Trac #10483: deprecate the misuse of symbolic variables as polynomial variable

Also-by: Simon King <[email protected]>

Author: rwst

src/sage/rings/cfinite_sequence.py

@@ -160,6 +160,8 @@ def CFiniteSequences(base_ring, names = None, category = None):
         names = ['x']
     elif len(names)>1:
         raise NotImplementedError("Multidimensional o.g.f. not implemented.")
+    else:
+        names = [str(names[0])]
     if category is None:
         category = Fields()
     if not(base_ring in (QQ, ZZ)):

src/sage/rings/polynomial/multi_polynomial.pyx

@@ -457,12 +457,12 @@ cdef class MPolynomial(CommutativeRingElement):
         if R.ngens() <= 1:
             return self.univariate_polynomial()
 
-        other_vars = Z
-        del other_vars[ind]
+        del Z[ind]
+        other_vars = [str(v) for v in Z]
 
         # Make polynomial ring over all variables except var.
         S = R.base_ring()[tuple(other_vars)]
-        ring = S[var]
+        ring = S[str(var)]
         if not self:
             return ring(0)
 

src/sage/rings/polynomial/multi_polynomial_libsingular.pyx

@@ -5436,9 +5436,10 @@ cdef class MPolynomial_libsingular(MPolynomial):
             # Trac ticket #11780: Create the polynomial ring over
             # the integers using the (cached) polynomial ring constructor:
             from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-            integer_polynomial_ring = PolynomialRing(ZZ,\
-            self.parent().ngens(), self.parent().gens(), order =\
-            self.parent().term_order())
+            integer_polynomial_ring = PolynomialRing(ZZ,
+                                                     self.parent().ngens(),
+                                                     self.parent().variable_names(),
+                                                     order=self.parent().term_order())
             return integer_polynomial_ring(self * self.denominator())
         else:
             return self * self.denominator()

src/sage/rings/polynomial/multi_polynomial_sequence.py

@@ -645,16 +645,16 @@ def algebraic_dependence(self):
         """
         R = self.ring()
         K = R.base_ring()
-        Xs = list(R.gens())
+        Xs = R.variable_names()
         r = len(self)
         d = len(Xs)
 
         # Expand R by r new variables.
         T = 'T'
-        while T in [str(x) for x in Xs]:
+        while T in Xs:
             T = T+'T'
         Ts = [T + str(j) for j in range(r)]
-        RR = PolynomialRing(K,d+r,tuple(Xs+Ts))
+        RR = PolynomialRing(K, d+r, Xs+tuple(Ts))
         Vs = list(RR.gens())
         Xs = Vs[0 :d]
         Ts = Vs[d:]
@@ -670,7 +670,7 @@ def algebraic_dependence(self):
 
         # Coerce JJ into `K[T_1,\ldots,T_r]`.
         # Choosing the negdeglex order simply because i find it useful in my work.
-        RRR = PolynomialRing(K,r,tuple(Ts),order='negdeglex')
+        RRR = PolynomialRing(K, r, RR.variable_names()[d:], order='negdeglex')
         return RRR.ideal(JJ.gens())
 
     def coefficient_matrix(self, sparse=True):

src/sage/rings/polynomial/polynomial_ring_constructor.py

@@ -91,6 +91,14 @@ def PolynomialRing(base_ring, *args, **kwds):
       implemented with ``'NTL'`` or ``'FLINT'``; default is ``'FLINT'``).
       For many base rings, the ``"singular"`` implementation is available.
 
+    REMARK:
+
+    In earlier versions of Sage, the names have not necessarily been
+    strings. Some users provided a symbolic variable instead of a string,
+    and expected that this symbolic variable is the same as the generator
+    of the resulting polynomial ring, which is of course not the case.
+    This common mistake is now deprecated.
+
     .. NOTE::
 
         The following rules were introduced in :trac:`9944`, in order
@@ -426,13 +434,6 @@ def PolynomialRing(base_ring, *args, **kwds):
         sage: R.0 == 0
         True
 
-    We verify that :trac:`13187` is fixed::
-
-        sage: var('t')
-        t
-        sage: PolynomialRing(ZZ, name=t) == PolynomialRing(ZZ, name='t')
-        True
-
     We verify that polynomials with interval coefficients from
     :trac:`7712` and :trac:`13760` are fixed::
 

src/sage/rings/quotient_ring.py

@@ -139,6 +139,14 @@ def QuotientRing(R, I, names=None):
     - ``names`` -- (optional) a list of strings to be used as names for
       the variables in the quotient ring `R/I`.
 
