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from sympy.testing.pytest import raises
from sympy.matrices.exceptions import NonSquareMatrixError, NonInvertibleMatrixError
from sympy import Matrix, Rational
def test_lll():
A = Matrix([[1, 0, 0, 0, -20160],
[0, 1, 0, 0, 33768],
[0, 0, 1, 0, 39578],
[0, 0, 0, 1, 47757]])
L = Matrix([[ 10, -3, -2, 8, -4],
[ 3, -9, 8, 1, -11],
[ -3, 13, -9, -3, -9],
[-12, -7, -11, 9, -1]])
T = Matrix([[ 10, -3, -2, 8],
[ 3, -9, 8, 1],
[ -3, 13, -9, -3],
[-12, -7, -11, 9]])
assert A.lll() == L
assert A.lll_transform() == (L, T)
assert T * A == L
def test_matrix_inv_mod():
A = Matrix(2, 1, [1, 0])
raises(NonSquareMatrixError, lambda: A.inv_mod(2))
A = Matrix(2, 2, [1, 0, 0, 0])
raises(NonInvertibleMatrixError, lambda: A.inv_mod(2))
A = Matrix(2, 2, [1, 2, 3, 4])
Ai = Matrix(2, 2, [1, 1, 0, 1])
assert A.inv_mod(3) == Ai
A = Matrix(2, 2, [1, 0, 0, 1])
assert A.inv_mod(2) == A
A = Matrix(3, 3, [1, 2, 3, 4, 5, 6, 7, 8, 9])
raises(NonInvertibleMatrixError, lambda: A.inv_mod(5))
A = Matrix(3, 3, [5, 1, 3, 2, 6, 0, 2, 1, 1])
Ai = Matrix(3, 3, [6, 8, 0, 1, 5, 6, 5, 6, 4])
assert A.inv_mod(9) == Ai
A = Matrix(3, 3, [1, 6, -3, 4, 1, -5, 3, -5, 5])
Ai = Matrix(3, 3, [4, 3, 3, 1, 2, 5, 1, 5, 1])
assert A.inv_mod(6) == Ai
A = Matrix(3, 3, [1, 6, 1, 4, 1, 5, 3, 2, 5])
Ai = Matrix(3, 3, [6, 0, 3, 6, 6, 4, 1, 6, 1])
assert A.inv_mod(7) == Ai
A = Matrix([[1, 2], [3, Rational(3,4)]])
raises(ValueError, lambda: A.inv_mod(2))
A = Matrix([[1, 2], [3, 4]])
raises(TypeError, lambda: A.inv_mod(Rational(1, 2)))
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