):
+ PNames[P.ngens(): len(PNames): P.ngens()+1] = list(Names[self.ngens(): len(Names): self.ngens()+1])[:P.degbound()]
+ x = Ppoly.hom([Gens[Names.index(asdf)] for asdf in PNames])(x.letterplace_polynomial())
+ return FreeAlgebraElement_letterplace(self,self._current_ring(x))
++
++cdef class FreeAlgebra_letterplace_libsingular():
++ """
++ Internally used wrapper around a Singular Letterplace polynomial ring.
++ """
++
++ def __cinit__(self, MPolynomialRing_libsingular commutative_ring,
++ int degbound):
++ cdef RingWrap rw = freeAlgebra(commutative_ring, degbound)
++ self._lp_ring = singular_ring_reference(rw._ring)
++ # `_lp_ring` viewed as `MPolynomialRing_libsingular` with additional
++ # letterplace attributes set (for internal use only)
++ self._lp_ring_internal = new_CRing(rw, commutative_ring.base_ring())
++ self._commutative_ring = commutative_ring
++
++ def __init__(self, commutative_ring, degbound):
++ self.__ngens = commutative_ring.ngens() * degbound
++
++ def __dealloc__(self):
++ r"""
++ Carefully deallocate the ring, without changing ``currRing``
++ (since this method can be at unpredictable times due to garbage
++ collection).
++ """
++ singular_ring_delete(self._lp_ring)
+diff --git a/src/sage/algebras/letterplace/letterplace_ideal.pyx b/src/sage/algebras/letterplace/letterplace_ideal.pyx
+index d7214d1..5b8cf48 100644
+--- a/src/sage/algebras/letterplace/letterplace_ideal.pyx
++++ b/src/sage/algebras/letterplace/letterplace_ideal.pyx
+@@ -18,7 +18,11 @@ One can compute Groebner bases out to a finite degree, can compute normal
+ forms and can test containment in the ideal::
+
+ sage: I.groebner_basis(degbound=3)
+- Twosided Ideal (y*y*y - y*y*z + y*z*y - y*z*z, y*y*x + y*y*z + y*z*x + y*z*z, x*y + y*z, x*x - y*x - y*y - y*z) of Free Associative Unital Algebra on 3 generators (x, y, z) over Rational Field
++ Twosided Ideal (x*y + y*z,
++ x*x - y*x - y*y - y*z,
++ y*y*y - y*y*z + y*z*y - y*z*z,
++ y*y*x + y*y*z + y*z*x + y*z*z) of Free Associative Unital Algebra
++ on 3 generators (x, y, z) over Rational Field
+ sage: (x*y*z*y*x).normal_form(I)
+ y*z*z*y*z + y*z*z*z*x + y*z*z*z*z
+ sage: x*y*z*y*x - (x*y*z*y*x).normal_form(I) in I
+@@ -42,14 +46,14 @@ AUTHOR:
+
+ from sage.rings.noncommutative_ideals import Ideal_nc
+ from sage.libs.singular.function import lib, singular_function
+-from sage.algebras.letterplace.free_algebra_letterplace cimport FreeAlgebra_letterplace
++from sage.algebras.letterplace.free_algebra_letterplace cimport FreeAlgebra_letterplace, FreeAlgebra_letterplace_libsingular
+ from sage.algebras.letterplace.free_algebra_element_letterplace cimport FreeAlgebraElement_letterplace
+ from sage.rings.infinity import Infinity
+
+ #####################
+ # Define some singular functions
+ lib("freegb.lib")
+-singular_system=singular_function("system")
++singular_twostd=singular_function("twostd")
+ poly_reduce=singular_function("NF")
+
+ class LetterplaceIdeal(Ideal_nc):
+@@ -69,14 +73,22 @@ class LetterplaceIdeal(Ideal_nc):
+ sage: I.groebner_basis(2)
+ Twosided Ideal (x*y + y*z, x*x - y*x - y*y - y*z) of Free Associative Unital Algebra on 3 generators (x, y, z) over Rational Field
+ sage: I.groebner_basis(4)
+- Twosided Ideal (y*z*y*y - y*z*y*z + y*z*z*y - y*z*z*z, y*z*y*x + y*z*y*z + y*z*z*x + y*z*z*z, y*y*z*y - y*y*z*z + y*z*z*y - y*z*z*z, y*y*z*x + y*y*z*z + y*z*z*x + y*z*z*z, y*y*y - y*y*z + y*z*y - y*z*z, y*y*x + y*y*z + y*z*x + y*z*z, x*y + y*z, x*x - y*x - y*y - y*z) of Free Associative Unital Algebra on 3 generators (x, y, z) over Rational Field
++ Twosided Ideal (x*y + y*z,
++ x*x - y*x - y*y - y*z,
++ y*y*y - y*y*z + y*z*y - y*z*z,
++ y*y*x + y*y*z + y*z*x + y*z*z,
++ y*y*z*y - y*y*z*z + y*z*z*y - y*z*z*z,
++ y*z*y*y - y*z*y*z + y*z*z*y - y*z*z*z,
++ y*y*z*x + y*y*z*z + y*z*z*x + y*z*z*z,
++ y*z*y*x + y*z*y*z + y*z*z*x + y*z*z*z) of Free Associative Unital
++ Algebra on 3 generators (x, y, z) over Rational Field
+
+ Groebner bases are cached. If one has computed a Groebner basis
+ out to a high degree then it will also be returned if a Groebner
+ basis with a lower degree bound is requested::
+
+- sage: I.groebner_basis(2)
+- Twosided Ideal (y*z*y*y - y*z*y*z + y*z*z*y - y*z*z*z, y*z*y*x + y*z*y*z + y*z*z*x + y*z*z*z, y*y*z*y - y*y*z*z + y*z*z*y - y*z*z*z, y*y*z*x + y*y*z*z + y*z*z*x + y*z*z*z, y*y*y - y*y*z + y*z*y - y*z*z, y*y*x + y*y*z + y*z*x + y*z*z, x*y + y*z, x*x - y*x - y*y - y*z) of Free Associative Unital Algebra on 3 generators (x, y, z) over Rational Field
++ sage: I.groebner_basis(2) is I.groebner_basis(4)
++ True
+
+ Of course, the normal form of any element has to satisfy the following::
+
+@@ -116,8 +128,11 @@ class LetterplaceIdeal(Ideal_nc):
+ sage: F.<x,y,z> = FreeAlgebra(QQ, implementation='letterplace',degrees=[1,2,3])
+ sage: I = F*[x*y+z-y*x,x*y*z-x^6+y^3]*F
+ sage: I.groebner_basis(Infinity)
+- Twosided Ideal (x*z*z - y*x*x*z - y*x*y*y + y*x*z*x + y*y*y*x + z*x*z + z*y*y - z*z*x,
+- x*y - y*x + z,
++ Twosided Ideal (x*y - y*x + z,
++ x*x*x*x*x*x - y*x*z - y*y*y + z*z,
++ x*z*z - y*x*x*z + y*x*z*x + y*y*z + y*z*y + z*x*z + z*y*y - z*z*x,
++ x*x*x*x*x*z + x*x*x*x*z*x + x*x*x*z*x*x + x*x*z*x*x*x + x*z*x*x*x*x +
++ y*x*z*y - y*y*x*z + y*z*z + z*x*x*x*x*x - z*z*y,
+ x*x*x*x*z*y*y + x*x*x*z*y*y*x - x*x*x*z*y*z - x*x*z*y*x*z + x*x*z*y*y*x*x +
+ x*x*z*y*y*y - x*x*z*y*z*x - x*z*y*x*x*z - x*z*y*x*z*x +
+ x*z*y*y*x*x*x + 2*x*z*y*y*y*x - 2*x*z*y*y*z - x*z*y*z*x*x -
+@@ -135,10 +150,7 @@ class LetterplaceIdeal(Ideal_nc):
+ z*y*y*y*y - 3*z*y*y*z*x - z*y*z*x*x*x - 2*z*y*z*y*x +
+ 2*z*y*z*z - z*z*x*x*x*x*x + 4*z*z*x*x*z + 4*z*z*x*z*x -
+ 4*z*z*y*x*x*x - 3*z*z*y*y*x + 4*z*z*y*z + 4*z*z*z*x*x +
+- 2*z*z*z*y,
+- x*x*x*x*x*z + x*x*x*x*z*x + x*x*x*z*x*x + x*x*z*x*x*x + x*z*x*x*x*x +
+- y*x*z*y - y*y*x*z + y*z*z + z*x*x*x*x*x - z*z*y,
+- x*x*x*x*x*x - y*x*z - y*y*y + z*z)
++ 2*z*z*z*y)
+ of Free Associative Unital Algebra on 3 generators (x, y, z) over Rational Field
+
+ Again, we can compute normal forms::
+@@ -226,7 +238,15 @@ class LetterplaceIdeal(Ideal_nc):
+ sage: I.groebner_basis() # not tested
+ Twosided Ideal (y*y*y - y*y*z + y*z*y - y*z*z, y*y*x + y*y*z + y*z*x + y*z*z, x*y + y*z, x*x - y*x - y*y - y*z) of Free Associative Unital Algebra on 3 generators (x, y, z) over Rational Field
+ sage: I.groebner_basis(4)
+- Twosided Ideal (y*z*y*y - y*z*y*z + y*z*z*y - y*z*z*z, y*z*y*x + y*z*y*z + y*z*z*x + y*z*z*z, y*y*z*y - y*y*z*z + y*z*z*y - y*z*z*z, y*y*z*x + y*y*z*z + y*z*z*x + y*z*z*z, y*y*y - y*y*z + y*z*y - y*z*z, y*y*x + y*y*z + y*z*x + y*z*z, x*y + y*z, x*x - y*x - y*y - y*z) of Free Associative Unital Algebra on 3 generators (x, y, z) over Rational Field
++ Twosided Ideal (x*y + y*z,
++ x*x - y*x - y*y - y*z,
++ y*y*y - y*y*z + y*z*y - y*z*z,
++ y*y*x + y*y*z + y*z*x + y*z*z,
++ y*y*z*y - y*y*z*z + y*z*z*y - y*z*z*z,
++ y*z*y*y - y*z*y*z + y*z*z*y - y*z*z*z,
++ y*y*z*x + y*y*z*z + y*z*z*x + y*z*z*z,
++ y*z*y*x + y*z*y*z + y*z*z*x + y*z*z*z) of Free Associative
++ Unital Algebra on 3 generators (x, y, z) over Rational Field
+ sage: I.groebner_basis(2) is I.groebner_basis(4)
+ True
+ sage: G = I.groebner_basis(4)
+@@ -238,7 +258,14 @@ class LetterplaceIdeal(Ideal_nc):
+
+ sage: I = F*[x*y-y*x,x*z-z*x,y*z-z*y,x^2*y-z^3,x*y^2+z*x^2]*F
+ sage: I.groebner_basis(Infinity)
+- Twosided Ideal (z*z*z*y*y + z*z*z*z*x, z*x*x*x + z*z*z*y, y*z - z*y, y*y*x + z*x*x, y*x*x - z*z*z, x*z - z*x, x*y - y*x) of Free Associative Unital Algebra on 3 generators (x, y, z) over Rational Field
++ Twosided Ideal (-y*z + z*y,
++ -x*z + z*x,
++ -x*y + y*x,
++ x*x*z + x*y*y,
++ x*x*y - z*z*z,
++ x*x*x*z + y*z*z*z,
++ x*z*z*z*z + y*y*z*z*z) of Free Associative Unital Algebra
++ on 3 generators (x, y, z) over Rational Field
+
+ Since the commutators of the generators are contained in the ideal,
+ we can verify the above result by a computation in a polynomial ring
+@@ -276,9 +303,32 @@ class LetterplaceIdeal(Ideal_nc):
+ libsingular_options['redSB'] = True
+ A.set_degbound(degbound)
+ P = A._current_ring
+- out = [FreeAlgebraElement_letterplace(A,X,check=False) for X in
+- singular_system("freegb",P.ideal([x._poly for x in self.__GB.gens()]),
+- degbound,A.__ngens, ring = P)]
++
++ # note that degbound might be smaller than A._degbound due to caching,
++ # but degbound must be large enough to map all generators to the
++ # letterplace ring L
++ if degbound < A._degbound:
++ max_deg = max([x._poly.degree() for x in self.__GB.gens()])
++ if degbound < max_deg:
++ degbound = max_deg
++
++ # The following is a workaround for calling Singular's new Letterplace
++ # API (see :trac:`25993`). We construct a temporary polynomial ring L
++ # with letterplace attributes set as required by the API. As L has
++ # duplicate variable names, we need to handle this ring carefully; in
++ # particular, we cannot coerce to and from L, so we use homomorphisms
++ # for the conversion.
++
++ cdef FreeAlgebra_letterplace_libsingular lp_ring = \
++ FreeAlgebra_letterplace_libsingular(A._commutative_ring, degbound)
++ L = lp_ring._lp_ring_internal
++ to_L = P.hom(L.gens(), L, check=False)
++ from_L = L.hom(P.gens(), P, check=False)
++ I = L.ideal([to_L(x._poly) for x in self.__GB.gens()])
++ gb = singular_twostd(I)
++ out = [FreeAlgebraElement_letterplace(A, from_L(X), check=False)
++ for X in gb]
++
+ libsingular_options['redTail'] = bck[0]
+ libsingular_options['redSB'] = bck[1]
+ self.__GB = A.ideal(out,side='twosided',coerce=False)
+diff --git a/src/sage/combinat/root_system/hecke_algebra_representation.py b/src/sage/combinat/root_system/hecke_algebra_representation.py
+index 51f4113..ba42ed1 100644
+--- a/src/sage/combinat/root_system/hecke_algebra_representation.py
++++ b/src/sage/combinat/root_system/hecke_algebra_representation.py
+@@ -746,7 +746,7 @@ class HeckeAlgebraRepresentation(WithEqualityById, SageObject):
+ -2121 + 212,
+ (q2/(q1-q2))*2121 + (q2/(-q1+q2))*121 + (q2/(-q1+q2))*212 - 12 + ((-q2)/(-q1+q2))*21 + 2,
+ ((-q2^2)/(-q1^2+q1*q2-q2^2))*2121 - 121 + (q2^2/(-q1^2+q1*q2-q2^2))*212 + 21,
+- ((q1^2+q2^2)/(-q1^2+q1*q2-q2^2))*2121 + ((-q1^2-q2^2)/(-q1^2+q1*q2-q2^2))*121 + ((-q2^2)/(-q1^2+q1*q2-q2^2))*212 + (q2^2/(-q1^2+q1*q2-q2^2))*12 - 21 + 1,
++ ((-q1^2-q2^2)/(q1^2-q1*q2+q2^2))*2121 + ((-q1^2-q2^2)/(-q1^2+q1*q2-q2^2))*121 + ((-q2^2)/(-q1^2+q1*q2-q2^2))*212 + (q2^2/(-q1^2+q1*q2-q2^2))*12 - 21 + 1,
+ 2121,
+ (q2/(-q1+q2))*2121 + ((-q2)/(-q1+q2))*121 - 212 + 12,
+ -2121 + 121]
+diff --git a/src/sage/combinat/root_system/non_symmetric_macdonald_polynomials.py b/src/sage/combinat/root_system/non_symmetric_macdonald_polynomials.py
+index 3537772..ee8ddec 100644
+--- a/src/sage/combinat/root_system/non_symmetric_macdonald_polynomials.py
++++ b/src/sage/combinat/root_system/non_symmetric_macdonald_polynomials.py
+@@ -555,8 +555,7 @@ class NonSymmetricMacdonaldPolynomials(CherednikOperatorsEigenvectors):
+ B[(1, 0, 0)]
+
+ sage: E[-omega[1]]
+- B[(-1, 0, 0)] + ((-q*q1^6-q*q1^5*q2-q1*q2^5-q2^6)/(-q^3*q1^6-q^2*q1^5*q2-q*q1*q2^5-q2^6))*B[(1, 0, 0)] + ((-q1-q2)/(-q*q1-q2))*B[(0, -1, 0)]
+- + ((q1+q2)/(q*q1+q2))*B[(0, 1, 0)] + ((-q1-q2)/(-q*q1-q2))*B[(0, 0, -1)] + ((-q1-q2)/(-q*q1-q2))*B[(0, 0, 1)]
++ B[(-1, 0, 0)] + ((q*q1^6+q*q1^5*q2+q1*q2^5+q2^6)/(q^3*q1^6+q^2*q1^5*q2+q*q1*q2^5+q2^6))*B[(1, 0, 0)] + ((q1+q2)/(q*q1+q2))*B[(0, -1, 0)] + ((q1+q2)/(q*q1+q2))*B[(0, 1, 0)] + ((q1+q2)/(q*q1+q2))*B[(0, 0, -1)] + ((q1+q2)/(q*q1+q2))*B[(0, 0, 1)]
+
+ sage: E[omega[2]]
+ ((-q1*q2^3-q2^4)/(q*q1^4-q2^4))*B[(1, 0, 0)] + B[(0, 1, 0)]
+@@ -567,14 +566,7 @@ class NonSymmetricMacdonaldPolynomials(CherednikOperatorsEigenvectors):
+ + ((-q1*q2-q2^2)/(q*q1^2-q2^2))*B[(0, 0, -1)] + ((q1*q2+q2^2)/(-q*q1^2+q2^2))*B[(0, 0, 1)]
+
+ sage: E[-omega[1]-omega[2]]
+- ((-q^3*q1^6-q^3*q1^5*q2-2*q^2*q1^6-3*q^2*q1^5*q2+q^2*q1^4*q2^2+2*q^2*q1^3*q2^3+q*q1^5*q2+2*q*q1^4*q2^2-q*q1^3*q2^3-2*q*q1^2*q2^4+q*q1*q2^5+q*q2^6-q1^3*q2^3-q1^2*q2^4+2*q1*q2^5+2*q2^6)/(-q^4*q1^6-q^3*q1^5*q2+q^3*q1^4*q2^2-q*q1^2*q2^4+q*q1*q2^5+q2^6))*B[(0, 0, 0)] + B[(-1, -1, 0)]
+- + ((q*q1^4+q*q1^3*q2+q1*q2^3+q2^4)/(q^3*q1^4+q^2*q1^3*q2+q*q1*q2^3+q2^4))*B[(-1, 1, 0)] + ((q1+q2)/(q*q1+q2))*B[(-1, 0, -1)] + ((-q1-q2)/(-q*q1-q2))*B[(-1, 0, 1)]
+- + ((q*q1^4+q*q1^3*q2+q1*q2^3+q2^4)/(q^3*q1^4+q^2*q1^3*q2+q*q1*q2^3+q2^4))*B[(1, -1, 0)]
+- + ((-q^2*q1^6-q^2*q1^5*q2-q*q1^5*q2+q*q1^3*q2^3+q1^5*q2+q1^4*q2^2-q1^3*q2^3-q1^2*q2^4+q1*q2^5+q2^6)/(-q^4*q1^6-q^3*q1^5*q2+q^3*q1^4*q2^2-q*q1^2*q2^4+q*q1*q2^5+q2^6))*B[(1, 1, 0)]
+- + ((-q*q1^4-2*q*q1^3*q2-q*q1^2*q2^2+q1^3*q2+q1^2*q2^2-q1*q2^3-q2^4)/(-q^3*q1^4-q^2*q1^3*q2-q*q1*q2^3-q2^4))*B[(1, 0, -1)]
+- + ((-q*q1^4-2*q*q1^3*q2-q*q1^2*q2^2+q1^3*q2+q1^2*q2^2-q1*q2^3-q2^4)/(-q^3*q1^4-q^2*q1^3*q2-q*q1*q2^3-q2^4))*B[(1, 0, 1)] + ((q1+q2)/(q*q1+q2))*B[(0, -1, -1)]
+- + ((-q1-q2)/(-q*q1-q2))*B[(0, -1, 1)] + ((q*q1^4+2*q*q1^3*q2+q*q1^2*q2^2-q1^3*q2-q1^2*q2^2+q1*q2^3+q2^4)/(q^3*q1^4+q^2*q1^3*q2+q*q1*q2^3+q2^4))*B[(0, 1, -1)]
+- + ((q*q1^4+2*q*q1^3*q2+q*q1^2*q2^2-q1^3*q2-q1^2*q2^2+q1*q2^3+q2^4)/(q^3*q1^4+q^2*q1^3*q2+q*q1*q2^3+q2^4))*B[(0, 1, 1)]
