def _pow_by_base_mul(self, other, base_mul, max_j=False):
"""
return self * other with respect to basis (gamma_i),
where self, other are matrix.
(base_mul)_ij express gamma_i * gamma_j
This function uses right-left binary method.
"""
func = algorithm.powering_func(
lambda x, y: _vect_mul_by_base_mul(x, y, base_mul, max_j))
return func(self, other)
def _pow_by_base_mul(self, other, base_mul, max_j=False):
"""
return self * other with respect to basis (gamma_i),
where self, other are matrix.
(base_mul)_ij express gamma_i * gamma_j
This function uses right-left binary method.
"""
func = algorithm.powering_func(
lambda x,y:_vect_mul_by_base_mul(x, y, base_mul, max_j))
return func(self, other)
def _substitution_by_base_mul(P, ele, base_mul, one_gamma, max_j=False):
"""
return P(ele) with respect to basis (gamma_i),
where P is a polynomial, ele is a vector w.r.t. gamma_i.
(base_mul)_ij express gamma_i * gamma_j
This function uses digital method (Horner method).
"""
coeff = reversed(P.sorted)
mul = lambda x, y: _vect_mul_by_base_mul(x, y, base_mul, max_j)
return algorithm.digital_method(
coeff, ele, lambda x, y: x + y, mul, lambda a, x: a * x,
algorithm.powering_func(one_gamma, mul),
vector.Vector([base_mul.coeff_ring.zero] * base_mul.row), one_gamma)
def _substitution_by_base_mul(P, ele, base_mul, one_gamma, max_j=False):
"""
return P(ele) with respect to basis (gamma_i),
where P is a polynomial, ele is a vector w.r.t. gamma_i.
(base_mul)_ij express gamma_i * gamma_j
This function uses digital method (Horner method).
"""
coeff = reversed(P.sorted)
mul = lambda x, y : _vect_mul_by_base_mul(x, y, base_mul, max_j)
return algorithm.digital_method(
coeff, ele, lambda x, y : x + y, mul,
lambda a, x : a * x,
algorithm.powering_func(one_gamma, mul),
vector.Vector([base_mul.coeff_ring.zero] * base_mul.row),
one_gamma
)