Making imports more local in matrices.

src/sage/matrix/args.pyx

@@ -21,7 +21,9 @@ from cypari2.gen cimport Gen
 from cypari2.types cimport typ, t_MAT, t_VEC, t_COL, t_VECSMALL, t_LIST, t_STR, t_CLOSURE
 
 from .matrix_space import MatrixSpace
-from sage.rings.all import ZZ, RDF, CDF
+from sage.rings.integer_ring import ZZ
+from sage.rings.real_double import RDF
+from sage.rings.complex_double import CDF
 from sage.structure.coerce cimport (coercion_model,
         is_numpy_type, py_scalar_parent)
 from sage.structure.element cimport Element, RingElement, Vector

src/sage/matrix/benchmark.py

@@ -20,7 +20,9 @@
 from __future__ import absolute_import
 
 from .constructor import random_matrix, Matrix
-from sage.rings.all import ZZ, QQ, GF
+from sage.rings.integer_ring import ZZ
+from sage.rings.rational_field import QQ
+from sage.rings.finite_rings.finite_field_constructor import FiniteField as GF
 from sage.misc.misc import cputime
 from cysignals.alarm import AlarmInterrupt, alarm, cancel_alarm
 

src/sage/matrix/matrix2.pyx

@@ -13265,7 +13265,8 @@ cdef class Matrix(Matrix1):
             sage: len(str(a.det()))
             12215
         """
-        from sage.rings.all import RDF, RealField
+        from sage.rings.real_double import RDF
+        from sage.rings.real_mpfr import RealField
         try:
             A = self.change_ring(RDF)
             m1 = A._hadamard_row_bound()

src/sage/matrix/matrix_cyclo_dense.pyx

@@ -62,7 +62,7 @@ from .misc import matrix_integer_dense_rational_reconstruction
 from sage.rings.rational_field import QQ
 from sage.rings.integer_ring import ZZ
 from sage.arith.all import previous_prime, binomial
-from sage.rings.all import RealNumber
+from sage.rings.real_mpfr import create_RealNumber as RealNumber
 from sage.rings.integer cimport Integer
 from sage.rings.rational cimport Rational
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
@@ -1499,7 +1499,7 @@ cdef class Matrix_cyclo_dense(Matrix_dense):
             pass
         K = self.base_ring()
         phi = K.defining_polynomial()
-        from sage.rings.all import GF
+        from sage.rings.finite_rings.finite_field_constructor import FiniteField as GF
         from .constructor import matrix
         F = GF(p)
         aa = [a for a, _ in phi.change_ring(F).roots()]

src/sage/matrix/matrix_gf2e_dense.pyx

@@ -89,7 +89,7 @@ from sage.structure.element cimport Matrix, Vector
 from sage.structure.element cimport ModuleElement, Element, RingElement
 from sage.structure.richcmp cimport rich_to_bool
 
-from sage.rings.all import FiniteField as GF
+from sage.rings.finite_rings.finite_field_constructor import FiniteField as GF
 from sage.misc.randstate cimport randstate, current_randstate
 
 from sage.matrix.matrix_mod2_dense cimport Matrix_mod2_dense

src/sage/matrix/matrix_integer_dense_hnf.py

@@ -13,7 +13,10 @@
 from sage.misc.misc import verbose, cputime
 from sage.matrix.constructor import (random_matrix, matrix, identity_matrix)
 
-from sage.rings.all import ZZ, Integer, RR
+from sage.rings.integer_ring import ZZ
+from sage.rings.rational_field import QQ
+from sage.rings.real_mpfr import RR
+from sage.rings.integer import Integer
 from sage.arith.all import previous_prime, CRT_list
 
 

src/sage/matrix/matrix_integer_dense_saturation.py

@@ -4,7 +4,8 @@
 from __future__ import absolute_import
 from six.moves import range
 
