Python MatrixSpace.identity_matrix方法代码示例

# 需要导入模块: from sage.matrix.matrix_space import MatrixSpace [as 别名]
# 或者: from sage.matrix.matrix_space.MatrixSpace import identity_matrix [as 别名]
def matId(n):
    Id = []
    n2 = n.quo_rem(2)[0]
    for j in range(n2):
        MSn = MatrixSpace(F, n2-j, n2-j)
        Id.append(MSn.identity_matrix())
    return Id

# 需要导入模块: from sage.matrix.matrix_space import MatrixSpace [as 别名]
# 或者: from sage.matrix.matrix_space.MatrixSpace import identity_matrix [as 别名]
def matA(n):
    A = []
    n2 = n.quo_rem(2)[0]
    for j in range(n2+2):
        MS0 = MatrixSpace(F, j, j)
        I = MS0.identity_matrix()
        O = MS0(j*j*[1])
        A.append(I+O)
    return A

# 需要导入模块: from sage.matrix.matrix_space import MatrixSpace [as 别名]
# 或者: from sage.matrix.matrix_space.MatrixSpace import identity_matrix [as 别名]
def RandomLinearCode(n,k,F):
    r"""
    The method used is to first construct a `k \times n`
    matrix using Sage's random_element method for the MatrixSpace
    class. The construction is probabilistic but should only fail
    extremely rarely.

    INPUT: Integers n,k, with `n>k`, and a finite field F

    OUTPUT: Returns a "random" linear code with length n, dimension k
    over field F.

    EXAMPLES::

        sage: C = codes.RandomLinearCode(30,15,GF(2))
        sage: C
        Linear code of length 30, dimension 15 over Finite Field of size 2
        sage: C = codes.RandomLinearCode(10,5,GF(4,'a'))
        sage: C
        Linear code of length 10, dimension 5 over Finite Field in a of size 2^2

    AUTHORS:

    - David Joyner (2007-05)
    """
    MS = MatrixSpace(F,k,n)
    for i in range(50):
        G = MS.random_element()
        if G.rank() == k:
            V = span(G.rows(), F)
            return LinearCodeFromVectorSpace(V)  # may not be in standard form
    MS1 = MatrixSpace(F,k,k)
    MS2 = MatrixSpace(F,k,n-k)
    Ik = MS1.identity_matrix()
    A = MS2.random_element()
    G = Ik.augment(A)
    return LinearCode(G)                          # in standard form

# 需要导入模块: from sage.matrix.matrix_space import MatrixSpace [as 别名]
# 或者: from sage.matrix.matrix_space.MatrixSpace import identity_matrix [as 别名]
    def __call__(self, A, name=''):
        r"""
        Create an element of the homspace ``self`` from `A`.

        INPUT:

        - ``A`` -- one of the following:

          - an element of a Hecke algebra

          - a Hecke module morphism

          - a matrix

          - a list of elements of the codomain specifying the images
            of the basis elements of the domain.

        EXAMPLES::

            sage: M = ModularForms(Gamma0(7), 4)
            sage: H = M.Hom(M)
            sage: H(M.hecke_operator(7))
            Hecke module morphism T_7 defined by the matrix
            [ -7   0   0]
            [  0   1 240]
            [  0   0 343]
            Domain: Modular Forms space of dimension 3 for Congruence Subgroup Gamma0(7) ...
            Codomain: Modular Forms space of dimension 3 for Congruence Subgroup Gamma0(7) ...
            sage: H(H(M.hecke_operator(7)))
            Hecke module morphism T_7 defined by the matrix
            [ -7   0   0]
            [  0   1 240]
            [  0   0 343]
            Domain: Modular Forms space of dimension 3 for Congruence Subgroup Gamma0(7) ...
            Codomain: Modular Forms space of dimension 3 for Congruence Subgroup Gamma0(7) ...
            sage: H(matrix(QQ, 3, srange(9)))
            Hecke module morphism defined by the matrix
            [0 1 2]
            [3 4 5]
            [6 7 8]
            Domain: Modular Forms space of dimension 3 for Congruence Subgroup Gamma0(7) ...
            Codomain: Modular Forms space of dimension 3 for Congruence Subgroup Gamma0(7) ...

