gh-35076: Add ABCs CommutativePolynomial, MPolynomial_libsingular, InfinitePolynomial; deprecate is_Polynomial, is_MPolynomial 
    
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Closes #32709

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URL: #35076
Reported by: Matthias Köppe
Reviewer(s): Travis Scrimshaw

Author: Release Manager

src/sage/algebras/fusion_rings/shm_managers.pyx

@@ -22,7 +22,7 @@ from multiprocessing import shared_memory
 from sage.algebras.fusion_rings.poly_tup_engine cimport poly_to_tup, tup_fixes_sq, _flatten_coeffs
 from sage.rings.integer cimport Integer
 from sage.rings.rational cimport Rational
-from sage.rings.polynomial.multi_polynomial_libsingular cimport MPolynomial_libsingular
+from sage.rings.polynomial.multi_polynomial cimport MPolynomial_libsingular
 from sage.rings.polynomial.polydict cimport ETuple
 
 import numpy as np

src/sage/combinat/kazhdan_lusztig.py

@@ -20,7 +20,7 @@
 #*****************************************************************************
 
 
-from sage.rings.polynomial.polynomial_element import is_Polynomial
+from sage.rings.polynomial.polynomial_element import Polynomial
 from sage.misc.cachefunc import cached_method
 from sage.rings.polynomial.laurent_polynomial import LaurentPolynomial
 from sage.structure.sage_object import SageObject
@@ -76,7 +76,7 @@ def __init__(self, W, q, trace=False):
         self._trace = trace
         self._one = W.one()
         self._base_ring = q.parent()
-        if is_Polynomial(q):
+        if isinstance(q, Polynomial):
             self._base_ring_type = "polynomial"
         elif isinstance(q, LaurentPolynomial):
             self._base_ring_type = "laurent"

src/sage/combinat/schubert_polynomial.py

@@ -80,10 +80,9 @@
 from sage.misc.cachefunc import cached_method
 from sage.rings.integer import Integer
 from sage.rings.integer_ring import ZZ
-from sage.rings.polynomial.infinite_polynomial_element import InfinitePolynomial_sparse
+from sage.rings.polynomial.infinite_polynomial_element import InfinitePolynomial
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-from sage.rings.polynomial.multi_polynomial import is_MPolynomial
-
+from sage.rings.polynomial.multi_polynomial import MPolynomial
 import sage.libs.symmetrica.all as symmetrica
 
 
@@ -150,7 +149,7 @@ def expand(self):
             x0
         """
         p = symmetrica.t_SCHUBERT_POLYNOM(self)
-        if not is_MPolynomial(p):
+        if not isinstance(p, MPolynomial):
             R = PolynomialRing(self.parent().base_ring(), 1, 'x0')
             p = R(p)
         return p
@@ -462,9 +461,9 @@ def _element_constructor_(self, x):
         elif isinstance(x, Permutation):
             perm = x.remove_extra_fixed_points()
             return self._from_dict({perm: self.base_ring().one()})
-        elif is_MPolynomial(x):
+        elif isinstance(x, MPolynomial):
             return symmetrica.t_POLYNOM_SCHUBERT(x)
-        elif isinstance(x, InfinitePolynomial_sparse):
+        elif isinstance(x, InfinitePolynomial):
             R = x.polynomial().parent()
             # massage the term order to be what symmetrica expects
             S = PolynomialRing(R.base_ring(),

src/sage/combinat/sf/sfa.py

@@ -217,8 +217,8 @@
 from sage.rings.integer import Integer
 from sage.rings.infinity import infinity
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-from sage.rings.polynomial.polynomial_element import is_Polynomial
-from sage.rings.polynomial.multi_polynomial import is_MPolynomial
+from sage.rings.polynomial.polynomial_element import Polynomial
+from sage.rings.polynomial.multi_polynomial import MPolynomial
 from sage.combinat.partition import _Partitions, Partitions, Partitions_n, Partition
 from sage.categories.hopf_algebras import HopfAlgebras
 from sage.categories.hopf_algebras_with_basis import HopfAlgebrasWithBasis
@@ -6409,7 +6409,7 @@ def _nonnegative_coefficients(x):
         sage: _nonnegative_coefficients(x^2-4)
         False
     """
-    if is_Polynomial(x) or is_MPolynomial(x):
+    if isinstance(x, Polynomial) or isinstance(x, MPolynomial):
         return all(c >= 0 for c in x.coefficients(sparse=False))
     else:
         return x >= 0

src/sage/crypto/boolean_function.pyx

@@ -40,7 +40,7 @@ from sage.rings.finite_rings.finite_field_constructor import GF
 from sage.rings.polynomial.pbori.pbori import BooleanPolynomial
 from sage.rings.finite_rings.finite_field_constructor import is_FiniteField
 from sage.rings.finite_rings.finite_field_givaro import FiniteField_givaro
-from sage.rings.polynomial.polynomial_element import is_Polynomial
+from sage.rings.polynomial.polynomial_element import Polynomial
 
 from sage.misc.superseded import deprecated_function_alias
 
@@ -327,7 +327,7 @@ cdef class BooleanFunction(SageObject):
             bitset_init(self._truth_table, <mp_bitcnt_t> (1<<self._nvariables))
             bitset_zero(self._truth_table)
 
