sage.structure.element: Add ABCs Polynomial, MPolynomial, use for isi…

…nstance testing

src/sage/combinat/kazhdan_lusztig.py

@@ -20,7 +20,7 @@
 #*****************************************************************************
 
 
-from sage.rings.polynomial.polynomial_element import is_Polynomial
+from sage.structure.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
@@ -75,7 +75,7 @@ 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/sf/sfa.py

@@ -217,7 +217,7 @@
 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.structure.element import Polynomial
 from sage.rings.polynomial.multi_polynomial import is_MPolynomial
 from sage.combinat.partition import _Partitions, Partitions, Partitions_n, Partition
 from sage.categories.hopf_algebras import HopfAlgebras
@@ -6404,7 +6404,7 @@ def _nonnegative_coefficients(x):
         sage: _nonnegative_coefficients(x^2-4)
         False
     """
-    if is_Polynomial(x) or is_MPolynomial(x):
+    if isinstance(x, Polynomial) or is_MPolynomial(x):
         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.structure.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superseded import deprecated_function_alias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/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.structure.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.structure.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

@@ -414,8 +414,8 @@ 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.structure.element import Polynomial
+        if isinstance(v, Polynomial) and parent.degree() == 1:
             ring = v.parent()
             return ring([self._A[0,0], self._b[0]])
 

src/sage/groups/perm_gps/permgroup_element.pyx

@@ -114,7 +114,7 @@ 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.structure.element import Polynomial
 from sage.rings.polynomial.multi_polynomial import is_MPolynomial
 from sage.structure.element import is_Matrix
 from sage.matrix.all     import MatrixSpace
@@ -1225,7 +1225,7 @@ 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()))

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.structure.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/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.structure.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/rings/finite_rings/element_ntl_gf2e.pyx

@@ -1004,7 +1004,7 @@ 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: from sage.structure.element import Polynomial
             sage: is_Polynomial(e.polynomial())
             True
 

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.structure.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.structure.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.structure.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.structure.element import Polynomial
+        if not isinstance(modulus, Polynomial):
             raise TypeError("modulus must be a polynomial")
 
         self._cache = Cache_ntl_gf2e(self, k, modulus)

src/sage/rings/finite_rings/residue_field.pyx

@@ -170,7 +170,7 @@ from sage.rings.fraction_field import is_FractionField
 
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.rings.polynomial.polynomial_ring import is_PolynomialRing
-from sage.rings.polynomial.polynomial_element import is_Polynomial
+from sage.structure.element import Polynomial
 
 from sage.structure.factory import UniqueFactory
 from sage.structure.element cimport parent
@@ -300,7 +300,7 @@ class ResidueFieldFactory(UniqueFactory):
                         p = p.parent().ring_of_integers().ideal(p)
                     else:
                         p = p.parent().ideal(p)
-                elif is_Polynomial(p):
+                elif isinstance(p, Polynomial):
                     p = p.parent().ideal(p)
                 #elif isinstance(p.parent(), FractionField_1poly_field):
                 #    p = p.parent().ring_of_integers().ideal(p)

src/sage/rings/function_field/function_field.py

@@ -1307,8 +1307,8 @@ def __init__(self, polynomial, names, category=None):
             TypeError: unable to evaluate 'x' in Fraction Field of Univariate
             Polynomial Ring in t over Rational Field
         """
-        from sage.rings.polynomial.polynomial_element import is_Polynomial
-        if polynomial.parent().ngens()>1 or not is_Polynomial(polynomial):
+        from sage.structure.element import Polynomial
+        if polynomial.parent().ngens()>1 or not isinstance(polynomial, Polynomial):
             raise TypeError("polynomial must be univariate a polynomial")
         if names is None:
             names = (polynomial.variable_name(), )

src/sage/rings/laurent_series_ring.py

@@ -466,7 +466,7 @@ def _element_constructor_(self, x, n=0, prec=infinity):
             x^-3
         """
         from sage.rings.fraction_field_element import is_FractionFieldElement
-        from sage.rings.polynomial.polynomial_element import is_Polynomial
+        from sage.structure.element import Polynomial
         from sage.rings.polynomial.multi_polynomial_element import is_MPolynomial
         from sage.structure.element import parent
         from sage.libs.pari.all import pari_gen

src/sage/rings/number_field/number_field.py

@@ -114,7 +114,7 @@
 import sage.interfaces.gap
 
 import sage.rings.complex_mpfr
-from sage.rings.polynomial.polynomial_element import is_Polynomial
+from sage.structure.element import Polynomial
 import sage.rings.real_mpfr
 import sage.rings.real_mpfi
 import sage.rings.complex_double
@@ -647,7 +647,7 @@ def create_key_and_extra_args(self, polynomial, name, check, embedding, latex_na
             raise TypeError("You must specify the name of the generator.")
         name = normalize_names(1, name)
 
-        if not is_Polynomial(polynomial):
+        if not isinstance(polynomial, Polynomial):
             try:
                 polynomial = polynomial.polynomial(QQ)
             except (AttributeError, TypeError):
@@ -868,7 +868,7 @@ def NumberFieldTower(polynomials, names, check=True, embeddings=None, latex_name
     f = polynomials[0]
     name = names[0]
     w = NumberFieldTower(polynomials[1:], names=names[1:], check=check, embeddings=embeddings[1:], latex_names=latex_names[1:], assume_disc_small=assume_disc_small, maximize_at_primes=maximize_at_primes, structures=structures[1:])
-    var = f.variable_name() if is_Polynomial(f) else 'x'
+    var = f.variable_name() if isinstance(f, Polynomial) else 'x'
 