-from sage.rings.all import ZZ, GF
+from sage.rings.integer_ring import ZZ
+from sage.rings.finite_rings.finite_field_constructor import FiniteField as GF
 from sage.arith.all import binomial, gcd
 from sage.matrix.constructor import identity_matrix, random_matrix
 from sage.misc.misc import verbose

src/sage/matrix/matrix_modn_sparse.pyx

@@ -107,12 +107,11 @@ cimport sage.matrix.matrix_sparse as matrix_sparse
 cimport sage.matrix.matrix_dense as matrix_dense
 from sage.rings.finite_rings.integer_mod cimport IntegerMod_int, IntegerMod_abstract
 from sage.rings.integer cimport Integer
+from sage.rings.rational_field import QQ
 from sage.rings.integer_ring import ZZ
 
 from sage.misc.misc import verbose, get_verbose
 
-import sage.rings.all as rings
-
 from sage.matrix.matrix2 import Matrix as Matrix2
 from .args cimport SparseEntry, MatrixArgs_init
 from sage.arith.all import is_prime
@@ -519,7 +518,7 @@ cdef class Matrix_modn_sparse(matrix_sparse.Matrix_sparse):
         for i from 0 <= i < self._nrows:
             nonzero_entries += self.rows[i].num_nonzero
 
-        return rings.ZZ(nonzero_entries)/rings.ZZ(self._nrows*self._ncols)
+        return ZZ(nonzero_entries) / ZZ(self._nrows*self._ncols)
 
     def transpose(self):
         """
@@ -926,7 +925,6 @@ cdef class Matrix_modn_sparse(matrix_sparse.Matrix_sparse):
             return Matrix_sparse.solve_right(self, B)
         else:
             if isinstance(B, sage.structure.element.Matrix):
-                from sage.rings.rational_field import QQ
                 from sage.matrix.special import diagonal_matrix
                 m, d = self._solve_matrix_linbox(B, algorithm)
                 return m  * diagonal_matrix([QQ((1,x)) for x in d])

src/sage/matrix/matrix_mpolynomial_dense.pyx

@@ -280,7 +280,7 @@ cdef class Matrix_mpolynomial_dense(Matrix_generic_dense):
                 for c in xrange(self.ncols()):
                     self.set_unsafe(r, c, R._zero_element)
 
-            from sage.rings.all import ZZ
+            from sage.rings.integer_ring import ZZ
             l = [ZZ(e-1) for e in l]
 
             self.cache('in_echelon_form_bareiss',True)

src/sage/matrix/special.py

@@ -66,12 +66,13 @@
 from six.moves import range
 from six import integer_types
 
-import sage.rings.all as rings
 from sage.rings.ring import is_Ring
 import sage.matrix.matrix_space as matrix_space
 from sage.modules.free_module_element import vector
 from sage.structure.element import is_Matrix
-from sage.rings.all import ZZ, QQ
+from sage.rings.integer_ring import ZZ
+from sage.rings.rational_field import QQ
+from sage.rings.integer import Integer
 from sage.misc.misc_c import running_total
 from copy import copy
 from .constructor import matrix
@@ -801,7 +802,7 @@ def diagonal_matrix(arg0=None, arg1=None, arg2=None, sparse=True):
     # Size of matrix specified?
     # Formats 2, 4
     nrows = None
-    if isinstance(arg0, integer_types + (rings.Integer,)):
+    if isinstance(arg0, integer_types + (Integer,)):
         nrows = arg0
         arg0 = arg1
     # Object holding entries
@@ -826,7 +827,7 @@ def diagonal_matrix(arg0=None, arg1=None, arg2=None, sparse=True):
 
     # provide a default ring for an empty list
     if not len(entries) and ring is None:
-      ring = rings.ZZ
+       ring = ZZ
 
     # Convert entries to a list v over a common ring
     from sage.modules.free_module_element import prepare
@@ -876,9 +877,9 @@ def identity_matrix(ring, n=0, sparse=False):
         sage: M.is_mutable()
         True
     """
-    if isinstance(ring, integer_types  + (rings.Integer,)):
+    if isinstance(ring, integer_types  + (Integer,)):
         n = ring
-        ring = rings.ZZ
+        ring = ZZ
     return matrix_space.MatrixSpace(ring, n, n, sparse)(1)
 
 @matrix_method
@@ -902,9 +903,9 @@ def lehmer(ring, n=0):
     """
     from sage.sets.integer_range import IntegerRange
 
-    if isinstance(ring, integer_types + (rings.Integer,)):
+    if isinstance(ring, integer_types + (Integer,)):
         n = ring
-        ring = rings.QQ
+        ring = QQ
     return matrix_space.MatrixSpace(ring, n, n).matrix([[min(i, j)/max(i, j) for i in IntegerRange(1, n+1)] for j in IntegerRange(1, n+1)])
 
 @matrix_method
@@ -945,9 +946,9 @@ def zero_matrix(ring, nrows=None, ncols=None, sparse=False):
         [0 0 0 0 0]
 
     """
-    if isinstance(ring, integer_types + (rings.Integer,)):
+    if isinstance(ring, integer_types + (Integer,)):
         nrows, ncols = (ring, nrows)
-        ring = rings.ZZ
+        ring = ZZ
     return matrix_space.MatrixSpace(ring, nrows, ncols, sparse)(0)
 
 @matrix_method
@@ -1030,9 +1031,9 @@ def ones_matrix(ring, nrows=None, ncols=None, sparse=False):
         ...
         ValueError: constructing an all ones matrix requires at least one dimension
     """
-    if isinstance(ring, integer_types + (rings.Integer,)):
+    if isinstance(ring, integer_types + (Integer,)):
         nrows, ncols = (ring, nrows)
-        ring = rings.ZZ
+        ring = ZZ
     if nrows is None:
         raise ValueError("constructing an all ones matrix requires at least one dimension")
     if ncols is None:
@@ -1363,11 +1364,11 @@ def elementary_matrix(arg0, arg1=None, **kwds):
             raise TypeError('scale must be an element of some ring, not {0}'.format(scale))
         R = scale.parent()
     else:
-        R = rings.ZZ
+        R = ZZ
     if arg0 is None:
         raise ValueError('size of elementary matrix must be given')
     try:
-        n = rings.Integer(arg0)
+        n = Integer(arg0)
     except TypeError:
         raise TypeError('size of elementary matrix must be an integer, not {0}'.format(arg0))
     if n <= 0:
@@ -1395,14 +1396,14 @@ def elementary_matrix(arg0, arg1=None, **kwds):
 
     # analyze parameters to determine matrix type
     try:
-        row1 = rings.Integer(row1)
+        row1 = Integer(row1)
     except TypeError:
         raise TypeError('{0} of elementary matrix must be an integer, not {1}'.format(opstring, row1))
     if row1 < 0 or row1 >= n :
         raise ValueError('{0} of elementary matrix must be positive and smaller than {1}, not {2}'.format(opstring, n, row1))
     if not row2 is None:
         try:
-            row2 = rings.Integer(row2)
+            row2 = Integer(row2)
         except TypeError:
             raise TypeError('{0} of elementary matrix must be an integer, not {1}'.format(opstring, row2))
         if row2 < 0 or row2 >= n :
@@ -1884,9 +1885,9 @@ def block_matrix(*args, **kwds):
 
     if not args:
         if sparse is not None:
-            return matrix_space.MatrixSpace(rings.ZZ, 0, 0, sparse=sparse)([])
+            return matrix_space.MatrixSpace(ZZ, 0, 0, sparse=sparse)([])
         else:
-            return matrix_space.MatrixSpace(rings.ZZ, 0, 0)([])
+            return matrix_space.MatrixSpace(ZZ, 0, 0)([])
 
     if len(args) >= 1 and is_Ring(args[0]):
         # A ring is specified

src/sage/matrix/symplectic_basis.py

@@ -62,7 +62,8 @@
 #                  https://www.gnu.org/licenses/
 ######################################################################
 
-from sage.rings.all import ZZ, Infinity
+from sage.rings.integer_ring import ZZ
+from sage.rings.infinity import Infinity
 
 
 def _inplace_move_to_positive_pivot(G, row, col, B, pivot):