sage.rings: Update # optional / # needs

Author: Matthias Koeppe

src/sage/rings/polynomial/cyclotomic.pyx

@@ -265,7 +265,7 @@ def cyclotomic_value(n, x):
         ....:         if val1.parent() is not val2.parent():
         ....:             print("Wrong parent for cyclotomic_value(%s, %s) in %s"%(n,y,parent(y)))
 
-        sage: cyclotomic_value(20, I)
+        sage: cyclotomic_value(20, I)                                                   # optional - sage.symbolic
         5
         sage: a = cyclotomic_value(10, mod(3, 11)); a
         6

src/sage/rings/polynomial/infinite_polynomial_ring.py

@@ -86,10 +86,10 @@
 There is a permutation action on the variables, by permuting positive
 variable indices::
 
-    sage: P = Permutation(((10,1)))                                                     # optional - sage.combinat
-    sage: p^P                                                                           # optional - sage.combinat
+    sage: P = Permutation(((10,1)))
+    sage: p^P
     x_5*x_1^2 + 3*x_1^2*y_10 + 2*x_1^2
-    sage: p2^P                                                                          # optional - sage.combinat
+    sage: p2^P
     alpha_5*alpha_1^2 + 3*alpha_1^2*beta_10 + 2*alpha_1^2
 
 Note that `x_0^P = x_0`, since the permutations only change *positive*
@@ -103,7 +103,7 @@
 base ring is a field, one can compute Symmetric Groebner Bases::
 
     sage: J = A * (alpha[1]*beta[2])
-    sage: J.groebner_basis()                                                            # optional - sage.combinat sage.libs.singular
+    sage: J.groebner_basis()                                                            # needs sage.combinat sage.libs.singular
     [alpha_1*beta_2, alpha_2*beta_1]
 
 For more details, see :class:`~sage.rings.polynomial.symmetric_ideal.SymmetricIdeal`.
@@ -1297,10 +1297,10 @@ def characteristic(self):
 
         EXAMPLES::
 
-            sage: X.<x,y> = InfinitePolynomialRing(GF(25,'a'))                          # optional - sage.rings.finite_rings
-            sage: X                                                                     # optional - sage.rings.finite_rings
+            sage: X.<x,y> = InfinitePolynomialRing(GF(25,'a'))                          # needs sage.rings.finite_rings
+            sage: X                                                                     # needs sage.rings.finite_rings
             Infinite polynomial ring in x, y over Finite Field in a of size 5^2
-            sage: X.characteristic()                                                    # optional - sage.rings.finite_rings
+            sage: X.characteristic()                                                    # needs sage.rings.finite_rings
             5
 
         """
@@ -1364,7 +1364,7 @@ def key_basis(self):
         EXAMPLES::
 
             sage: R.<x> = InfinitePolynomialRing(GF(2))
-            sage: R.key_basis()                                                         # optional - sage.rings.finite_rings
+            sage: R.key_basis()                                                         # needs sage.rings.finite_rings
             Key polynomial basis over Finite Field of size 2
         """
         from sage.combinat.key_polynomial import KeyPolynomialBasis

src/sage/rings/polynomial/multi_polynomial.pyx

@@ -40,6 +40,7 @@ cdef class MPolynomial(CommutativePolynomial):
         r"""
         TESTS::
 
+            sage: # needs sage.rings.real_mpfr
             sage: ZZ(RR['x,y'](0)) # indirect doctest
             0
             sage: ZZ(RR['x,y'](0.5))
@@ -51,34 +52,39 @@ cdef class MPolynomial(CommutativePolynomial):
             ...
             TypeError: unable to convert non-constant polynomial x to Integer Ring
 
+            sage: # needs sage.rings.real_mpfr
             sage: RR(RR['x,y'](0)) # indirect doctest
             0.000000000000000
             sage: RR(ZZ['x,y'].gen(0))
             Traceback (most recent call last):
             ...
             TypeError: unable to convert non-constant polynomial x to Real Field with 53 bits of precision
 
+            sage: # needs sage.rings.real_mpfr
             sage: CC(RR['x,y'](0)) # indirect doctest
             0.000000000000000
             sage: CC(ZZ['x,y'].gen(0))
             Traceback (most recent call last):
             ...
             TypeError: unable to convert non-constant polynomial x to Complex Field with 53 bits of precision
 
+            sage: # needs sage.rings.real_mpfr
             sage: RDF(RR['x,y'](0))
             0.0
             sage: RDF(ZZ['x,y'].gen(0))
             Traceback (most recent call last):
             ...
             TypeError: unable to convert non-constant polynomial x to Real Double Field
 
+            sage: # needs sage.rings.real_mpfr
             sage: CDF(RR['x,y'](0)) # indirect doctest
             0.0
             sage: CDF(ZZ['x,y'].gen(0))
             Traceback (most recent call last):
             ...
             TypeError: unable to convert non-constant polynomial x to Complex Double Field
 
+            sage: # needs sage.rings.real_mpfr
             sage: a = RR['x,y'](1)
             sage: RBF(a)                                                                # needs sage.libs.flint
             1.000000000000000

src/sage/rings/polynomial/multi_polynomial_ring_base.pyx

@@ -1384,7 +1384,7 @@ cdef class MPolynomialRing_base(sage.rings.ring.CommutativeRing):
 
             sage: R.<x,y,z> = ZZ[]
             sage: mons = R.monomials_of_degree(2)                                       # optional - sage.combinat
-            sage: mons
+            sage: mons                                                                  # optional - sage.combinat
             [z^2, y*z, x*z, y^2, x*y, x^2]
             sage: P = PolynomialRing(QQ, 3, 'x, y, z', order=TermOrder('wdeglex', [1, 2, 1]))
             sage: P.monomials_of_degree(2)                                              # optional - sage.combinat

src/sage/rings/polynomial/polynomial_element.pyx

@@ -4127,14 +4127,16 @@ cdef class Polynomial(CommutativePolynomial):
 
         Arbitrary precision real and complex factorization::
 
+            sage: # needs sage.libs.pari sage.rings.real_mpfr
             sage: R.<x> = RealField(100)[]                                              # optional - sage.rings.real_mpfr
-            sage: F = factor(x^2 - 3); F                                                # optional - sage.rings.real_mpfr
+            sage: F = factor(x^2 - 3); F
             (x - 1.7320508075688772935274463415) * (x + 1.7320508075688772935274463415)
             sage: expand(F)                                                             # optional - sage.rings.real_mpfr
             x^2 - 3.0000000000000000000000000000
             sage: factor(x^2 + 1)                                                       # optional - sage.rings.real_mpfr
             x^2 + 1.0000000000000000000000000000
 
+            sage: # needs sage.libs.pari sage.rings.real_mpfr
             sage: R.<x> = ComplexField(100)[]                                           # optional - sage.rings.real_mpfr
             sage: F = factor(x^2 + 3); F                                                # optional - sage.rings.real_mpfr
             (x - 1.7320508075688772935274463415*I) * (x + 1.7320508075688772935274463415*I)

src/sage/rings/polynomial/polynomial_ring_constructor.py

@@ -355,6 +355,7 @@ def PolynomialRing(base_ring, *args, **kwds):
     You can alternatively create a polynomial ring over a ring `R` with
     square brackets::
 
+        sage: # needs sage.rings.real_mpfr
         sage: RR["x"]
         Univariate Polynomial Ring in x over Real Field with 53 bits of precision
         sage: RR["x,y"]