Dense Matrices over a general ring - Matrices and Spaces of Matrices

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# Dense Matrices over a general ring

class sage.matrix.matrix_generic_dense.Matrix_generic_dense

  Bases: `Matrix_dense`

  The `Matrix_generic_dense` class derives from `Matrix`, and defines functionality for dense matrices over any base ring. Matrices are represented by a list of elements in the base ring, and element access operations are implemented in this class.

  EXAMPLES:

  Sage

      sage: A = random_matrix(Integers(25)['x'], 2)
      sage: type(A)
      <class 'sage.matrix.matrix_generic_dense.Matrix_generic_dense'>
      sage: TestSuite(A).run(skip='_test_minpoly')

  Python

      >>> from sage.all import *
      >>> A = random_matrix(Integers(Integer(25))['x'], Integer(2))
      >>> type(A)
      <class 'sage.matrix.matrix_generic_dense.Matrix_generic_dense'>
      >>> TestSuite(A).run(skip='_test_minpoly')

  Test comparisons:

  Sage

      sage: A = random_matrix(Integers(25)['x'], 2)
      sage: A == A
      True
      sage: A < A + 1 or A[0, 0].coefficients()[0] == 24
      True
      sage: A+1 < A and A[0, 0].coefficients()[0] != 24
      False

  [Python]

      >>> from sage.all import *
      >>> A = random_matrix(Integers(Integer(25))['x'], Integer(2))
      >>> A == A
      True
      >>> A < A + Integer(1) or A[Integer(0), Integer(0)].coefficients()[Integer(0)] == Integer(24)
      True
      >>> A+Integer(1) < A and A[Integer(0), Integer(0)].coefficients()[Integer(0)] != Integer(24)
      False

  Test hashing:

  Sage

      sage: A = random_matrix(Integers(25)['x'], 2)
      sage: hash(A)
      Traceback (most recent call last):
      ...
      TypeError: mutable matrices are unhashable
      sage: A.set_immutable()
      sage: H = hash(A)

  Python

      >>> from sage.all import *
      >>> A = random_matrix(Integers(Integer(25))['x'], Integer(2))
      >>> hash(A)
      Traceback (most recent call last):
      ...
      TypeError: mutable matrices are unhashable
      >>> A.set_immutable()
      >>> H = hash(A)