        TESTS:

        Make sure that the element is created correctly when the codomain is
        not the full module (related to :trac:`21497`)::

            sage: M = ModularSymbols(Gamma0(3),weight=22,sign=1)
            sage: S = M.cuspidal_subspace()
            sage: H = S.Hom(S)
            sage: H(S.gens())
            Hecke module morphism defined by the matrix
            [1 0 0 0 0 0]
            [0 1 0 0 0 0]
            [0 0 1 0 0 0]
            [0 0 0 1 0 0]
            [0 0 0 0 1 0]
            [0 0 0 0 0 1]
            Domain: Modular Symbols subspace of dimension 6 of Modular Symbols space ...
            Codomain: Modular Symbols subspace of dimension 6 of Modular Symbols space ...

            sage: H.zero() in H
            True
            sage: H.one() in H
            True
        """
        try:
            if A.parent() == self:
                A._set_parent(self)
                return A
            A = A.hecke_module_morphism()
            if A.parent() == self:
                A._set_parent(self)
                return A
            else:
                raise TypeError("unable to coerce A to self")
        except AttributeError:
            pass
        if A in self.base_ring():
            dim_dom = self.domain().rank()
            dim_codom = self.codomain().rank()
            MS = MatrixSpace(self.base_ring(), dim_dom, dim_codom)
            if self.domain() == self.codomain():
                A = A * MS.identity_matrix()
            elif A == 0:
                A = MS.zero()
            else:
                raise ValueError('scalars do not coerce to this homspace')
        elif isinstance(A, (list, tuple)):
            A = matrix([self.codomain().coordinate_vector(f) for f in A])
        return HeckeModuleMorphism_matrix(self, A, name)

# 需要导入模块: from sage.matrix.matrix_space import MatrixSpace [as 别名]
# 或者: from sage.matrix.matrix_space.MatrixSpace import identity_matrix [as 别名]

#.........这里部分代码省略.........

    def _element_constructor_(self, asm):
        """
        Construct an element of ``self``.

        EXAMPLES::

            sage: A = AlternatingSignMatrices(3)
            sage: elt = A([[1, 0, 0],[0, 1, 0],[0, 0, 1]]); elt
            [1 0 0]
            [0 1 0]
            [0 0 1]
            sage: elt.parent() is A
            True
            sage: A([[3, 2, 1], [2, 1], [1]])
            [1 0 0]
            [0 1 0]
            [0 0 1]
        """
        if isinstance(asm, AlternatingSignMatrix):
            if asm.parent() is self:
                return asm
            raise ValueError("Cannot convert between alternating sign matrices of different sizes")
        if asm in MonotoneTriangles(self._n):
            return self.from_monotone_triangle(asm)
        return self.element_class(self, self._matrix_space(asm))

    Element = AlternatingSignMatrix

    def _an_element_(self):
        """
        Return an element of ``self``.
        """
        return self.element_class(self, self._matrix_space.identity_matrix())

    def from_monotone_triangle(self, triangle):
        r"""
        Return an alternating sign matrix from a monotone triangle.

        EXAMPLES::

            sage: A = AlternatingSignMatrices(3)
            sage: A.from_monotone_triangle([[3, 2, 1], [2, 1], [1]])
            [1 0 0]
            [0 1 0]
            [0 0 1]
            sage: A.from_monotone_triangle([[3, 2, 1], [3, 2], [3]])
            [0 0 1]
            [0 1 0]
            [1 0 0]
        """
        n = len(triangle)
        if n != self._n:
            raise ValueError("Incorrect size")
        asm = []

        prev = [0]*n
        for line in reversed(triangle):
            v = [1 if j+1 in reversed(line) else 0 for j in range(n)]
            row = [a-b for (a, b) in zip(v, prev)]
            asm.append(row)
            prev = v

        return self.element_class(self, self._matrix_space(asm))

    def size(self):