Deprecate is_Element, ...

src/sage/algebras/finite_dimensional_algebras/finite_dimensional_algebra.py

@@ -18,8 +18,8 @@
 from sage.rings.integer_ring import ZZ
 
 from sage.categories.magmatic_algebras import MagmaticAlgebras
-from sage.matrix.constructor import Matrix, matrix
-from sage.structure.element import is_Matrix
+from sage.matrix.constructor import matrix
+from sage.structure.element import Matrix
 from sage.rings.ring import Algebra
 from sage.structure.category_object import normalize_names
 from sage.structure.unique_representation import UniqueRepresentation
@@ -136,7 +136,7 @@ def __classcall_private__(cls, k, table, names='e', assume_associative=False,
         table = [b.base_extend(k) for b in table]
         for b in table:
             b.set_immutable()
-            if not (is_Matrix(b) and b.dimensions() == (n, n)):
+            if not (isinstance(b, Matrix) and b.dimensions() == (n, n)):
                 raise ValueError("input is not a multiplication table")
         table = tuple(table)
 
@@ -389,7 +389,7 @@ def left_table(self):
         """
         B = self.table()
         n = self.degree()
-        table = [Matrix([B[j][i] for j in range(n)]) for i in range(n)]
+        table = [matrix([B[j][i] for j in range(n)]) for i in range(n)]
         for b in table:
             b.set_immutable()
         return tuple(table)
@@ -596,9 +596,9 @@ def is_unitary(self):
             self._one = matrix(k, 1, n)
             return True
         B1 = reduce(lambda x, y: x.augment(y),
-                    self._table, Matrix(k, n, 0))
+                    self._table, matrix(k, n, 0))
         B2 = reduce(lambda x, y: x.augment(y),
-                    self.left_table(), Matrix(k, n, 0))
+                    self.left_table(), matrix(k, n, 0))
         # This is the vector obtained by concatenating the rows of the
         # n times n identity matrix:
         kone = k.one()
@@ -882,7 +882,7 @@ def primary_decomposition(self):
                 and (self._assume_associative or self.is_associative())):
             raise TypeError("algebra must be unitary, commutative and associative")
         # Start with the trivial decomposition of self.
-        components = [Matrix.identity(k, n)]
+        components = [matrix.identity(k, n)]
         for b in self.table():
             # Use the action of the basis element b to refine our
             # decomposition of self.
@@ -903,7 +903,7 @@ def primary_decomposition(self):
             components = components_new
         quotients = []
         for i in range(len(components)):
-            I = Matrix(k, 0, n)
+            I = matrix(k, 0, n)
             for j,c in enumerate(components):
                 if j != i:
                     I = I.stack(c)

src/sage/algebras/finite_dimensional_algebras/finite_dimensional_algebra_element.pyx

@@ -15,7 +15,6 @@ Elements of Finite Algebras
 import re
 
 from sage.matrix.matrix_space import MatrixSpace
-from sage.structure.element import is_Matrix
 from sage.rings.integer import Integer
 
 from cpython.object cimport PyObject_RichCompare as richcmp
@@ -119,7 +118,7 @@ cdef class FiniteDimensionalAlgebraElement(AlgebraElement):
                     raise TypeError("algebra is not unitary")
             elif isinstance(elt, Vector):
                 self._vector = MatrixSpace(k, 1, n)(list(elt))
-            elif is_Matrix(elt):
+            elif isinstance(elt, Matrix):
                 if elt.ncols() != n:
                     raise ValueError("matrix does not define an element of the algebra")
                 if elt.nrows() == 1:

src/sage/algebras/finite_dimensional_algebras/finite_dimensional_algebra_ideal.py

@@ -15,10 +15,9 @@
 
 from .finite_dimensional_algebra_element import FiniteDimensionalAlgebraElement
 
-from sage.matrix.constructor import Matrix
-from sage.structure.element import is_Matrix
+from sage.matrix.constructor import matrix
 from sage.rings.ideal import Ideal_generic
-from sage.structure.element import parent
+from sage.structure.element import Matrix, parent
 
