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quaternion_algebra_element.pxd
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quaternion_algebra_element.pxd
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from sage.libs.gmp.types cimport mpz_t
from sage.libs.flint.types cimport fmpz_poly_t
import sage.structure.element
cimport sage.structure.element
from sage.structure.element cimport AlgebraElement, RingElement, ModuleElement, Element
from sage.categories.morphism cimport Morphism
cdef class QuaternionAlgebraElement_abstract(AlgebraElement):
cpdef bint is_constant(self)
cdef _do_print(self, x,y,z,w)
cpdef conjugate(self)
cpdef reduced_norm(self)
cpdef reduced_trace(self)
cdef class QuaternionAlgebraElement_generic(QuaternionAlgebraElement_abstract):
cdef object x, y, z, w
# we will assume that our element has the representation
# x + yi + zj + wk, where i^2 = a, j^2 = b
cdef class QuaternionAlgebraElement_number_field(QuaternionAlgebraElement_abstract):
cdef fmpz_poly_t x, y, z, w, a, b, modulus
cdef mpz_t d
cdef inline canonicalize(self)
cdef class QuaternionAlgebraElement_rational_field(QuaternionAlgebraElement_abstract):
cdef mpz_t x, y, z, w, a, b, d
cdef inline canonicalize(self)