path: root/sagemath-singular-4.1.2.patch

diff --git a/src/doc/en/constructions/algebraic_geometry.rst b/src/doc/en/constructions/algebraic_geometry.rst
index 3933bf0839..76b173d80a 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: L       # random
@@ -329,7 +329,7 @@ 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 7391dd9812..7234f91456 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 e7fed21ada..e9c1c9d908 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 7e5f2bbe97..d1d162c3b4 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 39cfa4dfed..b520c4cab8 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 cannot 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))
@@ -662,7 +679,7 @@ 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")
@@ -678,8 +695,10 @@ 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)
 
     ###########################
@@ -875,3 +894,28 @@ 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 f1430ee77c..c16803280b 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
@@ -275,9 +302,32 @@ 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 51f4113706..ba42ed1524 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 35377724c9..ee8ddec7dd 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 e664e21b5a..cc525b4d7e 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 e0faf1409e..5c02e8f0fb 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 0fea70ad25..26c74d0d7f 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 8b9367ea1a..ef04d4f2b0 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 72e25ebd02..49b4298bc0 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 e45a47f4d9..2a6d9fc93a 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::
 
@@ -4012,7 +4012,7 @@ 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::
@@ -4115,9 +4115,9 @@ 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 836afdcdcd..4129c2c8fd 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 c2792aec88..aa2ef59e79 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 37f131b585..d9c33d9c2b 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 1091c29c20..4f5936edb8 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::