Add ABCs CommutativePolynomial, MPolynomial_libsingular, InfinitePolynomial; deprecate is_Polynomial, is_MPolynomial

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:

src/sage/libs/symmetrica/sb.pxi

@@ -111,7 +111,7 @@ def t_POLYNOM_SCHUBERT_symmetrica(a):
 
     cdef OP ca = callocobject(), cres = callocobject()
 
-    if not is_MPolynomial(a):
+    if not isinstance(a, MPolynomial):
         freeall(ca)
         freeall(cres)
         raise TypeError("a (= %s) must be a multivariate polynomial")

src/sage/libs/symmetrica/symmetrica.pxi

@@ -401,7 +401,7 @@ cdef void late_import():
            SymmetricFunctions, \
            sqrt, \
            builtinlist, \
-           MPolynomialRing_base, is_MPolynomial,\
+           MPolynomialRing_base, MPolynomial,\
            SchubertPolynomialRing, SchubertPolynomial_class,\
            two, fifteen, thirty, zero, sage_maxint
 
@@ -453,8 +453,8 @@ cdef void late_import():
 
     import sage.rings.polynomial.multi_polynomial_ring
     MPolynomialRing_base = sage.rings.polynomial.multi_polynomial_ring.MPolynomialRing_base
-    import sage.rings.polynomial.multi_polynomial_element
-    is_MPolynomial = sage.rings.polynomial.multi_polynomial_element.is_MPolynomial
+    import sage.rings.polynomial.multi_polynomial
+    MPolynomial = sage.rings.polynomial.multi_polynomial.MPolynomial
 
     import sage.combinat.schubert_polynomial
     SchubertPolynomialRing = sage.combinat.schubert_polynomial.SchubertPolynomialRing

src/sage/manifolds/differentiable/characteristic_cohomology_class.py

@@ -290,7 +290,7 @@
 from .bundle_connection import BundleConnection
 from .levi_civita_connection import LeviCivitaConnection
 from sage.symbolic.expression import Expression
-from sage.rings.polynomial.polynomial_element import is_Polynomial
+from sage.rings.polynomial.polynomial_element import Polynomial
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 
 
@@ -795,7 +795,7 @@ def _element_constructor_(self, x, **kwargs):
             Characteristic cohomology class pontr(TM) of the Tangent bundle
              TM over the 8-dimensional differentiable manifold M
         """
-        if isinstance(x, (str, Expression)) or is_Polynomial(x):
+        if isinstance(x, (str, Expression)) or isinstance(x, Polynomial):
             return self._build_element(x, **kwargs)
 
         R = self.base_ring()
@@ -983,7 +983,7 @@ def _build_element(self, *args, **kwargs):
             val = P(val.taylor(x, 0, pow_range))
 
         # turn polynomial into a characteristic cohomology class via sequences
-        if is_Polynomial(val):
+        if isinstance(val, Polynomial):
             if class_type is None:
                 raise TypeError(f'class_type must be stated if {val} '
                                 f'is a polynomial')

src/sage/modular/modsym/ambient.py

@@ -95,7 +95,7 @@ class ``ModularSymbolsAmbient``, derived from
 from sage.modules.free_module_element import FreeModuleElement
 from sage.rings.integer import Integer
 from sage.rings.integer_ring import ZZ
-from sage.rings.polynomial.multi_polynomial import is_MPolynomial
+from sage.rings.polynomial.multi_polynomial import MPolynomial
 from sage.rings.rational_field import QQ
 from sage.rings.ring import Ring
 from sage.structure.factorization import Factorization
@@ -474,7 +474,7 @@ def _element_constructor_(self, x, computed_with_hecke=False):
             return sum([c*self(y) for c, y in x], self(0))
 
         elif isinstance(x, list):
-            if len(x) == 3 and is_MPolynomial(x[0]):
+            if len(x) == 3 and isinstance(x[0], MPolynomial):
                 return self.modular_symbol_sum(x)
             else:
                 return self.modular_symbol(x)

src/sage/quadratic_forms/binary_qf.py

@@ -130,14 +130,14 @@ def __init__(self, a, b=None, c=None):
             sage: BinaryQF(0)
             0
         """
-        from sage.rings.polynomial.multi_polynomial_element import is_MPolynomial
+        from sage.rings.polynomial.multi_polynomial import MPolynomial
         if b is None and c is None:
             if (isinstance(a, (list, tuple))
                 and len(a) == 3):
                 a, b, c = a
             elif a == 0:
                 a = b = c = 0
-            elif (is_MPolynomial(a) and a.is_homogeneous() and a.base_ring() == ZZ
+            elif (isinstance(a, MPolynomial) and a.is_homogeneous() and a.base_ring() == ZZ
                   and a.degree() == 2 and a.parent().ngens() == 2):
                 x, y = a.parent().gens()
                 a, b, c = [a.monomial_coefficient(mon) for mon in [x**2, x*y, y**2]]

src/sage/quadratic_forms/constructions.py

@@ -6,7 +6,7 @@
 ##
 
 from sage.rings.integer_ring import ZZ
-from sage.rings.polynomial.polynomial_element import is_Polynomial
+from sage.rings.polynomial.polynomial_element import Polynomial
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.quadratic_forms.quadratic_form import QuadraticForm
 
@@ -46,7 +46,7 @@ def BezoutianQuadraticForm(f, g):
 
     """
     # Check that f and g are polynomials with a common base ring
-    if not is_Polynomial(f) or not is_Polynomial(g):
+    if not isinstance(f, Polynomial) or not isinstance(g, Polynomial):
         raise TypeError("one of your inputs is not a polynomial")
     if f.base_ring() != g.base_ring():   # TO DO:  Change this to allow coercion!
         raise TypeError("these polynomials are not defined over the same coefficient ring")

src/sage/quadratic_forms/quadratic_form.py

@@ -32,8 +32,8 @@
 from sage.rings.ring import is_Ring, PrincipalIdealDomain
 from sage.structure.element import is_Vector
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-from sage.rings.polynomial.polynomial_element import is_Polynomial
-from sage.rings.polynomial.multi_polynomial_element import is_MPolynomial
+from sage.rings.polynomial.polynomial_element import Polynomial
+from sage.rings.polynomial.multi_polynomial import MPolynomial
 from sage.modules.free_module_element import vector
 from sage.quadratic_forms.genera.genus import genera
 from sage.quadratic_forms.quadratic_form__evaluate import QFEvaluateVector, QFEvaluateMatrix
@@ -576,9 +576,9 @@ def __init__(self, R, n=None, entries=None, unsafe_initialization=False, number_
             M_ring = M.base_ring()
             matrix_init_flag = True
 
-        elif is_Polynomial(R) or is_MPolynomial(R):
+        elif isinstance(R, (Polynomial, MPolynomial)):
             p = R
-            
+
             if not p.is_zero() and not (p.is_homogeneous() and p.degree() == 2):
                 raise ValueError("polynomial is neither zero nor homogeneous of degree 2")
 

src/sage/rings/finite_rings/element_ntl_gf2e.pyx

@@ -1004,8 +1004,8 @@ cdef class FiniteField_ntl_gf2eElement(FinitePolyExtElement):
             sage: e.polynomial()
             a^15 + a^13 + a^11 + a^10 + a^9 + a^8 + a^7 + a^6 + a^4 + a + 1
 
-            sage: from sage.rings.polynomial.polynomial_element import is_Polynomial
-            sage: is_Polynomial(e.polynomial())
+            sage: from sage.rings.polynomial.polynomial_element import Polynomial
+            sage: isinstance(e.polynomial(), Polynomial)
             True
 
             sage: e.polynomial('x')

src/sage/rings/finite_rings/finite_field_base.pyx

@@ -1521,7 +1521,7 @@ cdef class FiniteField(Field):
             True
         """
         from .finite_field_constructor import GF
-        from sage.rings.polynomial.polynomial_element import is_Polynomial
+        from sage.rings.polynomial.polynomial_element import Polynomial
         from sage.rings.integer import Integer
         if name is None and names is not None:
             name = names
@@ -1532,7 +1532,7 @@ cdef class FiniteField(Field):
                 E = GF((self.characteristic(), modulus), name=name, **kwds)
             elif isinstance(modulus, (list, tuple)):
                 E = GF((self.characteristic(), len(modulus) - 1), name=name, modulus=modulus, **kwds)
-            elif is_Polynomial(modulus):
+            elif isinstance(modulus, Polynomial):
                 if modulus.change_ring(self).is_irreducible():
                     E = GF((self.characteristic(), modulus.degree()), name=name, modulus=modulus, **kwds)
                 else:

src/sage/rings/finite_rings/finite_field_constructor.py

@@ -173,7 +173,7 @@
 
 from collections import defaultdict
 from sage.structure.category_object import normalize_names
-
+from sage.rings.polynomial.polynomial_element import Polynomial
 from sage.rings.integer import Integer
 
 # the import below is just a redirection
@@ -641,7 +641,7 @@ def create_key_and_extra_args(self, order, name=None, modulus=None, names=None,
                     else:
                         self._modulus_cache[order][modulus] = modulus = R.irreducible_element(n, algorithm=modulus)
                 else:
-                    if sage.rings.polynomial.polynomial_element.is_Polynomial(modulus):
+                    if isinstance(modulus, Polynomial):
                         modulus = modulus.change_variable_name('x')
                     modulus = R(modulus).monic()
 

src/sage/rings/finite_rings/finite_field_givaro.py

@@ -137,8 +137,8 @@ def __init__(self, q, name="a", modulus=None, repr="poly", cache=False):
         from .finite_field_constructor import GF
         FiniteField.__init__(self, GF(p), name, normalize=False)
 
-        from sage.rings.polynomial.polynomial_element import is_Polynomial
-        if not is_Polynomial(modulus):
+        from sage.rings.polynomial.polynomial_element import Polynomial
+        if not isinstance(modulus, Polynomial):
             raise TypeError("modulus must be a polynomial")
 
         self._cache = Cache_givaro(self, p, k, modulus, repr, cache)

src/sage/rings/finite_rings/finite_field_ntl_gf2e.py

@@ -138,8 +138,8 @@ def __init__(self, q, names="a", modulus=None, repr="poly"):
             raise ValueError("q must be a 2-power")
         FiniteField.__init__(self, GF2, names, normalize=True)
 
-        from sage.rings.polynomial.polynomial_element import is_Polynomial
-        if not is_Polynomial(modulus):
+        from sage.rings.polynomial.polynomial_element import Polynomial
+        if not isinstance(modulus, Polynomial):
             raise TypeError("modulus must be a polynomial")
 
         self._cache = Cache_ntl_gf2e(self, k, modulus)