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r"""

Wrappers on GAP matrices

"""

#*****************************************************************************

# This program is free software: you can redistribute it and/or modify

# it under the terms of the GNU General Public License as published by

# the Free Software Foundation, either version 2 of the License, or

# (at your option) any later version.

# http://www.gnu.org/licenses/

#*****************************************************************************

from __future__ import print_function, absolute_import

from sage.libs.gap.libgap import libgap

from . import matrix_space

from sage.structure.element cimport Matrix

cdef class Matrix_gap(Matrix_dense):

r"""

A Sage matrix wrapper over a GAP matrix.

EXAMPLES::

sage: M = MatrixSpace(ZZ, 2, implementation='gap')

sage: m1 = M([1, 0, 2, -3])

sage: m2 = M([2, 2, 5, -1])

sage: type(m1)

sage: m1 * m2

[ 2 2]

[-11 7]

sage: type(m1 * m2)

sage: M = MatrixSpace(QQ, 5, 3, implementation='gap')

sage: m = M(range(15))

sage: m.left_kernel()

Vector space of degree 5 and dimension 3 over Rational Field

Basis matrix:

[ 1 0 0 -4 3]

[ 0 1 0 -3 2]

[ 0 0 1 -2 1]

sage: M = MatrixSpace(ZZ, 10, implementation='gap')

sage: m = M(range(100))

sage: m.transpose().parent() is M

True

sage: UCF = UniversalCyclotomicField()

sage: M = MatrixSpace(UCF, 3, implementation='gap')

sage: m = M([UCF.zeta(i) for i in range(1,10)])

sage: m

[ 1 -1 E(3)]

[ E(4) E(5) -E(3)^2]

[ E(7) E(8) -E(9)^4 - E(9)^7]

sage: (m^2)[1,2]

E(180)^32 - E(180)^33 + E(180)^68 - E(180)^69 + E(180)^104 - E(180)^141 - E(180)^156 + E(180)^176 - E(180)^177

TESTS::

sage: for ring in [ZZ, QQ, UniversalCyclotomicField(), GF(2), GF(3)]:

....: M = MatrixSpace(ring, 2, implementation='gap')

....: TestSuite(M).run()

....: M = MatrixSpace(ring, 2, 3, implementation='gap')

....: TestSuite(M).run()

"""

def __init__(self, parent, entries, coerce, copy):

r"""

TESTS::

sage: M = MatrixSpace(ZZ, 2, implementation='gap')

sage: M(0)

[0 0]

sage: M(1)

[1 0]

[0 1]

sage: M(2)

[2 0]

[0 2]

sage: type(M(0))

sage: type(M(1))

sage: type(M(2))

sage: M = MatrixSpace(QQ, 2, 3, implementation='gap')

sage: M(0)

[0 0 0]

sage: M(1)

Traceback (most recent call last):

...

TypeError: identity matrix must be square

sage: MatrixSpace(QQ, 1, 2)(0)

[0 0]

sage: MatrixSpace(QQ, 2, 1)(0)

[0]

"""

Matrix_dense.__init__(self, parent)

R = self._base_ring

if isinstance(entries, (tuple, list)):

entries = [[R(x) for x in entries[i * self._ncols: (i+1) * self._ncols]] for i in range(self._nrows)]

else:

zero = R.zero()

if entries is None:

elt = zero

else:

elt = R(entries)

entries = [[zero] * self._ncols for i in range(self._nrows)]

if not elt.is_zero():

if self._nrows != self._ncols:

raise TypeError('non diagonal matrices can not be initialized from a scalar')

for i in range(self._nrows):

entries[i][i] = elt

self._libgap = libgap(entries)

cdef Matrix_gap _new(self, Py_ssize_t nrows, Py_ssize_t ncols):

if nrows == self._nrows and ncols == self._ncols:

P = self._parent

else:

P = self.matrix_space(nrows, ncols)

cdef Matrix_gap M = Matrix_gap.__new__(Matrix_gap, P, None, None, None)

Matrix_dense.__init__(M, P)

return M

def __copy__(self):

r"""

TESTS::

sage: M = MatrixSpace(QQ, 2, implementation='gap')

sage: m1 = M([1,2,0,3])

sage: m2 = m1.__copy__()

sage: m2

[1 2]

[0 3]

sage: m1[0,1] = -2

sage: m1

[ 1 -2]

[ 0 3]

sage: m2

[1 2]

[0 3]

"""

cdef Matrix_gap M = self._new(self._nrows, self._ncols)

M._libgap = self._libgap.deepcopy(1)

return M

def __reduce__(self):

r"""

TESTS::

sage: M = MatrixSpace(ZZ, 2, implementation='gap')

sage: m = M([1,2,1,2])

sage: loads(dumps(m)) == m

True

"""

return self._parent, (self.list(),)

cpdef GapElement gap(self):

r"""

Return the underlying gap object.

EXAMPLES::

sage: M = MatrixSpace(ZZ, 2, implementation='gap')

sage: m = M([1,2,2,1]).gap()

sage: m

[ [ 1, 2 ], [ 2, 1 ] ]

sage: type(m)

sage: m.MatrixAutomorphisms()

Group([ (1,2) ])

"""

return self._libgap

cdef get_unsafe(self, Py_ssize_t i, Py_ssize_t j):

return self._base_ring(self._libgap[i,j])

cdef set_unsafe(self, Py_ssize_t i, Py_ssize_t j, object x):

r"""

TESTS::

sage: M = MatrixSpace(ZZ, 2, implementation='gap')

sage: m = M(0)

sage: m[0,1] = 13

sage: m

[ 0 13]

[ 0 0]

sage: m[1,0] = -1/2

Traceback (most recent call last):

...

TypeError: no conversion of this rational to integer

"""

self._libgap[i,j] = x

cpdef _richcmp_(self, other, int op):

r"""

Compare ``self`` and ``right``.

EXAMPLES::

sage: M = MatrixSpace(ZZ, 2, implementation='gap')

sage: m1 = M([1,2,3,4])

sage: m2 = M([1,2,3,4])

sage: m3 = M([1,2,0,4])

sage: m1 == m2

True

sage: m1 != m2

False

sage: m1 == m3

False

sage: m1 != m3

True

sage: M = MatrixSpace(QQ, 2, implementation='gap')

sage: m1 = M([1/2, 1/3, 2, -5])

sage: m2 = M([1/2, 1/3, 2, -5])

sage: m3 = M([1/2, 0, 2, -5])

sage: m1 == m2

True

sage: m1 != m2

False

sage: m1 == m3

False

sage: m1 != m3

True

sage: UCF = UniversalCyclotomicField()

sage: M = MatrixSpace(UCF, 2, implementation='gap')

sage: m1 = M([E(2), E(3), 0, E(4)])

sage: m2 = M([E(2), E(3), 0, E(4)])

sage: m3 = M([E(2), E(3), 0, E(5)])

sage: m1 == m2

True

sage: m1 != m2

False

sage: m1 == m3

False

sage: m1 != m3

True

"""

return (<Matrix_gap> self)._libgap._richcmp_((<Matrix_gap> other)._libgap, op)

def __neg__(self):

r"""

TESTS::

sage: M = MatrixSpace(ZZ, 2, 3, implementation='gap')

sage: m = M([1, -1, 3, 2, -5, 1])

sage: -m

[-1 1 -3]

[-2 5 -1]

"""

cdef Matrix_gap M = self._new(self._nrows, self._ncols)

M._libgap = self._libgap.AdditiveInverse()

return M

def __invert__(self):

r"""

TESTS::

sage: M = MatrixSpace(QQ, 2)

sage: ~M([4,2,2,2])

[ 1/2 -1/2]

[-1/2 1]

"""

cdef Matrix_gap M

if self._base_ring.is_field():

M = self._new(self._nrows, self._ncols)

M._libgap = self._libgap.Inverse()

return M

else:

return Matrix_dense.__invert__(self)

cpdef _add_(left, right):

r"""

TESTS::

sage: M = MatrixSpace(ZZ, 2, 3, implementation='gap')

sage: M([1,2,3,4,3,2]) + M([1,1,1,1,1,1]) == M([2,3,4,5,4,3])

True

"""

cdef Matrix_gap cleft = <Matrix_gap> left

cdef Matrix_gap ans = cleft._new(cleft._nrows, cleft._ncols)

ans._libgap = left._libgap + (<Matrix_gap> right)._libgap

return ans

cpdef _sub_(left, right):

r"""

TESTS::

sage: M = MatrixSpace(ZZ, 2, 3, implementation='gap')

sage: M([1,2,3,4,3,2]) - M([1,1,1,1,1,1]) == M([0,1,2,3,2,1])

True

"""

cdef Matrix_gap cleft = <Matrix_gap> left

cdef Matrix_gap ans = cleft._new(cleft._nrows, cleft._ncols)

ans._libgap = left._libgap - (<Matrix_gap> right)._libgap

return ans

cdef Matrix _matrix_times_matrix_(left, Matrix right):

r"""

TESTS::

sage: M = MatrixSpace(QQ, 2, implementation='gap')

sage: m1 = M([1,2,-4,3])

sage: m2 = M([-1,1,1,-1])

sage: m1 * m2

[ 1 -1]

[ 7 -7]

"""

if left._ncols != right._nrows:

raise IndexError("Number of columns of self must equal number of rows of right.")

cdef Matrix_gap M = left._new(left._nrows, right._ncols)

M._libgap = <Matrix_gap> ((<Matrix_gap> left)._libgap * (<Matrix_gap> right)._libgap)

return M

def determinant(self):

r"""

Return the determinant of this matrix.

EXAMPLES::

sage: M = MatrixSpace(ZZ, 2, implementation='gap')

sage: M([2, 1, 1, 1]).determinant()

sage: M([2, 1, 3, 3]).determinant()

TESTS::

sage: M = MatrixSpace(ZZ, 1, implementation='gap')

sage: parent(M(1).determinant())

Integer Ring

sage: M = MatrixSpace(QQ, 1, implementation='gap')

sage: parent(M(1).determinant())

Rational Field

sage: M = MatrixSpace(UniversalCyclotomicField(), 1, implementation='gap')

sage: parent(M(1).determinant())

Universal Cyclotomic Field

"""

return self._base_ring(self._libgap.Determinant())

def trace(self):

r"""

Return the trace of this matrix.

EXAMPLES::

sage: M = MatrixSpace(ZZ, 2, implementation='gap')

sage: M([2, 1, 1, 1]).trace()

sage: M([2, 1, 3, 3]).trace()

TESTS::

sage: M = MatrixSpace(ZZ, 1, implementation='gap')

sage: parent(M(1).trace())

Integer Ring

sage: M = MatrixSpace(QQ, 1, implementation='gap')

sage: parent(M(1).trace())

Rational Field

sage: M = MatrixSpace(UniversalCyclotomicField(), 1, implementation='gap')

sage: parent(M(1).trace())

Universal Cyclotomic Field

"""

return self._base_ring(self._libgap.Trace())

def rank(self):

r"""

Return the rank of this matrix.

EXAMPLES::

sage: M = MatrixSpace(ZZ, 2, implementation='gap')

sage: M([2, 1, 1, 1]).rank()

sage: M([2, 1, 4, 2]).rank()

"""

return int(self._libgap.Rank())

Coverage for local/lib/python2.7/site-packages/sage/matrix/matrix_gap.pyx : 73%

71 statements 52 run 19 missing 0 excluded