+    REMARK:
+
+    In earlier versions of Sage, the names have not necessarily been
+    strings. Some users provided a symbolic variable instead of a string,
+    and expected that this symbolic variable is the same as the generator
+    of the resulting quotient ring, which is of course not the case.
+    This common mistake is now deprecated.
+
     OUTPUT: `R/I` - the quotient ring `R` mod the ideal `I`
 
     ASSUMPTION:

src/sage/schemes/product_projective/wehlerK3.py

@@ -741,7 +741,7 @@ def is_degenerate(self):
         R = PP.coordinate_ring()
         PS = PP[0] #check for x fibers
         vars = list(PS.gens())
-        R0 = PolynomialRing(K, 3, vars) #for dimension calculation to work,
+        R0 = PolynomialRing(K, 3, PS.variable_names()) #for dimension calculation to work,
             #must be done with Polynomial ring over a field
         #Degenerate is equivalent to a common zero, see Prop 1.4 in [CaSi]_
         I = R.ideal(self.Gpoly(1, 0), self.Gpoly(1, 1), self.Gpoly(1, 2), self.Hpoly(1, 0, 1),
@@ -752,8 +752,7 @@ def is_degenerate(self):
             return True
 
         PS = PP[1] #check for y fibers
-        vars = list(PS.gens())
-        R0 = PolynomialRing(K,3,vars) #for dimension calculation to work,
+        R0 = PolynomialRing(K, 3, PS.variable_names()) #for dimension calculation to work,
         #must be done with Polynomial ring over a field
         #Degenerate is equivalent to a common zero, see Prop 1.4 in [CaSi]_
         I = R.ideal(self.Gpoly(0, 0), self.Gpoly(0, 1), self.Gpoly(0, 2), self.Hpoly(0, 0, 1),
@@ -824,15 +823,15 @@ def degenerate_fibers(self):
         PSX = PP[0];
         vars = list(PSX.gens())
         K = FractionField(PSX.base_ring())
-        R0 = PolynomialRing(K, 3, vars)
+        R0 = PolynomialRing(K, 3, PSX.variable_names())
         I = R.ideal(self.Gpoly(1, 0), self.Gpoly(1, 1), self.Gpoly(1, 2), self.Hpoly(1, 0,1 ), \
                     self.Hpoly(1, 0, 2), self.Hpoly(1, 1, 2))
-        phi = R.hom(vars + [0, 0, 0], R0)
+        phi = R.hom(list(PSX.gens()) + [0, 0, 0], R0)
         I = phi(I)
         xFibers = []
         #check affine charts
         for n in range(3):
-            affvars = list(R0.gens())
+            affvars = list(R0.variable_names())
             del affvars[n]
             R1 = PolynomialRing(K, 2, affvars, order = 'lex')
             mapvars = list(R1.gens())
@@ -853,17 +852,16 @@ def degenerate_fibers(self):
                         if MP not in xFibers:
                             xFibers.append(MP)
         PSY = PP[1]
-        vars = list(PSY.gens())
         K = FractionField(PSY.base_ring())
-        R0 = PolynomialRing(K, 3, vars)
+        R0 = PolynomialRing(K, 3, PSY.variable_names())
         I = R.ideal(self.Gpoly(0, 0), self.Gpoly(0, 1), self.Gpoly(0, 2), self.Hpoly(0, 0, 1), \
                     self.Hpoly(0, 0, 2), self.Hpoly(0, 1, 2))
-        phi = PP.coordinate_ring().hom([0, 0, 0] + vars, R0)
+        phi = PP.coordinate_ring().hom([0, 0, 0] + list(PSY.gens()), R0)
         I = phi(I)
         yFibers = []
         #check affine charts
         for n in range(3):
-            affvars = list(R0.gens())
+            affvars = list(R0.variable_names())
             del affvars[n]
             R1 = PolynomialRing(K, 2, affvars, order = 'lex')
             mapvars = list(R1.gens())
@@ -937,7 +935,7 @@ def degenerate_primes(self,check = True):
         PSX = PP[0]
         vars = list(PSX.gens())
         K = PSX.base_ring()
-        R = PolynomialRing(K, 3, vars)
+        R = PolynomialRing(K, 3, PSX.variable_names())
         I = RR.ideal(self.Gpoly(1, 0), self.Gpoly(1, 1), self.Gpoly(1, 2), self.Hpoly(1, 0, 1),
                      self.Hpoly(1, 0, 2), self.Hpoly(1, 1, 2))
         phi = PP.coordinate_ring().hom(vars + [0, 0, 0], R)
@@ -946,7 +944,7 @@ def degenerate_primes(self,check = True):
 
