sage.rings.polynomial: Update from #35095

Author: Matthias Koeppe

src/sage/rings/polynomial/multi_polynomial_element.py

@@ -1090,7 +1090,7 @@ def global_height(self, prec=None):
         from sage.categories.number_fields import NumberFields
 
         K = self.base_ring()
-        if K in NumberFields() or isinstance(K, (sage.rings.abc.Order, IntegerRing_class)):
+        if K in NumberFields() or isinstance(K, (sage.rings.abc.Order, sage.rings.integer_ring.IntegerRing_class)):
             from sage.schemes.projective.projective_space import ProjectiveSpace
             Pr = ProjectiveSpace(K, self.number_of_terms()-1)
             return Pr.point(self.coefficients()).global_height(prec=prec)

src/sage/rings/polynomial/multi_polynomial_ideal.py

@@ -4650,10 +4650,10 @@ def groebner_basis(self, algorithm='', deg_bound=None, mult_bound=None, prot=Fal
         if not algorithm:
             try:
                 gb = self._groebner_basis_libsingular("groebner", deg_bound=deg_bound, mult_bound=mult_bound, *args, **kwds)
-            except (TypeError, NameError): # conversion to Singular not supported
+            except (TypeError, NameError, ImportError): # conversion to Singular not supported
                 try:
                     gb = self._groebner_basis_singular("groebner", deg_bound=deg_bound, mult_bound=mult_bound, *args, **kwds)
-                except (TypeError, NameError, NotImplementedError): # conversion to Singular not supported
+                except (TypeError, NameError, NotImplementedError, ImportError): # conversion to Singular not supported
                     R = self.ring()
                     B = R.base_ring()
                     if R.ngens() == 0:

src/sage/rings/polynomial/ore_polynomial_element.pyx

@@ -1290,7 +1290,8 @@ cdef class OrePolynomial(AlgebraElement):
             sage: a.left_gcd(b)
             Traceback (most recent call last):
             ...
-            NotImplementedError: inversion of the twisting morphism Ring endomorphism of Fraction Field of Univariate Polynomial Ring in t over Rational Field
+            NotImplementedError: inversion of the twisting morphism Ring endomorphism
+            of Fraction Field of Univariate Polynomial Ring in t over Rational Field
                 Defn: t |--> t^2
         """
         if self.base_ring() not in _Fields:

src/sage/rings/polynomial/polynomial_element.pyx

@@ -7946,7 +7946,9 @@ cdef class Polynomial(CommutativePolynomial):
              (-0.1666666666666667? + 0.552770798392567?*I, 1),
              (0.1812324444698754? + 1.083954101317711?*I, 2)]
             sage: p.roots(ring=CIF)
-            [(-0.1666666666666667? - 0.552770798392567?*I, 1), (-0.1666666666666667? + 0.552770798392567?*I, 1), (0.1812324444698754? + 1.083954101317711?*I, 2)]
+            [(-0.1666666666666667? - 0.552770798392567?*I, 1),
+             (-0.1666666666666667? + 0.552770798392567?*I, 1),
+             (0.1812324444698754? + 1.083954101317711?*I, 2)]
 
         In some cases, it is possible to isolate the roots of polynomials over
         complex ball fields::
@@ -8294,7 +8296,8 @@ cdef class Polynomial(CommutativePolynomial):
             sage: K.<a> = Qq(3).extension(x^2 + 1)                                      # needs sage.rings.padics
             sage: (x^2 + 1).roots(K)                                                    # needs sage.rings.padics
             [(a + O(3^20), 1),
-             (2*a + 2*a*3 + 2*a*3^2 + 2*a*3^3 + 2*a*3^4 + 2*a*3^5 + 2*a*3^6 + 2*a*3^7 + 2*a*3^8 + 2*a*3^9 + 2*a*3^10 + 2*a*3^11 + 2*a*3^12 + 2*a*3^13 + 2*a*3^14 + 2*a*3^15 + 2*a*3^16 + 2*a*3^17 + 2*a*3^18 + 2*a*3^19 + O(3^20),
+             (2*a + 2*a*3 + 2*a*3^2 + 2*a*3^3 + 2*a*3^4 + 2*a*3^5 + 2*a*3^6 + 2*a*3^7 + 2*a*3^8 + 2*a*3^9 + 2*a*3^10
+                + 2*a*3^11 + 2*a*3^12 + 2*a*3^13 + 2*a*3^14 + 2*a*3^15 + 2*a*3^16 + 2*a*3^17 + 2*a*3^18 + 2*a*3^19 + O(3^20),
               1)]
 
         Check that :trac:`31710` is fixed::

src/sage/rings/polynomial/polynomial_ring.py

@@ -391,7 +391,7 @@ def _element_constructor_(self, x=None, check=True, is_gen=False,
         Throw a TypeError if any of the coefficients cannot be coerced
         into the base ring (:trac:`6777`)::
 