++ ((q^3*q1^6+q^3*q1^5*q2+2*q^2*q1^6+3*q^2*q1^5*q2-q^2*q1^4*q2^2-2*q^2*q1^3*q2^3-q*q1^5*q2-2*q*q1^4*q2^2+q*q1^3*q2^3+2*q*q1^2*q2^4-q*q1*q2^5-q*q2^6+q1^3*q2^3+q1^2*q2^4-2*q1*q2^5-2*q2^6)/(q^4*q1^6+q^3*q1^5*q2-q^3*q1^4*q2^2+q*q1^2*q2^4-q*q1*q2^5-q2^6))*B[(0, 0, 0)] + B[(-1, -1, 0)] + ((q*q1^4+q*q1^3*q2+q1*q2^3+q2^4)/(q^3*q1^4+q^2*q1^3*q2+q*q1*q2^3+q2^4))*B[(-1, 1, 0)] + ((q1+q2)/(q*q1+q2))*B[(-1, 0, -1)] + ((-q1-q2)/(-q*q1-q2))*B[(-1, 0, 1)] + ((q*q1^4+q*q1^3*q2+q1*q2^3+q2^4)/(q^3*q1^4+q^2*q1^3*q2+q*q1*q2^3+q2^4))*B[(1, -1, 0)] + ((q^2*q1^6+q^2*q1^5*q2+q*q1^5*q2-q*q1^3*q2^3-q1^5*q2-q1^4*q2^2+q1^3*q2^3+q1^2*q2^4-q1*q2^5-q2^6)/(q^4*q1^6+q^3*q1^5*q2-q^3*q1^4*q2^2+q*q1^2*q2^4-q*q1*q2^5-q2^6))*B[(1, 1, 0)] + ((q*q1^4+2*q*q1^3*q2+q*q1^2*q2^2-q1^3*q2-q1^2*q2^2+q1*q2^3+q2^4)/(q^3*q1^4+q^2*q1^3*q2+q*q1*q2^3+q2^4))*B[(1, 0, -1)] + ((q*q1^4+2*q*q1^3*q2+q*q1^2*q2^2-q1^3*q2-q1^2*q2^2+q1*q2^3+q2^4)/(q^3*q1^4+q^2*q1^3*q2+q*q1*q2^3+q2^4))*B[(1, 0, 1)] + ((q1+q2)/(q*q1+q2))*B[(0, -1, -1)] + ((q1
+q2)/(q*q1+q2))*B[(0, -1, 1)] + ((q*q1^4+2*q*q1^3*q2+q*q1^2*q2^2-q1^3*q2-q1^2*q2^2+q1*q2^3+q2^4)/(q^3*q1^4+q^2*q1^3*q2+q*q1*q2^3+q2^4))*B[(0, 1, -1)] + ((q*q1^4+2*q*q1^3*q2+q*q1^2*q2^2-q1^3*q2-q1^2*q2^2+q1*q2^3+q2^4)/(q^3*q1^4+q^2*q1^3*q2+q*q1*q2^3+q2^4))*B[(0, 1, 1)]
+
+ sage: E[omega[1]-omega[2]]
+ ((q^3*q1^7+q^3*q1^6*q2-q*q1*q2^6-q*q2^7)/(q^3*q1^7-q^2*q1^5*q2^2+q*q1^2*q2^5-q2^7))*B[(0, 0, 0)] + B[(1, -1, 0)]
+@@ -812,7 +804,7 @@ class NonSymmetricMacdonaldPolynomials(CherednikOperatorsEigenvectors):
+ ((-q*q1*q2^3-q*q2^4)/(q^2*q1^4-q2^4))*B[(0, 0)] + B[(1, 0)]
+
+ sage: E[2*omega[2]] # long time # not checked against Bogdan's notes, but a good self-consistency test
+- ((-q^12*q1^6-q^12*q1^5*q2+2*q^10*q1^5*q2+5*q^10*q1^4*q2^2+3*q^10*q1^3*q2^3+2*q^8*q1^5*q2+4*q^8*q1^4*q2^2+q^8*q1^3*q2^3-q^8*q1^2*q2^4+q^8*q1*q2^5+q^8*q2^6-q^6*q1^3*q2^3+q^6*q1^2*q2^4+4*q^6*q1*q2^5+2*q^6*q2^6+q^4*q1^3*q2^3+3*q^4*q1^2*q2^4+4*q^4*q1*q2^5+2*q^4*q2^6)/(-q^12*q1^6-q^10*q1^5*q2-q^8*q1^3*q2^3+q^6*q1^4*q2^2-q^6*q1^2*q2^4+q^4*q1^3*q2^3+q^2*q1*q2^5+q2^6))*B[(0, 0)] + ((q^7*q1^2*q2+2*q^7*q1*q2^2+q^7*q2^3+q^5*q1^2*q2+2*q^5*q1*q2^2+q^5*q2^3)/(-q^8*q1^3-q^6*q1^2*q2+q^2*q1*q2^2+q2^3))*B[(-1, 0)] + ((q^6*q1*q2+q^6*q2^2)/(-q^6*q1^2+q2^2))*B[(-1, -1)] + ((q^6*q1^2*q2+2*q^6*q1*q2^2+q^6*q2^3+q^4*q1^2*q2+2*q^4*q1*q2^2+q^4*q2^3)/(-q^8*q1^3-q^6*q1^2*q2+q^2*q1*q2^2+q2^3))*B[(-1, 1)] + ((q^3*q1*q2+q^3*q2^2)/(-q^6*q1^2+q2^2))*B[(-1, 2)] + ((-q^7*q1^3-q^7*q1^2*q2+q^7*q1*q2^2+q^7*q2^3+2*q^5*q1^2*q2+4*q^5*q1*q2^2+2*q^5*q2^3+2*q^3*q1^2*q2+4*q^3*q1*q2^2+2*q^3*q2^3)/(-q^8*q1^3-q^6*q1^2*q2+q^2*q1*q2^2+q2^3))*B[(1, 0)] + ((-q^6*q1^2*q2-2*q^6*q1*q2^2-q^6*q2^3-q^4*q1^2*q2-2*q^4*q1*q2^2-q^4*q2^3
)/(q^8*q1^3+q^6*q1^2*q2-q^2*q1*q2^2-q2^3))*B[(1, -1)] + ((q^8*q1^3+q^8*q1^2*q2+q^6*q1^3+q^6*q1^2*q2-q^6*q1*q2^2-q^6*q2^3-2*q^4*q1^2*q2-4*q^4*q1*q2^2-2*q^4*q2^3-q^2*q1^2*q2-3*q^2*q1*q2^2-2*q^2*q2^3)/(q^8*q1^3+q^6*q1^2*q2-q^2*q1*q2^2-q2^3))*B[(1, 1)] + ((-q^5*q1^2-q^5*q1*q2+q^3*q1*q2+q^3*q2^2+q*q1*q2+q*q2^2)/(-q^6*q1^2+q2^2))*B[(1, 2)] + ((-q^6*q1^2-q^6*q1*q2+q^4*q1*q2+q^4*q2^2+q^2*q1*q2+q^2*q2^2)/(-q^6*q1^2+q2^2))*B[(2, 0)] + ((q^3*q1*q2+q^3*q2^2)/(-q^6*q1^2+q2^2))*B[(2, -1)] + ((-q^5*q1^2-q^5*q1*q2+q^3*q1*q2+q^3*q2^2+q*q1*q2+q*q2^2)/(-q^6*q1^2+q2^2))*B[(2, 1)] + B[(2, 2)] + ((-q^7*q1^2*q2-2*q^7*q1*q2^2-q^7*q2^3-q^5*q1^2*q2-2*q^5*q1*q2^2-q^5*q2^3)/(q^8*q1^3+q^6*q1^2*q2-q^2*q1*q2^2-q2^3))*B[(0, -1)] + ((q^7*q1^3+q^7*q1^2*q2-q^7*q1*q2^2-q^7*q2^3-2*q^5*q1^2*q2-4*q^5*q1*q2^2-2*q^5*q2^3-2*q^3*q1^2*q2-4*q^3*q1*q2^2-2*q^3*q2^3)/(q^8*q1^3+q^6*q1^2*q2-q^2*q1*q2^2-q2^3))*B[(0, 1)] + ((-q^6*q1^2-q^6*q1*q2+q^4*q1*q2+q^4*q2^2+q^2*q1*q2+q^2*q2^2)/(-q^6*q1^2+q2^2))*B[(0, 2)]
++ ((-q^12*q1^6-q^12*q1^5*q2+2*q^10*q1^5*q2+5*q^10*q1^4*q2^2+3*q^10*q1^3*q2^3+2*q^8*q1^5*q2+4*q^8*q1^4*q2^2+q^8*q1^3*q2^3-q^8*q1^2*q2^4+q^8*q1*q2^5+q^8*q2^6-q^6*q1^3*q2^3+q^6*q1^2*q2^4+4*q^6*q1*q2^5+2*q^6*q2^6+q^4*q1^3*q2^3+3*q^4*q1^2*q2^4+4*q^4*q1*q2^5+2*q^4*q2^6)/(-q^12*q1^6-q^10*q1^5*q2-q^8*q1^3*q2^3+q^6*q1^4*q2^2-q^6*q1^2*q2^4+q^4*q1^3*q2^3+q^2*q1*q2^5+q2^6))*B[(0, 0)] + ((q^7*q1^2*q2+2*q^7*q1*q2^2+q^7*q2^3+q^5*q1^2*q2+2*q^5*q1*q2^2+q^5*q2^3)/(-q^8*q1^3-q^6*q1^2*q2+q^2*q1*q2^2+q2^3))*B[(-1, 0)] + ((-q^6*q1*q2-q^6*q2^2)/(q^6*q1^2-q2^2))*B[(-1, -1)] + ((q^6*q1^2*q2+2*q^6*q1*q2^2+q^6*q2^3+q^4*q1^2*q2+2*q^4*q1*q2^2+q^4*q2^3)/(-q^8*q1^3-q^6*q1^2*q2+q^2*q1*q2^2+q2^3))*B[(-1, 1)] + ((-q^3*q1*q2-q^3*q2^2)/(q^6*q1^2-q2^2))*B[(-1, 2)] + ((q^7*q1^3+q^7*q1^2*q2-q^7*q1*q2^2-q^7*q2^3-2*q^5*q1^2*q2-4*q^5*q1*q2^2-2*q^5*q2^3-2*q^3*q1^2*q2-4*q^3*q1*q2^2-2*q^3*q2^3)/(q^8*q1^3+q^6*q1^2*q2-q^2*q1*q2^2-q2^3))*B[(1, 0)] + ((q^6*q1^2*q2+2*q^6*q1*q2^2+q^6*q2^3+q^4*q1^2*q2+2*q^4*q1*q2^2+q^4*q2^3)/(
-q^8*q1^3-q^6*q1^2*q2+q^2*q1*q2^2+q2^3))*B[(1, -1)] + ((q^8*q1^3+q^8*q1^2*q2+q^6*q1^3+q^6*q1^2*q2-q^6*q1*q2^2-q^6*q2^3-2*q^4*q1^2*q2-4*q^4*q1*q2^2-2*q^4*q2^3-q^2*q1^2*q2-3*q^2*q1*q2^2-2*q^2*q2^3)/(q^8*q1^3+q^6*q1^2*q2-q^2*q1*q2^2-q2^3))*B[(1, 1)] + ((q^5*q1^2+q^5*q1*q2-q^3*q1*q2-q^3*q2^2-q*q1*q2-q*q2^2)/(q^6*q1^2-q2^2))*B[(1, 2)] + ((-q^6*q1^2-q^6*q1*q2+q^4*q1*q2+q^4*q2^2+q^2*q1*q2+q^2*q2^2)/(-q^6*q1^2+q2^2))*B[(2, 0)] + ((-q^3*q1*q2-q^3*q2^2)/(q^6*q1^2-q2^2))*B[(2, -1)] + ((-q^5*q1^2-q^5*q1*q2+q^3*q1*q2+q^3*q2^2+q*q1*q2+q*q2^2)/(-q^6*q1^2+q2^2))*B[(2, 1)] + B[(2, 2)] + ((q^7*q1^2*q2+2*q^7*q1*q2^2+q^7*q2^3+q^5*q1^2*q2+2*q^5*q1*q2^2+q^5*q2^3)/(-q^8*q1^3-q^6*q1^2*q2+q^2*q1*q2^2+q2^3))*B[(0, -1)] + ((q^7*q1^3+q^7*q1^2*q2-q^7*q1*q2^2-q^7*q2^3-2*q^5*q1^2*q2-4*q^5*q1*q2^2-2*q^5*q2^3-2*q^3*q1^2*q2-4*q^3*q1*q2^2-2*q^3*q2^3)/(q^8*q1^3+q^6*q1^2*q2-q^2*q1*q2^2-q2^3))*B[(0, 1)] + ((q^6*q1^2+q^6*q1*q2-q^4*q1*q2-q^4*q2^2-q^2*q1*q2-q^2*q2^2)/(q^6*q1^2-q2^2))*B[(0, 2)]
+ sage: E.recursion(2*omega[2])
+ [0, 1, 0, 2, 1, 0, 2, 1, 0]
+
+@@ -997,7 +989,7 @@ class NonSymmetricMacdonaldPolynomials(CherednikOperatorsEigenvectors):
+ sage: L0 = E.keys()
+ sage: omega = L0.fundamental_weights()
+ sage: E[2*omega[2]]
+- ((q*q1+q*q2)/(q*q1+q2))*B[(1, 2, 1)] + ((q*q1+q*q2)/(q*q1+q2))*B[(2, 1, 1)] + B[(2, 2, 0)]
++ ((-q*q1-q*q2)/(-q*q1-q2))*B[(1, 2, 1)] + ((-q*q1-q*q2)/(-q*q1-q2))*B[(2, 1, 1)] + B[(2, 2, 0)]
+ sage: for d in range(4): # long time (9s)
+ ....: for weight in IntegerVectors(d,3).map(list).map(L0):
+ ....: eigenvalues = E.eigenvalues(E[L0(weight)])
+diff --git a/src/sage/combinat/sf/macdonald.py b/src/sage/combinat/sf/macdonald.py
+index e664e21..cc525b4 100644
+--- a/src/sage/combinat/sf/macdonald.py
++++ b/src/sage/combinat/sf/macdonald.py
+@@ -483,7 +483,7 @@ class Macdonald(UniqueRepresentation):
+ sage: Ht = Sym.macdonald().Ht()
+ sage: s = Sym.schur()
+ sage: Ht(s([2,1]))
+- ((-q)/(-q*t^2+t^3+q^2-q*t))*McdHt[1, 1, 1] + ((q^2+q*t+t^2)/(-q^2*t^2+q^3+t^3-q*t))*McdHt[2, 1] + (t/(-q^3+q^2*t+q*t-t^2))*McdHt[3]
++ (q/(q*t^2-t^3-q^2+q*t))*McdHt[1, 1, 1] + ((-q^2-q*t-t^2)/(q^2*t^2-q^3-t^3+q*t))*McdHt[2, 1] + (t/(-q^3+q^2*t+q*t-t^2))*McdHt[3]
+ sage: Ht(s([2]))
+ ((-q)/(-q+t))*McdHt[1, 1] + (t/(-q+t))*McdHt[2]
+ """
+@@ -901,7 +901,7 @@ class MacdonaldPolynomials_generic(sfa.SymmetricFunctionAlgebra_generic):
+ sage: Q._multiply(Q[1],Q[2])
+ McdQ[2, 1] + ((q^2*t-q^2+q*t-q+t-1)/(q^2*t-1))*McdQ[3]
+ sage: Ht._multiply(Ht[1],Ht[2])
+- ((-q^2+1)/(-q^2+t))*McdHt[2, 1] + ((-t+1)/(q^2-t))*McdHt[3]
++ ((q^2-1)/(q^2-t))*McdHt[2, 1] + ((t-1)/(-q^2+t))*McdHt[3]
+ """
+ return self( self._s(left)*self._s(right) )
+
+diff --git a/src/sage/interfaces/singular.py b/src/sage/interfaces/singular.py
+index 88a33b0..a7cf5ea 100644
+--- a/src/sage/interfaces/singular.py
++++ b/src/sage/interfaces/singular.py
+@@ -191,13 +191,21 @@ The 1x1 and 2x2 minors::
+ 6*y+2*x^3-6*x^2*y,
+ 6*x^2*y-6*x*y^2,
+ 6*x^2*y-6*x*y^2,
+- 6*x+6*x*y^2-2*y^3
++ 6*x+6*x*y^2-2*y^3,
++ 0,
++ 0,
++ 0,
++ 0
+ sage: H.minor(2)
+ 12*y+4*x^3-12*x^2*y,
+ 12*x^2*y-12*x*y^2,
+ 12*x^2*y-12*x*y^2,
+ 12*x+12*x*y^2-4*y^3,
+- -36*x*y-12*x^4+36*x^3*y-36*x*y^3+12*y^4+24*x^4*y^2-32*x^3*y^3+24*x^2*y^4
++ -36*x*y-12*x^4+36*x^3*y-36*x*y^3+12*y^4+24*x^4*y^2-32*x^3*y^3+24*x^2*y^4,
++ 0,
++ 0,
++ 0,
++ 0
+
+ ::
+
+diff --git a/src/sage/libs/singular/function.pyx b/src/sage/libs/singular/function.pyx
+index 0fea70a..26c74d0 100644
+--- a/src/sage/libs/singular/function.pyx
++++ b/src/sage/libs/singular/function.pyx
+@@ -1257,7 +1257,7 @@ cdef class SingularFunction(SageObject):
+ Traceback (most recent call last):
+ ...
+ RuntimeError: error in Singular function call 'size':
+- Wrong number of arguments (got 2 arguments, arity code is 300)
++ Wrong number of arguments (got 2 arguments, arity code is 302)
+ sage: size('foobar', ring=P)
+ 6
+
+@@ -1308,7 +1308,7 @@ cdef class SingularFunction(SageObject):
+ ...
+ RuntimeError: error in Singular function call 'triangL':
+ The input is no groebner basis.
+- leaving triang.lib::triangL
++ leaving triang.lib::triangL (0)
+
+ Flush any stray output -- see :trac:`28622`::
+
+@@ -1671,17 +1671,17 @@ def singular_function(name):
+ Traceback (most recent call last):
+ ...
+ RuntimeError: error in Singular function call 'factorize':
+- Wrong number of arguments (got 0 arguments, arity code is 303)
++ Wrong number of arguments (got 0 arguments, arity code is 305)
+ sage: factorize(f, 1, 2)
+ Traceback (most recent call last):
+ ...
+ RuntimeError: error in Singular function call 'factorize':
+- Wrong number of arguments (got 3 arguments, arity code is 303)
++ Wrong number of arguments (got 3 arguments, arity code is 305)
+ sage: factorize(f, 1, 2, 3)
+ Traceback (most recent call last):
+ ...
+ RuntimeError: error in Singular function call 'factorize':
+- Wrong number of arguments (got 4 arguments, arity code is 303)
++ Wrong number of arguments (got 4 arguments, arity code is 305)
+
+ The Singular function ``list`` can be called with any number of
+ arguments::
+diff --git a/src/sage/rings/asymptotic/asymptotics_multivariate_generating_functions.py b/src/sage/rings/asymptotic/asymptotics_multivariate_generating_functions.py
+index 8b9367e..ef04d4f 100644
+--- a/src/sage/rings/asymptotic/asymptotics_multivariate_generating_functions.py
++++ b/src/sage/rings/asymptotic/asymptotics_multivariate_generating_functions.py
+@@ -1579,7 +1579,7 @@ class FractionWithFactoredDenominator(RingElement):
+ (1, [(x*y + x + y - 1, 2)])
+ sage: alpha = [4, 3]
+ sage: decomp = F.asymptotic_decomposition(alpha); decomp
+- (0, []) + (-3/2*r*(1/y + 1) - 1/2/y - 1/2, [(x*y + x + y - 1, 1)])
++ (0, []) + (-2*r*(1/x + 1) - 1/2/x - 1/2, [(x*y + x + y - 1, 1)])
+ sage: F1 = decomp[1]
+ sage: p = {y: 1/3, x: 1/2}
+ sage: asy = F1.asymptotics(p, alpha, 2, verbose=True)
+@@ -1613,7 +1613,7 @@ class FractionWithFactoredDenominator(RingElement):
+ sage: alpha = [3, 3, 2]
+ sage: decomp = F.asymptotic_decomposition(alpha); decomp
+ (0, []) +
+- (-16*r*(3/y - 4/z) - 16/y + 32/z,
++ (16*r*(3/x - 2/z) + 16/x - 16/z,
+ [(x + 2*y + z - 4, 1), (2*x + y + z - 4, 1)])
+ sage: F1 = decomp[1]
+ sage: p = {x: 1, y: 1, z: 1}
+diff --git a/src/sage/rings/polynomial/multi_polynomial_element.py b/src/sage/rings/polynomial/multi_polynomial_element.py
+index d86833f..3742439 100644
+--- a/src/sage/rings/polynomial/multi_polynomial_element.py
++++ b/src/sage/rings/polynomial/multi_polynomial_element.py
+@@ -2231,7 +2231,7 @@ def degree_lowest_rational_function(r, x):
+ ::
+
+ sage: r = f/g; r
+- (-b*c^2 + 2)/(a*b^3*c^6 - 2*a*c)
++ (-2*b*c^2 - 1)/(2*a*b^3*c^6 + a*c)
+ sage: degree_lowest_rational_function(r,a)
+ -1
+ sage: degree_lowest_rational_function(r,b)
+diff --git a/src/sage/rings/polynomial/multi_polynomial_ideal.py b/src/sage/rings/polynomial/multi_polynomial_ideal.py
+index f025b3a..94e130d 100644
+--- a/src/sage/rings/polynomial/multi_polynomial_ideal.py
++++ b/src/sage/rings/polynomial/multi_polynomial_ideal.py
+@@ -154,7 +154,7 @@ when the system has no solutions over the rationals.
+ which is not 1. ::
+
+ sage: I.groebner_basis()
+- [x + 130433*y + 59079*z, y^2 + 3*y + 17220, y*z + 5*y + 14504, 2*y + 158864, z^2 + 17223, 2*z + 41856, 164878]
++ [x + y + 57119*z + 4, y^2 + 3*y + 17220, y*z + y + 26532, 2*y + 158864, z^2 + 17223, 2*z + 41856, 164878]
+
+ Now for each prime `p` dividing this integer 164878, the Groebner
+ basis of I modulo `p` will be non-trivial and will thus give a
+@@ -1567,8 +1567,8 @@ class MPolynomialIdeal_singular_repr(
+ sage: I2 = y*R
+ sage: I3 = (x, y)*R
+ sage: I4 = (x^2 + x*y*z, y^2 - z^3*y, z^3 + y^5*x*z)*R
+- sage: I1.intersection(I2, I3, I4)
+- Ideal (x*y*z^20 - x*y*z^3, x*y^2 - x*y*z^3, x^2*y + x*y*z^4) of Multivariate Polynomial Ring in x, y, z over Rational Field
++ sage: I1.intersection(I2, I3, I4).groebner_basis()
++ [x^2*y + x*y*z^4, x*y^2 - x*y*z^3, x*y*z^20 - x*y*z^3]
+
+ The ideals must share the same ring::
+
+@@ -4008,7 +4008,7 @@ class MPolynomialIdeal( MPolynomialIdeal_singular_repr, \
+
+ sage: J.groebner_basis.set_cache(gb)
+ sage: ideal(J.transformed_basis()).change_ring(P).interreduced_basis() # testing trac 21884
+- [a - 60*c^3 + 158/7*c^2 + 8/7*c - 1, b + 30*c^3 - 79/7*c^2 + 3/7*c, c^4 - 10/21*c^3 + 1/84*c^2 + 1/84*c]
++ ...[a - 60*c^3 + 158/7*c^2 + 8/7*c - 1, b + 30*c^3 - 79/7*c^2 + 3/7*c, c^4 - 10/21*c^3 + 1/84*c^2 + 1/84*c]
+
+ Giac's gbasis over `\QQ` can benefit from a probabilistic lifting and
+ multi threaded operations::
+@@ -4111,9 +4111,9 @@ 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 - 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,
++ [b^3 + b*c^2 + 12*c^3 + b^2 + b*c - 4*c^2,
++ 2*b*c^2 - 6*c^3 - b^2 - b*c + 2*c^2,
++ 42*c^3 + b^2 + 2*b*c - 14*c^2 + b,
+ 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]
+diff --git a/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx b/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx
+index 1758424..553d22d 100644
+--- a/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx
++++ b/src/sage/rings/polynomial/multi_polynomial_libsingular.pyx
+@@ -1349,7 +1349,7 @@ cdef class MPolynomialRing_libsingular(MPolynomialRing_base):
+ sage: R = IntegerModRing(15)['x,y']
+ sage: singular(R)
+ polynomial ring, over a ring (with zero-divisors), global ordering
+- // coefficients: ZZ/bigint(15)
++ // coefficients: ZZ/...(15)
+ // number of vars : 2
+ // block 1 : ordering dp
+ // : names x y
+diff --git a/src/sage/rings/polynomial/plural.pyx b/src/sage/rings/polynomial/plural.pyx
+index c2792ae..aa2ef59 100644
+--- a/src/sage/rings/polynomial/plural.pyx
++++ b/src/sage/rings/polynomial/plural.pyx
+@@ -390,28 +390,30 @@ cdef class NCPolynomialRing_plural(Ring):
+ TESTS:
+
+ This example caused a segmentation fault with a previous version
+- of this method::
++ of this method. This doctest still results in a segmentation fault
++ occasionally which is difficult to isolate, so this test is partially
++ disabled (:trac:`29528`)::
+
+ sage: import gc
+ sage: from sage.rings.polynomial.plural import NCPolynomialRing_plural
+ sage: from sage.algebras.free_algebra import FreeAlgebra
+ sage: A1.<x,y,z> = FreeAlgebra(QQ, 3)
+ sage: R1 = A1.g_algebra({y*x:x*y-z, z*x:x*z+2*x, z*y:y*z-2*y}, order=TermOrder('degrevlex', 2))
+- sage: A2.<x,y,z> = FreeAlgebra(GF(5), 3)
+- sage: R2 = A2.g_algebra({y*x:x*y-z, z*x:x*z+2*x, z*y:y*z-2*y}, order=TermOrder('degrevlex', 2))
+- sage: A3.<x,y,z> = FreeAlgebra(GF(11), 3)
+- sage: R3 = A3.g_algebra({y*x:x*y-z, z*x:x*z+2*x, z*y:y*z-2*y}, order=TermOrder('degrevlex', 2))
+- sage: A4.<x,y,z> = FreeAlgebra(GF(13), 3)
+- sage: R4 = A4.g_algebra({y*x:x*y-z, z*x:x*z+2*x, z*y:y*z-2*y}, order=TermOrder('degrevlex', 2))
++ sage: A2.<x,y,z> = FreeAlgebra(GF(5), 3) # not tested
++ sage: R2 = A2.g_algebra({y*x:x*y-z, z*x:x*z+2*x, z*y:y*z-2*y}, order=TermOrder('degrevlex', 2)) # not tested
++ sage: A3.<x,y,z> = FreeAlgebra(GF(11), 3) # not tested
++ sage: R3 = A3.g_algebra({y*x:x*y-z, z*x:x*z+2*x, z*y:y*z-2*y}, order=TermOrder('degrevlex', 2)) # not tested
++ sage: A4.<x,y,z> = FreeAlgebra(GF(13), 3) # not tested
++ sage: R4 = A4.g_algebra({y*x:x*y-z, z*x:x*z+2*x, z*y:y*z-2*y}, order=TermOrder('degrevlex', 2)) # not tested
+ sage: _ = gc.collect()
+ sage: foo = R1.gen(0)
+ sage: del foo
+ sage: del R1
+ sage: _ = gc.collect()
+- sage: del R2
+- sage: _ = gc.collect()
+- sage: del R3
+- sage: _ = gc.collect()
++ sage: del R2 # not tested
++ sage: _ = gc.collect() # not tested
++ sage: del R3 # not tested
++ sage: _ = gc.collect() # not tested
+ """
+ singular_ring_delete(self._ring)
+
+@@ -2886,7 +2888,8 @@ cpdef MPolynomialRing_libsingular new_CRing(RingWrap rw, base_ring):
+ self.__ngens = rw.ngens()
+ self.__term_order = TermOrder(rw.ordering_string(), force=True)
+
+- ParentWithGens.__init__(self, base_ring, rw.var_names())
++ ParentWithGens.__init__(self, base_ring, tuple(rw.var_names()),
++ normalize=False)
+ # self._populate_coercion_lists_() # ???
+
+ #MPolynomialRing_generic.__init__(self, base_ring, n, names, order)
+diff --git a/src/sage/rings/polynomial/polynomial_singular_interface.py b/src/sage/rings/polynomial/polynomial_singular_interface.py
+index 74b8b82..beee5ad 100644
+--- a/src/sage/rings/polynomial/polynomial_singular_interface.py
++++ b/src/sage/rings/polynomial/polynomial_singular_interface.py
+@@ -165,7 +165,7 @@ class PolynomialRing_singular_repr:
+ sage: R = IntegerModRing(15)['x,y']
+ sage: singular(R)
+ polynomial ring, over a ring (with zero-divisors), global ordering
+- // coefficients: ZZ/bigint(15)
++ // coefficients: ZZ/...(15)
+ // number of vars : 2
+ // block 1 : ordering dp
+ // : names x y
+diff --git a/src/sage/schemes/curves/projective_curve.py b/src/sage/schemes/curves/projective_curve.py
+index 1091c29..4f5936e 100644
+--- a/src/sage/schemes/curves/projective_curve.py
++++ b/src/sage/schemes/curves/projective_curve.py
+@@ -2001,7 +2001,7 @@ class ProjectivePlaneCurve_finite_field(ProjectivePlaneCurve_field):
+ sage: C = Curve(f); pts = C.rational_points()
+ sage: D = C.divisor([ (3, pts[0]), (-1,pts[1]), (10, pts[5]) ])
+ sage: C.riemann_roch_basis(D)
+- [(-x - 2*y)/(-2*x - 2*y), (-x + z)/(x + y)]
++ [(-2*x + y)/(x + y), (-x + z)/(x + y)]
+
+ .. NOTE::
+
+diff --git a/src/sage/interfaces/singular.py b/src/sage/interfaces/singular.py
+index 5ec54bfb15..1864fd1d37 100644
+--- a/src/sage/interfaces/singular.py
++++ b/src/sage/interfaces/singular.py
+@@ -248,7 +248,7 @@ Groebner basis for some ideal, using Singular through Sage.
+
+ ::
+
+- sage: singular.lib('poly.lib')
++ sage: singular.lib('polylib.lib')
+ sage: singular.ring(32003, '(a,b,c,d,e,f)', 'lp')
+ polynomial ring, over a field, global ordering
+ // coefficients: ZZ/32003
+@@ -268,7 +268,7 @@ We restart everything and try again, but correctly.