         #move the ideal to the ring of integers
         if R.base_ring().is_field():
-            S = PolynomialRing(R.base_ring().ring_of_integers(),R.gens(),R.ngens())
+            S = PolynomialRing(R.base_ring().ring_of_integers(),R.variable_names(),R.ngens())
             I = S.ideal(I.gens())
         GB = I.groebner_basis()
         #get the primes dividing the coefficients of the monomials x_i^k_i
@@ -963,14 +961,14 @@ def degenerate_primes(self,check = True):
         PSY = PP[1]
         vars = list(PSY.gens())
         K = PSY.base_ring()
-        R = PolynomialRing(K, 3, vars)
+        R = PolynomialRing(K, 3, PSY.variable_names())
         I = RR.ideal(self.Gpoly(0, 0), self.Gpoly(0, 1), self.Gpoly(0, 2), self.Hpoly(0, 0, 1),
                      self.Hpoly(0, 0, 2), self.Hpoly(0, 1, 2))
         phi = PP.coordinate_ring().hom([0, 0, 0] + vars, R)
         I = phi(I)
         #move the ideal to the ring of integers
         if R.base_ring().is_field():
-            S = PolynomialRing(R.base_ring().ring_of_integers(),R.gens(),R.ngens())
+            S = PolynomialRing(R.base_ring().ring_of_integers(),R.variable_names(),R.ngens())
             I = S.ideal(I.gens())
         GB = I.groebner_basis()
         #get the primes dividing the coefficients of the monomials x_i^k_i

src/sage/symbolic/expression.pyx

@@ -6734,7 +6734,7 @@ cdef class Expression(CommutativeRingElement):
         nu = ring.SR(self.numerator()).polynomial(base_ring)
         de = ring.SR(self.denominator()).polynomial(base_ring)
         vars = sorted(set(nu.variables() + de.variables()), key=repr)
-        R = FractionField(PolynomialRing(base_ring, vars))
+        R = FractionField(PolynomialRing(base_ring, list(str(v) for v in vars)))
         return R(self.numerator())/R(self.denominator())
 
     def power_series(self, base_ring):

src/sage/symbolic/expression_conversions.py

@@ -1029,7 +1029,7 @@ def __init__(self, ex, base_ring=None, ring=None):
             self.base_ring = base_ring
         elif base_ring is not None:
             self.base_ring = base_ring
-            vars = self.ex.variables()
+            vars = [str(x) for x in self.ex.variables()]
             if len(vars) == 0:
                 vars = ['x']
             from sage.rings.all import PolynomialRing

src/sage/symbolic/relation.py

@@ -1007,7 +1007,7 @@ def solve_mod(eqns, modulus, solution_dict = False):
     if modulus < 1:
         raise ValueError("the modulus must be a positive integer")
     vars = list(set(sum([list(e.variables()) for e in eqns], [])))
-    vars.sort(key=repr)
+    vars.sort(key=str)
 
     if modulus == 1: # degenerate case
         ans = [tuple(Integers(1)(0) for v in vars)]
@@ -1119,7 +1119,7 @@ def _solve_mod_prime_power(eqns, p, m, vars):
     for mi in range(m):
         mrunning *= p
         R = Integers(mrunning)
-        S = PolynomialRing(R, len(vars), vars)
+        S = PolynomialRing(R, len(vars), [str(var) for var in vars])
         eqns_mod = [S(eq) for eq in eqns]
         if mi == 0:
             possibles = cartesian_product_iterator([range(len(R)) for _ in range(len(vars))])