 from sage.misc.cachefunc import cached_method
 from functools import reduce
@@ -58,16 +57,16 @@ def __init__(self, A, gens=None, given_by_matrix=False):
             self._basis_matrix = gens
             gens = gens.rows()
         elif gens is None:
-            self._basis_matrix = Matrix(k, 0, n)
+            self._basis_matrix = matrix(k, 0, n)
         elif isinstance(gens, (list, tuple)):
             B = [FiniteDimensionalAlgebraIdeal(A, x).basis_matrix() for x in gens]
-            B = reduce(lambda x, y: x.stack(y), B, Matrix(k, 0, n))
+            B = reduce(lambda x, y: x.stack(y), B, matrix(k, 0, n))
             self._basis_matrix = B.echelon_form().image().basis_matrix()
-        elif is_Matrix(gens):
+        elif isinstance(gens, Matrix):
             gens = FiniteDimensionalAlgebraElement(A, gens)
         elif isinstance(gens, FiniteDimensionalAlgebraElement):
             gens = gens.vector()
-            B = Matrix([(gens * b).list() for b in A.table()])
+            B = matrix([(gens * b).list() for b in A.table()])
             self._basis_matrix = B.echelon_form().image().basis_matrix()
         Ideal_generic.__init__(self, A, gens)
 

src/sage/algebras/finite_dimensional_algebras/finite_dimensional_algebra_morphism.py

@@ -15,7 +15,7 @@
 from sage.misc.cachefunc import cached_method
 from sage.rings.morphism import RingHomomorphism_im_gens
 from sage.rings.homset import RingHomset_generic
-from sage.structure.element import is_Matrix
+from sage.structure.element import Matrix
 
 
 class FiniteDimensionalAlgebraMorphism(RingHomomorphism_im_gens):
@@ -240,10 +240,10 @@ def __call__(self, f, check=True, unitary=True):
                 return f
             if f.parent() == self:
                 return FiniteDimensionalAlgebraMorphism(self, f._matrix, check, unitary)
-        elif is_Matrix(f):
+        elif isinstance(f, Matrix):
             return FiniteDimensionalAlgebraMorphism(self, f, check, unitary)
         try:
-            from sage.matrix.constructor import Matrix
-            return FiniteDimensionalAlgebraMorphism(self, Matrix(f), check, unitary)
+            from sage.matrix.constructor import matrix
+            return FiniteDimensionalAlgebraMorphism(self, matrix(f), check, unitary)
         except Exception:
             return RingHomset_generic.__call__(self, f, check)

src/sage/algebras/jordan_algebra.py

@@ -22,7 +22,7 @@
 from sage.structure.richcmp import richcmp
 from sage.categories.magmatic_algebras import MagmaticAlgebras
 from sage.misc.cachefunc import cached_method
-from sage.structure.element import is_Matrix
+from sage.structure.element import Matrix
 from sage.modules.free_module import FreeModule
 from sage.matrix.constructor import matrix
 from sage.sets.family import Family
@@ -194,15 +194,15 @@ def __classcall_private__(self, arg0, arg1=None, names=None):
             names = tuple(names)
 
         if arg1 is None:
-            if not is_Matrix(arg0):
+            if not isinstance(arg0, Matrix):
                 from sage.algebras.octonion_algebra import OctonionAlgebra
                 if isinstance(arg0, OctonionAlgebra):
                     return ExceptionalJordanAlgebra(arg0)
                 if arg0.base_ring().characteristic() == 2:
                     raise ValueError("the base ring cannot have characteristic 2")
                 return SpecialJordanAlgebra(arg0, names)
             arg0, arg1 = arg0.base_ring(), arg0
-        elif is_Matrix(arg0):
+        elif isinstance(arg0, Matrix):
             arg0, arg1 = arg1, arg0
 
         # arg0 is the base ring and arg1 is a matrix

src/sage/algebras/quatalg/quaternion_algebra.py

@@ -61,7 +61,7 @@
 from sage.matrix.matrix_space import MatrixSpace
 from sage.matrix.constructor import diagonal_matrix, matrix
 from sage.structure.sequence import Sequence
-from sage.structure.element import is_RingElement
+from sage.structure.element import RingElement
 from sage.structure.factory import UniqueFactory
 from sage.modules.free_module import FreeModule
 from sage.modules.free_module_element import vector
@@ -248,7 +248,7 @@ def create_key(self, arg0, arg1=None, arg2=None, names='i,j,k'):
             # to the relevant Sage types. This is a bit inelegant.
             L = []
             for a in [arg0, arg1]:
-                if is_RingElement(a):
+                if isinstance(a, RingElement):
                     L.append(a)
                 elif isinstance(a, int):
                     L.append(Integer(a))

src/sage/calculus/expr.py

@@ -3,7 +3,7 @@
 """
 
 from sage.misc.lazy_import import lazy_import
-from sage.structure.element import is_Matrix
+from sage.structure.element import Matrix
 from sage.symbolic.expression import Expression
 from sage.symbolic.ring import SR
 
@@ -178,7 +178,7 @@ def symbolic_expression(x):
         if isinstance(expressions[0], FreeModuleElement):
             return matrix(expressions)
         return vector(expressions)
-    elif is_Matrix(x):
+    elif isinstance(x, Matrix):
         if not x.nrows() or not x.ncols():
             # Make sure it is symbolic and of correct dimensions
             # also when a matrix dimension is 0

src/sage/calculus/functions.py

@@ -3,7 +3,7 @@
 Calculus functions
 """
 from sage.misc.lazy_import import lazy_import
-from sage.structure.element import is_Matrix, is_Vector, Expression
+from sage.structure.element import Matrix, Vector, Expression
 
 lazy_import('sage.matrix.constructor', 'matrix')
 
@@ -138,13 +138,13 @@ def jacobian(functions, variables):
         [ cos(x)*cos(y) -sin(x)*sin(y)]
         [             0            e^x]
     """
-    if is_Matrix(functions) and (functions.nrows() == 1
+    if isinstance(functions, Matrix) and (functions.nrows() == 1
                                  or functions.ncols() == 1):
         functions = functions.list()
-    elif not (isinstance(functions, (tuple, list)) or is_Vector(functions)):
+    elif not (isinstance(functions, (tuple, list)) or isinstance(functions, Vector)):
         functions = [functions]
 
-    if not isinstance(variables, (tuple, list)) and not is_Vector(variables):
+    if not isinstance(variables, (tuple, list)) and not isinstance(variables, Vector):
         variables = [variables]
 
     return matrix([[diff(f, v) for v in variables] for f in functions])

src/sage/coding/binary_code.pyx

@@ -46,7 +46,7 @@ from cpython.mem cimport *
 from cpython.object cimport PyObject_RichCompare
 from cysignals.memory cimport sig_malloc, sig_realloc, sig_free
 
-from sage.structure.element import is_Matrix
+from sage.structure.element cimport Matrix
 from sage.misc.timing import cputime
 from sage.rings.integer cimport Integer
 from copy import copy
@@ -759,7 +759,7 @@ cdef class BinaryCode:
 
         self.radix = sizeof(int) << 3
 
-        if is_Matrix(arg1):
+        if isinstance(arg1, Matrix):
             self.ncols = arg1.ncols()
             self.nrows = arg1.nrows()
             nrows = self.nrows
@@ -795,7 +795,7 @@ cdef class BinaryCode:
         self_words = self.words
         self_basis = self.basis
 
-        if is_Matrix(arg1):
+        if isinstance(arg1, Matrix):
             rows = arg1.rows()
             for i from 0 <= i < nrows:
                 word = <codeword> 0
@@ -4185,9 +4185,9 @@ cdef class BinaryCodeClassifier:
                                 dealloc_word_perm(hwp)
                                 break
                         if bingo2:
-                            from sage.matrix.constructor import Matrix
+                            from sage.matrix.constructor import matrix
                             from sage.rings.finite_rings.finite_field_constructor import GF
-                            M = Matrix(GF(2), B_aug.nrows, B_aug.ncols)
+                            M = matrix(GF(2), B_aug.nrows, B_aug.ncols)
                             for i from 0 <= i < B_aug.ncols:
                                 for j from 0 <= j < B_aug.nrows:
                                     M[j,i] = B_aug.is_one(1 << j, i)

src/sage/coding/delsarte_bounds.py

@@ -693,9 +693,9 @@ def delsarte_bound_Q_matrix(q, d, return_data=False,
         [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
     """
     from sage.numerical.mip import MIPSolverException
-    from sage.structure.element import is_Matrix
+    from sage.structure.element import Matrix
 
-    if not is_Matrix(q):
+    if not isinstance(q, Matrix):
         raise ValueError("Input to delsarte_bound_Q_matrix "
                          "should be a sage Matrix()")
 

src/sage/coding/linear_rank_metric.py

@@ -112,8 +112,8 @@
 # ****************************************************************************
 
 from sage.categories.fields import Fields
-from sage.matrix.constructor import Matrix
-from sage.structure.element import is_Matrix, is_Vector
+from sage.matrix.constructor import matrix
+from sage.structure.element import Matrix, Vector
 from sage.modules.free_module_element import vector
 from sage.rings.infinity import Infinity
 
@@ -166,15 +166,15 @@ def to_matrix_representation(v, sub_field=None, basis=None):
         ...
         TypeError: Input must be a vector
     """
-    if not is_Vector(v):
+    if not isinstance(v, Vector):
         raise TypeError("Input must be a vector")
     base_field = v.base_ring()
     if not sub_field:
         sub_field = base_field.prime_subfield()
     n = v.length()
     m = base_field.degree()//sub_field.degree()
     extension, to_big_field, from_big_field = base_field.vector_space(sub_field, basis, map=True)
-    return Matrix(sub_field, m, n, lambda i, j: from_big_field(v[j])[i])
+    return matrix(sub_field, m, n, lambda i, j: from_big_field(v[j])[i])
 
 def from_matrix_representation(w, base_field=None, basis=None):
     r"""
@@ -214,7 +214,7 @@ def from_matrix_representation(w, base_field=None, basis=None):
         ...
         TypeError: Input must be a matrix
     """
-    if not is_Matrix(w):
+    if not isinstance(w, Matrix):
         raise TypeError("Input must be a matrix")
     sub_field = w.base_ring()
     if not base_field:
@@ -252,7 +252,7 @@ def rank_weight(c, sub_field=None, basis=None):
         sage: rank_weight(a, GF(4))
         2
     """
-    if is_Vector(c):
+    if isinstance(c, Vector):
         c = to_matrix_representation(c, sub_field, basis)
     return c.rank()
 
@@ -310,7 +310,7 @@ def rank_distance(a, b, sub_field=None, basis=None):
     """
     if not (a.base_ring() == b.base_ring()):
         raise ValueError("The base field of {} and {} has to be the same".format(a, b))
-    if not (is_Vector(a) and is_Vector(b)):
+    if not (isinstance(a, Vector) and isinstance(b, Vector)):
         raise TypeError("Both inputs have to be vectors")
     if not len(a) == len(b):
         raise ValueError("The length of {} and {} has to be the same".format(a, b))

src/sage/combinat/cluster_algebra_quiver/quiver.py

@@ -222,7 +222,7 @@ def __init__(self, data, frozen=None, user_labels=None):
             sage: TestSuite(Q).run()
         """
         from sage.combinat.cluster_algebra_quiver.cluster_seed import ClusterSeed
-        from sage.structure.element import is_Matrix
+        from sage.structure.element import Matrix
 
         if isinstance(user_labels, list):
             user_labels = [tuple(x) if isinstance(x, list) else x for x in user_labels]
@@ -334,7 +334,7 @@ def __init__(self, data, frozen=None, user_labels=None):
             self._description = data._description
 
         # constructs a quiver from a matrix
-        elif is_Matrix(data):
+        elif isinstance(data, Matrix):
             if not _principal_part(data).is_skew_symmetrizable( positive=True ):
                 raise ValueError('The principal part of the matrix data must be skew-symmetrizable.')
 
@@ -758,11 +758,11 @@ def qmu_save(self, filename=None):
         """
         M = self.b_matrix()
         if self.m():
-            from sage.matrix.constructor import Matrix
+            from sage.matrix.constructor import matrix
             from sage.matrix.constructor import block_matrix
             M1 = M.matrix_from_rows(list(range(self.n())))
             M2 = M.matrix_from_rows(list(range(self.n(), self.n() + self.m())))
-            M3 = Matrix(self.m(), self.m())
+            M3 = matrix(self.m(), self.m())
             M = block_matrix([[M1, -M2.transpose()], [M2, M3]])
         dg = self.digraph()
         dg.plot(save_pos=True)

src/sage/combinat/designs/incidence_structures.py

@@ -1147,9 +1147,9 @@ def incidence_matrix(self):
             [1 1 0 0]
             [0 1 1 1]
         """
-        from sage.matrix.constructor import Matrix
+        from sage.matrix.constructor import matrix
         from sage.rings.integer_ring import ZZ
-        A = Matrix(ZZ, self.num_points(), self.num_blocks(), sparse=True)
+        A = matrix(ZZ, self.num_points(), self.num_blocks(), sparse=True)
         for j, b in enumerate(self._blocks):
             for i in b:
                 A[i, j] = 1

src/sage/combinat/integer_matrices.py

@@ -167,8 +167,8 @@ def __contains__(self, x):
             sage: matrix([[-1, 3, 1]]) in IM
             False
         """
-        from sage.structure.element import is_Matrix
-        if not is_Matrix(x):
+        from sage.structure.element import Matrix
+        if not isinstance(x, Matrix):
             return False
         row_sums = [ZZ.zero()] * x.nrows()
         col_sums = [ZZ.zero()] * x.ncols()