+ ::
+
+ sage: singular.quit()
+- sage: singular.lib('poly.lib'); R = singular.ring(32003, '(a,b,c,d,e,f)', 'lp')
++ sage: singular.lib('polylib.lib'); R = singular.ring(32003, '(a,b,c,d,e,f)', 'lp')
+ sage: I = singular.ideal('cyclic(6)')
+ sage: I.groebner()
+ f^48-2554*f^42-15674*f^36+12326*f^30-12326*f^18+15674*f^12+2554*f^6-1,
+diff --git a/src/sage/libs/singular/function.pyx b/src/sage/libs/singular/function.pyx
+index 26c74d0d7f..b8a848312e 100644
+--- a/src/sage/libs/singular/function.pyx
++++ b/src/sage/libs/singular/function.pyx
+@@ -938,7 +938,7 @@ cdef class Converter(SageObject):
+ sage: C = Curve((x-y)*(y-z)*(z-x))
+ sage: I = C.defining_ideal()
+ sage: import sage.libs.singular.function_factory
+- sage: freerank = sage.libs.singular.function_factory.ff.poly__lib.freerank
++ sage: freerank = sage.libs.singular.function_factory.ff.polylib__lib.freerank
+ sage: freerank(I, true)
+ [-1, [x^2*y - x*y^2 - x^2*z + y^2*z + x*z^2 - y*z^2]]
+
+diff --git a/src/sage/rings/ideal.py b/src/sage/rings/ideal.py
+index 72548769de..53076ac62e 100644
+--- a/src/sage/rings/ideal.py
++++ b/src/sage/rings/ideal.py
+@@ -1709,7 +1709,7 @@ def Cyclic(R, n=None, homog=False, singular=None):
+ from sage.interfaces.singular import singular as singular_default
+ singular = singular_default
+
+- singular.lib("poly")
++ singular.lib("polylib")
+ R2 = R.change_ring(RationalField())
+ R2._singular_().set_ring()
+
+@@ -1760,7 +1760,7 @@ def Katsura(R, n=None, homog=False, singular=None):
+ if singular is None:
+ from sage.interfaces.singular import singular as singular_default
+ singular = singular_default
+- singular.lib("poly")
++ singular.lib("polylib")
+ R2 = R.change_ring(RationalField())
+ R2._singular_().set_ring()
+
+diff --git a/src/sage/rings/polynomial/laurent_polynomial_ideal.py b/src/sage/rings/polynomial/laurent_polynomial_ideal.py
+index 886458ff1e..ec8e83ea80 100644
+--- a/src/sage/rings/polynomial/laurent_polynomial_ideal.py
++++ b/src/sage/rings/polynomial/laurent_polynomial_ideal.py
+@@ -470,8 +470,8 @@ class LaurentPolynomialIdeal( Ideal_generic ):
+ sage: p = z^2 + 1; q = z^3 + 2
+ sage: I = P.ideal((p*q^2, y-z^2))
+ sage: I.associated_primes()
+- (Ideal (y + 1, z^2 + 1) of Multivariate Laurent Polynomial Ring in x, y, z over Rational Field,
+- Ideal (z^2 - y, y*z + 2, y^2 + 2*z) of Multivariate Laurent Polynomial Ring in x, y, z over Rational Field)
++ (Ideal (z^2 - y, y*z + 2, y^2 + 2*z) of Multivariate Laurent Polynomial Ring in x, y, z over Rational Field,
++ Ideal (y + 1, z^2 + 1) of Multivariate Laurent Polynomial Ring in x, y, z over Rational Field)
+ """
+ l = self.polynomial_ideal(saturate=False).associated_primes()
+ l2 = [self.ring().ideal(I.gens(), hint=I) for I in l]
+@@ -490,8 +490,8 @@ class LaurentPolynomialIdeal( Ideal_generic ):
+ sage: p = z^2 + 1; q = z^3 + 2
+ sage: I = P.ideal((p*q^2, y-z^2))
+ sage: I.minimal_associated_primes()
+- (Ideal (z^2 + 1, -z^2 + y) of Multivariate Laurent Polynomial Ring in x, y, z over Rational Field,
+- Ideal (z^3 + 2, -z^2 + y) of Multivariate Laurent Polynomial Ring in x, y, z over Rational Field)
++ (Ideal (z^3 + 2, -z^2 + y) of Multivariate Laurent Polynomial Ring in x, y, z over Rational Field,
++ Ideal (z^2 + 1, -z^2 + y) of Multivariate Laurent Polynomial Ring in x, y, z over Rational Field)
+ """
+ l = self.polynomial_ideal(saturate=saturate).minimal_associated_primes()
+ l2 = [self.ring().ideal(I.gens(), hint=I) for I in l]
+diff --git a/src/sage/rings/polynomial/multi_polynomial_ideal.py b/src/sage/rings/polynomial/multi_polynomial_ideal.py
+index 5cd58e99ce..b09123ac5c 100644
+--- a/src/sage/rings/polynomial/multi_polynomial_ideal.py
++++ b/src/sage/rings/polynomial/multi_polynomial_ideal.py
+@@ -711,16 +711,16 @@ 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^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,
+ Ideal (z^3 + 2, y - z^2) of Multivariate Polynomial Ring in x, y, z over Rational Field),
+- (Ideal (z^2 + 1, y - z^2) of Multivariate Polynomial Ring in x, y, z over Rational Field,
+- Ideal (z^2 + 1, 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)]
++
++ sage: I.primary_decomposition_complete(algorithm = 'gtz')
++ [(Ideal (z^2 + 1, y - z^2) of Multivariate Polynomial Ring in x, y, z over Rational Field,
++ Ideal (z^2 + 1, y - z^2) 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: from functools import reduce
+ sage: reduce(lambda Qi,Qj: Qi.intersection(Qj), [Qi for (Qi,radQi) in pd]) == I
+@@ -823,8 +823,8 @@ 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^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^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]
+
+ ::
+
+@@ -895,8 +895,8 @@ 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^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]
++ [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]
+
+ ALGORITHM:
+
+@@ -1617,10 +1617,8 @@ class MPolynomialIdeal_singular_repr(
+ sage: p = z^2 + 1; q = z^3 + 2
+ sage: I = (p*q^2, y-z^2)*R
+ sage: I.minimal_associated_primes ()
+- [Ideal (z^2 + 1, -z^2 + y) of Multivariate Polynomial Ring
+- in x, y, z over Rational Field, Ideal (z^3 + 2, -z^2 + y)
+- of Multivariate Polynomial Ring in x, y, z over Rational
+- Field]
++ [Ideal (z^3 + 2, -z^2 + y) of Multivariate Polynomial Ring in x, y, z over Rational Field,
++ Ideal (z^2 + 1, -z^2 + y) of Multivariate Polynomial Ring in x, y, z over Rational Field]
+
+ ALGORITHM:
+
+@@ -2699,7 +2697,7 @@ class MPolynomialIdeal_singular_repr(
+ return out
+ elif algorithm == 'singular':
+ import sage.libs.singular.function_factory
+- hilbPoly = sage.libs.singular.function_factory.ff.poly__lib.hilbPoly
++ hilbPoly = sage.libs.singular.function_factory.ff.polylib__lib.hilbPoly
+
+ hp = hilbPoly(self)
+ t = ZZ['t'].gen()
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