     R = w[var]  # polynomial ring
     return w.extension(R(f), name, check=check, embedding=embeddings[0], structure=structures[0], latex_name=latex_names[0])  # currently, extension does not accept assume_disc_small, or maximize_at_primes

src/sage/rings/padics/factory.py

@@ -35,7 +35,7 @@
 from sage.rings.infinity import Infinity
 from sage.structure.factorization import Factorization
 from sage.rings.integer_ring import ZZ
-from sage.rings.polynomial.polynomial_element import is_Polynomial
+from sage.structure.element import Polynomial
 from sage.structure.element import is_Element
 from .padic_base_leaves import (pAdicRingCappedRelative,
                                 pAdicRingCappedAbsolute,
@@ -2535,7 +2535,7 @@ def Zq(q, prec = None, type = 'capped-rel', modulus = None, names=None,
         if isinstance(names, (list, tuple)):
             names = names[0]
         from sage.structure.element import Expression
-        if not (modulus is None or is_Polynomial(modulus) or isinstance(modulus, Expression)):
+        if not (modulus is None or isinstance(modulus, Polynomial) or isinstance(modulus, Expression)):
             raise TypeError("modulus must be a polynomial")
         if names is not None and not isinstance(names, str):
             names = str(names)
@@ -3278,7 +3278,7 @@ def create_key_and_extra_args(self, base, modulus, prec = None, print_mode = Non
                     raise ValueError("symbolic expression must be in only one variable")
                 exact_modulus = modulus.polynomial(base.exact_field())
                 approx_modulus = modulus.polynomial(base)
-            elif is_Polynomial(modulus):
+            elif isinstance(modulus, Polynomial):
                 if modulus.parent().ngens() != 1:
                     raise ValueError("must use univariate polynomial")
                 exact_modulus = modulus.change_ring(base.exact_field())
@@ -3381,7 +3381,7 @@ def create_object(self, version, key, approx_modulus=None, shift_seed=None):
             from sage.structure.element import Expression
             if isinstance(premodulus, Expression):
                 exact_modulus = premodulus.polynomial(base.exact_field())
-            elif is_Polynomial(premodulus):
+            elif isinstance(premodulus, Polynomial):
                 exact_modulus = premodulus.change_ring(base.exact_field())
             show_prec = None
         else:

src/sage/rings/padics/padic_template_element.pxi

@@ -36,7 +36,7 @@ from sage.rings.infinity import infinity
 from sage.rings.rational import Rational
 from sage.rings.padics.precision_error import PrecisionError
 from sage.rings.padics.misc import trim_zeros
-from sage.structure.element import canonical_coercion
+from sage.structure.element import canonical_coercion, Polynomial
 import itertools
 
 cdef long maxordp = (1L << (sizeof(long) * 8 - 2)) - 1
@@ -156,7 +156,7 @@ cdef class pAdicTemplateElement(pAdicGenericElement):
                 x = x + [k.prime_subfield().zero()] * (k.degree() - len(x))
         elif isinstance(x, (Integer, Rational, list, tuple)):
             pass
-        elif sage.rings.polynomial.polynomial_element.is_Polynomial(x) and x.variable_name() == self.parent().variable_name():
+        elif isinstance(x, Polynomial) and x.variable_name() == self.parent().variable_name():
             x = x.list()
         else:
             x = Rational(x)

src/sage/rings/polynomial/multi_polynomial.pxd

@@ -1,6 +1,6 @@
-from sage.structure.element cimport CommutativeRingElement
+from sage.structure.element cimport MPolynomial as MPolynomial_base
 
-cdef class MPolynomial(CommutativeRingElement):
+cdef class MPolynomial(MPolynomial_base):
     cdef long _hash_c(self) except -1
     cpdef _mod_(self, right)
     cpdef dict _mpoly_dict_recursive(self, tuple vars=*, base_ring=*)

src/sage/rings/polynomial/multi_polynomial.pyx

@@ -30,7 +30,7 @@ from sage.rings.real_mpfr import RealField_class,RealField
 from sage.rings.polynomial.polydict cimport ETuple
 from sage.rings.polynomial.polynomial_element cimport Polynomial
 
-cdef class MPolynomial(CommutativeRingElement):
+cdef class MPolynomial(MPolynomial_base):
 
     ####################
     # Some standard conversions

src/sage/rings/polynomial/padics/polynomial_padic_capped_relative_dense.py

@@ -661,7 +661,7 @@ def rshift_coeffs(self, shift, no_list=False):
             return Polynomial_padic_capped_relative_dense(self.parent(), (self._poly // fdiv, 0, [0 if a <= shift else a - shift for a in self._relprecs], False, None, None), construct=True)
 
     # def __floordiv__(self, right):
-    #     if is_Polynomial(right) and right.is_constant() and right[0] in self.base_ring():
+    #     if isinstance(right, Polynomial) and right.is_constant() and right[0] in self.base_ring():
     #         d = self.base_ring()(right[0])
     #     elif (right in self.base_ring()):
     #         d = self.base_ring()(right)

src/sage/rings/polynomial/polynomial_element.pxd

@@ -1,11 +1,12 @@
-from sage.structure.element import Element, CommutativeAlgebraElement
+from sage.structure.element import Element
 from sage.structure.element cimport Element, CommutativeAlgebraElement, ModuleElement
+from sage.structure.element cimport Polynomial as Polynomial_base
 from sage.structure.parent cimport Parent
 from sage.rings.integer cimport Integer
 from .polynomial_compiled cimport CompiledPolynomialFunction
 
 
-cdef class Polynomial(CommutativeAlgebraElement):
+cdef class Polynomial(Polynomial_base):
     cdef Polynomial _new_generic(self, list coeffs)
     cdef char _is_gen
     cdef CompiledPolynomialFunction _compiled