-        elif is_Polynomial(x):
+        elif isinstance(x, Polynomial):
             K = x.base_ring()
             if is_FiniteField(K) and K.characteristic() == 2:
                 self._nvariables = K.degree()

src/sage/crypto/mq/rijndael_gf.py

@@ -1549,9 +1549,9 @@ def compose(self, f, g, algorithm='encrypt', f_attr=None, g_attr=None):
         if not isinstance(f, RijndaelGF.Round_Component_Poly_Constr):
             msg = "keyword 'f' must be a Round_Component_Poly_Constr"
             raise TypeError(msg)
-        from sage.rings.polynomial.multi_polynomial import is_MPolynomial
+        from sage.rings.polynomial.multi_polynomial import MPolynomial
         if not isinstance(g, RijndaelGF.Round_Component_Poly_Constr) and \
-           not is_MPolynomial(g):
+           not isinstance(g, MPolynomial):
             msg = ("keyword 'g' must be a Round_Component_Poly_Constr or a "
                    "polynomial over {0}")
             raise TypeError(msg.format(self._F))

src/sage/crypto/sbox.pyx

@@ -173,12 +173,12 @@ cdef class SBox(SageObject):
             sage: S.output_size()
             3
         """
-        from sage.rings.polynomial.polynomial_element import is_Polynomial
+        from sage.rings.polynomial.polynomial_element import Polynomial
 
         if "S" in kwargs:
             args = kwargs["S"]
 
-        if len(args) == 1 and is_Polynomial(args[0]):
+        if len(args) == 1 and isinstance(args[0], Polynomial):
             # SBox defined via Univariate Polynomial, compute lookup table
             # by evaluating the polynomial on every base_ring element
             poly = args[0]

src/sage/crypto/stream.py

@@ -20,7 +20,7 @@
 from sage.arith.all import gcd, power_mod
 from sage.rings.finite_rings.finite_field_constructor import FiniteField
 from sage.rings.finite_rings.integer_mod_ring import IntegerModFactory
-from sage.rings.polynomial.polynomial_element import is_Polynomial
+from sage.rings.polynomial.polynomial_element import Polynomial
 
 
 IntegerModRing = IntegerModFactory("IntegerModRing")
@@ -73,7 +73,7 @@ def __call__(self, key):
         if not isinstance(key, (list, tuple)) and len(key) == 2:
             raise TypeError("Argument key (= %s) must be a list of tuple of length 2" % key)
         poly, IS = key
-        if not is_Polynomial(poly):
+        if not isinstance(poly, Polynomial):
             raise TypeError("poly (= %s) must be a polynomial." % poly)
         if not isinstance(IS, (list, tuple)):
             raise TypeError("IS (= %s) must be an initial in the key space." % IS)

src/sage/groups/affine_gps/group_element.py

@@ -414,13 +414,13 @@ def __call__(self, v):
         if v in parent.vector_space():
             return self._A*v + self._b
 
-        from sage.rings.polynomial.polynomial_element import is_Polynomial
-        if is_Polynomial(v) and parent.degree() == 1:
+        from sage.rings.polynomial.polynomial_element import Polynomial
+        if isinstance(v, Polynomial) and parent.degree() == 1:
             ring = v.parent()
             return ring([self._A[0,0], self._b[0]])
 
-        from sage.rings.polynomial.multi_polynomial import is_MPolynomial
-        if is_MPolynomial(v) and parent.degree() == v.parent().ngens():
+        from sage.rings.polynomial.multi_polynomial import MPolynomial
+        if isinstance(v, MPolynomial) and parent.degree() == v.parent().ngens():
             ring = v.parent()
             from sage.modules.free_module_element import vector
             image_coords = self._A * vector(ring, ring.gens()) + self._b

src/sage/groups/perm_gps/permgroup_element.pyx

@@ -122,8 +122,8 @@ from cypari2.gen cimport Gen
 
 from sage.ext.stdsage cimport HAS_DICTIONARY
 from sage.rings.all      import ZZ, Integer
-from sage.rings.polynomial.polynomial_element import is_Polynomial
-from sage.rings.polynomial.multi_polynomial import is_MPolynomial
+from sage.rings.polynomial.polynomial_element import Polynomial
+from sage.rings.polynomial.multi_polynomial import MPolynomial
 from sage.structure.element import is_Matrix
 from sage.matrix.all     import MatrixSpace
 from sage.sets.finite_enumerated_set import FiniteEnumeratedSet
@@ -1233,12 +1233,12 @@ cdef class PermutationGroupElement(MultiplicativeGroupElement):
         """
         if not self_on_left:
             left = x
-            if is_Polynomial(left):
+            if isinstance(left, Polynomial):
                 if self != 1:
                     raise ValueError("%s does not act on %s" % (self,
                                                                 left.parent()))
                 return left
-            elif is_MPolynomial(left):
+            elif isinstance(left, MPolynomial):
                 R = left.parent()
                 vars = R.gens()
                 try: