Import matrix, not Matrix, from sage.matrix.constructor to avoid clashes

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 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 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

@@ -243,7 +243,7 @@ def __call__(self, f, check=True, unitary=True):
         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/coding/binary_code.pyx

@@ -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/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 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
 
@@ -174,7 +174,7 @@ def to_matrix_representation(v, sub_field=None, basis=None):
     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"""

src/sage/combinat/cluster_algebra_quiver/quiver.py

@@ -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/root_system/reflection_group_complex.py

@@ -209,7 +209,7 @@
 from sage.combinat.permutation import Permutation
 from sage.rings.integer_ring import ZZ
 from sage.rings.rational_field import QQ
-from sage.matrix.constructor import Matrix
+from sage.matrix.constructor import matrix
 from sage.matrix.special import identity_matrix
 from sage.structure.element import Matrix
 from sage.interfaces.gap3 import gap3
@@ -841,7 +841,7 @@ def discriminant_in_invariant_ring(self, invariants=None):
         D = D.change_ring(P)
         f = D - sum(X[i] * F for i,F in enumerate(FsPowers))
         coeffs = f.coefficients()
-        lhs = Matrix(R, [[coeff.coefficient(X[i]) for i in range(m)]
+        lhs = matrix(R, [[coeff.coefficient(X[i]) for i in range(m)]
                          for coeff in coeffs])
         rhs = vector([coeff.constant_coefficient() for coeff in coeffs])
 
@@ -1320,7 +1320,7 @@ def independent_roots(self):
         basis = {}
         for ind in self._index_set:
             vec = Delta[ind]
-            if Matrix(list(basis.values()) + [vec]).rank() == len(basis) + 1:
+            if matrix(list(basis.values()) + [vec]).rank() == len(basis) + 1:
                 basis[ind] = vec
         return Family(basis)
 
@@ -1459,7 +1459,7 @@ def jacobian_of_fundamental_invariants(self, invs=None):
             invs = self.fundamental_invariants()
         P = invs[0].parent()
         X = P.gens()
-        return Matrix(P, [[ P(g).derivative(x) for x in X ] for g in invs ])
+        return matrix(P, [[ P(g).derivative(x) for x in X ] for g in invs ])
 
     @cached_method
     def primitive_vector_field(self, invs=None):
@@ -1743,7 +1743,7 @@ def invariant_value(i,j):
                 coeff = QQ(coeff)
             coeffs.append(coeff)
 
-        return Matrix([[invariant_value(i,j) / self.cardinality() for j in range(n)]
+        return matrix([[invariant_value(i,j) / self.cardinality() for j in range(n)]
                        for i in range(n)])
 
     def invariant_form_standardization(self):

src/sage/combinat/similarity_class_type.py

@@ -203,7 +203,7 @@ class type, it is also possible to compute the number of classes of that type
 from sage.rings.integer_ring import ZZ
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 from sage.rings.rational_field import QQ
-from sage.structure.element import Element, is_Matrix
+from sage.structure.element import Element, Matrix
 from sage.structure.parent import Parent
 from sage.structure.unique_representation import UniqueRepresentation
 

src/sage/geometry/polyhedron/base5.py

@@ -32,7 +32,7 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-from sage.structure.element import coerce_binop, is_Vector, is_Matrix
+from sage.structure.element import coerce_binop, Vector, Matrix
 
 from sage.rings.integer_ring import ZZ
 from sage.rings.rational_field import QQ

src/sage/libs/ntl/ntl_mat_GF2.pyx

@@ -470,8 +470,8 @@ cdef class ntl_mat_GF2():
             True
         """
         from sage.rings.finite_rings.finite_field_constructor import FiniteField
-        from sage.matrix.constructor import Matrix
-        m =  Matrix(FiniteField(2),self.x.NumRows(),self.x.NumCols())
+        from sage.matrix.constructor import matrix
+        m = matrix(FiniteField(2),self.x.NumRows(),self.x.NumCols())
 
         cdef Py_ssize_t i, j
 

src/sage/libs/ntl/ntl_mat_GF2E.pyx

@@ -544,8 +544,8 @@ cdef class ntl_mat_GF2E():
 
         l = [e._sage_(k) for e in self.list()] # we actually can do faster than this
 
-        from sage.matrix.constructor import Matrix
-        return Matrix(k,self.x.NumRows(),self.x.NumCols(),l)
+        from sage.matrix.constructor import matrix
+        return matrix(k, self.x.NumRows(), self.x.NumCols(), l)
 
     def transpose(ntl_mat_GF2E self):
         """

src/sage/matroids/constructor.py

@@ -102,7 +102,7 @@
 
 
 from itertools import combinations
-from sage.matrix.constructor import Matrix
+from sage.matrix.constructor import matrix
 from sage.structure.element import Matrix
 from sage.rings.integer_ring import ZZ
 from sage.rings.rational_field import QQ
@@ -893,7 +893,7 @@ def Matroid(groundset=None, data=None, **kwds):
             # 2) Sage will sort the columns, making it impossible to keep labels!
             V = G.vertices(sort=True)
             n = G.num_verts()
-            A = Matrix(ZZ, n, m, 0)
+            A = matrix(ZZ, n, m, 0)
             mm = 0
             for i, j, k in G.edge_iterator():
                 A[V.index(i), mm] = -1
@@ -925,9 +925,9 @@ def Matroid(groundset=None, data=None, **kwds):
         # Fix the representation
         if not isinstance(A, Matrix):
             if base_ring is not None:
-                A = Matrix(base_ring, A)
+                A = matrix(base_ring, A)
             else:
-                A = Matrix(A)
+                A = matrix(A)
 
         # Fix the ring
         if base_ring is not None:

src/sage/numerical/backends/matrix_sdp_backend.pyx

@@ -20,7 +20,7 @@ other classes implementing solvers.
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
 
-from sage.matrix.constructor import Matrix
+from sage.matrix.constructor import matrix
 from sage.numerical.backends.generic_sdp_backend cimport GenericSDPBackend
 
 cdef class MatrixSDPBackend(GenericSDPBackend):
@@ -125,7 +125,7 @@ cdef class MatrixSDPBackend(GenericSDPBackend):
         i = 0
         for row in self.coeffs_matrix:
             if self.matrices_dim.get(i) is not None:
-                row.append( Matrix.zero(self.matrices_dim[i], self.matrices_dim[i]) )
+                row.append( matrix.zero(self.matrices_dim[i], self.matrices_dim[i]) )
             else:
                 row.append(0)
             i+=1
@@ -313,7 +313,7 @@ cdef class MatrixSDPBackend(GenericSDPBackend):
             ([], [])
         """
         for i in range(number):
-            self.add_linear_constraint(zip(range(self.ncols()+1),[Matrix.zero(1,1) for i in range(self.ncols()+1)]),
+            self.add_linear_constraint(zip(range(self.ncols()+1),[matrix.zero(1,1) for i in range(self.ncols()+1)]),
                                        name=None if names is None else names[i])
 
 
@@ -431,7 +431,7 @@ cdef class MatrixSDPBackend(GenericSDPBackend):
         indices = []
         matrices = []
         for index,m in self.coeffs_matrix[i]:
-            if m != Matrix.zero(self.matrices_dim[i],self.matrices_dim[i]):
+            if m != matrix.zero(self.matrices_dim[i],self.matrices_dim[i]):
                 indices.append(index)
                 matrices.append(m)
         return (indices, matrices)

src/sage/numerical/sdp.pyx

@@ -235,7 +235,7 @@ AUTHORS:
 from sage.structure.parent cimport Parent
 from sage.structure.element cimport Element
 from sage.numerical.linear_functions import is_LinearFunction, is_LinearConstraint
-from sage.matrix.constructor import Matrix
+from sage.matrix.constructor import matrix
 from sage.structure.element import Matrix
 
 
@@ -675,7 +675,7 @@ cdef class SemidefiniteProgram(SageObject):
             if l[-1][0] == -1:
                 last_i,last_value = l.pop()
             else:
-                last_value = Matrix.zero( l[0][1].dimensions()[0],l[0][1].dimensions()[1]  )
+                last_value = matrix.zero( l[0][1].dimensions()[0],l[0][1].dimensions()[1]  )
             l.reverse()
             for j, c in l:
                 if c == 0:

src/sage/quadratic_forms/ternary_qf.py

@@ -43,7 +43,7 @@
 from sage.rings.finite_rings.integer_mod import mod
 from sage.rings.integer_ring import ZZ
 from sage.rings.polynomial.polynomial_ring import polygens
-from sage.structure.element import Vector, is_Matrix
+from sage.structure.element import Vector, Matrix
 from sage.structure.sage_object import SageObject
 
 

src/sage/rings/polynomial/multi_polynomial_sequence.py

@@ -748,7 +748,7 @@ def coefficients_monomials(self, order=None, sparse=True):
              2*a*b + 2*b*c + 2*c*d - b, b^2 + 2*a*c + 2*b*d - c)
         """
         from sage.modules.free_module_element import vector
-        from sage.matrix.constructor import Matrix
+        from sage.matrix.constructor import matrix
 
         if order is None:
             v = sorted(self.monomials(), reverse=True)
@@ -759,7 +759,7 @@ def coefficients_monomials(self, order=None, sparse=True):
                 raise ValueError("order argument can only accept list or tuple")
 
         y = dict(zip(v, range(len(v))))  # construct dictionary for fast lookups
-        A = Matrix(self.ring().base_ring(), len(self), len(v), sparse=sparse)
+        A = matrix(self.ring().base_ring(), len(self), len(v), sparse=sparse)
         for x, poly in enumerate(self):
             for c, m in poly:
                 try:
@@ -825,13 +825,13 @@ def coefficient_matrix(self, sparse=True):
             [      2*a*b + 2*b*c + 2*c*d - b]
             [        b^2 + 2*a*c + 2*b*d - c]
         """
-        from sage.matrix.constructor import Matrix
+        from sage.matrix.constructor import matrix
         from sage.misc.superseded import deprecation
         deprecation(37035, "the function coefficient_matrix is deprecated; use coefficients_monomials instead")
 
         R = self.ring()
         A, v = self.coefficients_monomials(sparse=sparse)
-        return A, Matrix(R,len(v),1,v)
+        return A, matrix(R,len(v),1,v)
 
     def subs(self, *args, **kwargs):
         """
@@ -1739,7 +1739,7 @@ def coefficients_monomials(self, order=None, sparse=True):
             (a + b + c)
         """
         from sage.modules.free_module_element import vector
-        from sage.matrix.constructor import Matrix
+        from sage.matrix.constructor import matrix
         from sage.rings.polynomial.multi_polynomial_ring_base import \
             BooleanPolynomialRing_base
 
@@ -1754,7 +1754,7 @@ def coefficients_monomials(self, order=None, sparse=True):
         R = self.ring()
         K = R.base_ring()
         y = dict(zip(v, range(len(v))))  # construct dictionary for fast lookups
-        A = Matrix(K, len(self), len(v), sparse=sparse)
+        A = matrix(K, len(self), len(v), sparse=sparse)
 
         if isinstance(R, BooleanPolynomialRing_base):
             one = K.one()

src/sage/schemes/plane_conics/con_field.py

@@ -32,7 +32,7 @@
 from sage.structure.sequence import Sequence
 from sage.structure.element import Vector
 from sage.schemes.projective.projective_space import ProjectiveSpace
-from sage.matrix.constructor import Matrix
+from sage.matrix.constructor import matrix
 from sage.structure.element import Matrix
 
 from sage.schemes.curves.projective_curve import ProjectivePlaneCurve_field
@@ -209,7 +209,7 @@ def derivative_matrix(self):
             [t^2   1   0]
         """
         a, b, c, d, e, f = self.coefficients()
-        return Matrix([[2 * a, b, c],
+        return matrix([[2 * a, b, c],
                        [b, 2 * d, e],
                        [c, e, 2 * f]])
 
@@ -305,7 +305,7 @@ def diagonal_matrix(self):
                 for j in range(i+1,3):
                     basis[j] = basis[j] - \
                                (basis[i]*A*basis[j].column())/l * basis[i]
-        T = Matrix(basis).transpose()
+        T = matrix(basis).transpose()
         return T.transpose()*A*T, T
 
     def diagonalization(self, names=None):
@@ -1241,11 +1241,11 @@ def symmetric_matrix(self):
         a, b, c, d, e, f = self.coefficients()
         if self.base_ring().characteristic() == 2:
             if b == 0 and c == 0 and e == 0:
-                return Matrix([[a, 0, 0], [0, d, 0], [0, 0, f]])
+                return matrix([[a, 0, 0], [0, d, 0], [0, 0, f]])
             raise ValueError("The conic self (= %s) has no symmetric matrix "
                              "because the base field has characteristic 2" %
                              self)
-        return Matrix([[a, b / 2, c / 2],
+        return matrix([[a, b / 2, c / 2],
                        [b / 2, d, e / 2],
                        [c / 2, e / 2, f]])
 

src/sage/schemes/plane_conics/constructor.py

@@ -24,7 +24,7 @@
 #                  https://www.gnu.org/licenses/
 # ****************************************************************************
 
-from sage.matrix.constructor import Matrix
+from sage.matrix.constructor import matrix
 from sage.modules.free_module_element import vector
 from sage.categories.integral_domains import IntegralDomains
 from sage.rings.rational_field import is_RationalField
@@ -179,7 +179,7 @@ def Conic(base_field, F=None, names=None, unique=True):
                 L.append(Sequence([C[0]**2, C[0] * C[1],
                                    C[0] * C[2], C[1]**2,
                                    C[1] * C[2], C[2]**2], P.fraction_field()))
-            M = Matrix(L)
+            M = matrix(L)
             if unique and M.rank() != 5:
                 raise ValueError("points in F (=%s) do not define a unique "
                                  "conic" % F)