-            sage: RealField(300)['x']( [ 1, ComplexField(300).gen(), 0 ])               # optional - sage.rings.real_mpfr
+            sage: RealField(300)['x']( [ 1, ComplexField(300).gen(), 0 ])               # needs sage.rings.real_mpfr
             Traceback (most recent call last):
             ...
             TypeError: unable to convert '1.00...00*I' to a real number
@@ -884,7 +884,7 @@ def _magma_init_(self, magma):
 
             sage: k.<a> = GF(9)                                                         # needs sage.rings.finite_rings
             sage: R.<x> = k[]                                                           # needs sage.rings.finite_rings
-            sage: magma(a^2*x^3 + (a+1)*x + a)  # optional - magma, needs sage.rings.finite_rings
+            sage: magma(a^2*x^3 + (a+1)*x + a)  # optional - magma                      # needs sage.rings.finite_rings
             a^2*x^3 + a^2*x + a
         """
         B = magma(self.base_ring())
@@ -1185,6 +1185,7 @@ def cyclotomic_polynomial(self, n):
             x^4 + 1
             sage: R.cyclotomic_polynomial(12)
             x^4 - x^2 + 1
+
             sage: S = PolynomialRing(FiniteField(7), 'x')
             sage: S.cyclotomic_polynomial(12)
             x^4 + 6*x^2 + 1
@@ -2066,15 +2067,15 @@ def __init__(self, base_ring, name="x", sparse=False, implementation=None,
             Sparse Univariate Polynomial Ring in x over Rational Field
             sage: type(R.gen())
             <class 'sage.rings.polynomial.polynomial_ring.PolynomialRing_field_with_category.element_class'>
-            sage: R = PRing(CC, 'x'); R                                                 # optional - sage.rings.real_mpfr
+            sage: R = PRing(CC, 'x'); R                                                 # needs sage.rings.real_mpfr
             Univariate Polynomial Ring in x over Complex Field with 53 bits of precision
-            sage: type(R.gen())                                                         # optional - sage.rings.real_mpfr
+            sage: type(R.gen())                                                         # needs sage.rings.real_mpfr
             <class 'sage.rings.polynomial.polynomial_ring.PolynomialRing_field_with_category.element_class'>
 
         Demonstrate that :trac:`8762` is fixed::
 
             sage: R.<x> = PolynomialRing(GF(next_prime(10^20)), sparse=True)            # needs sage.rings.finite_rings
-            sage: x^(10^20) # this should be fast                                       # needs sage.rings.finite_rings
+            sage: x^(10^20)  # this should be fast                                      # needs sage.rings.finite_rings
             x^100000000000000000000
         """
         def _element_class():
@@ -2655,6 +2656,7 @@ def _roth_ruckenstein(self, p, degree_bound, precision):
 
         EXAMPLES::
 
+            sage: # needs sage.rings.finite_rings
             sage: F = GF(17)
             sage: Px.<x> = F[]
             sage: Pxy.<y> = Px[]
@@ -3281,11 +3283,11 @@ def residue_field(self, ideal, names=None):
             Traceback (most recent call last):
             ...
             ArithmeticError: ideal is not maximal
-            sage: R.residue_field(0)                                                    # needs sage.rings.finite_rings
+            sage: R.residue_field(0)
             Traceback (most recent call last):
             ...
             ArithmeticError: ideal is not maximal
-            sage: R.residue_field(1)                                                    # needs sage.rings.finite_rings
+            sage: R.residue_field(1)
             Traceback (most recent call last):
             ...
             ArithmeticError: ideal is not maximal
@@ -3311,12 +3313,13 @@ def __init__(self, base_ring, name="x", implementation=None, element_class=None,
             sage: from sage.rings.polynomial.polynomial_ring import PolynomialRing_dense_mod_p
             sage: P = PolynomialRing_dense_mod_p(GF(5), 'x'); P
             Univariate Polynomial Ring in x over Finite Field of size 5
-            sage: type(P.gen())                                                         # needs sage.rings.finite_rings
+            sage: type(P.gen())                                                         # needs sage.libs.flint
             <class 'sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint'>
 
-            sage: P = PolynomialRing_dense_mod_p(GF(5), 'x', implementation='NTL'); P   # needs sage.rings.finite_rings
+            sage: # needs sage.libs.ntl
+            sage: P = PolynomialRing_dense_mod_p(GF(5), 'x', implementation='NTL'); P
             Univariate Polynomial Ring in x over Finite Field of size 5 (using NTL)
-            sage: type(P.gen())                                                         # needs sage.rings.finite_rings
+            sage: type(P.gen())
             <class 'sage.rings.polynomial.polynomial_modn_dense_ntl.Polynomial_dense_mod_p'>
 
             sage: P = PolynomialRing_dense_mod_p(GF(9223372036854775837), 'x'); P       # needs sage.libs.ntl sage.rings.finite_rings
@@ -3326,12 +3329,13 @@ def __init__(self, base_ring, name="x", implementation=None, element_class=None,
 
         This caching bug was fixed in :trac:`24264`::
 
+            sage: # needs sage.rings.finite_rings
             sage: p = 2^64 + 13
-            sage: A = GF(p^2)                                                           # needs sage.rings.finite_rings
-            sage: B = GF(p^3)                                                           # needs sage.rings.finite_rings
-            sage: R = A.modulus().parent()                                              # needs sage.rings.finite_rings
-            sage: S = B.modulus().parent()                                              # needs sage.rings.finite_rings
-            sage: R is S                                                                # needs sage.rings.finite_rings
+            sage: A = GF(p^2)
+            sage: B = GF(p^3)
+            sage: R = A.modulus().parent()
+            sage: S = B.modulus().parent()
+            sage: R is S
             True
         """
         if element_class is None: