how to define Ring of gaussian integers modulo n? modulo operation defined as :
def modGI(x,n):
import math
E=(x*n.conjugate())/(n*n.conjugate())
return x-complex(math.floor(E.real),math.floor(E.imag))*n
You can take quotient of general ring (including the Gaussian integers).
sage: G = ZZ[I]
sage: J = G.ideal([3 * I + 5])
sage: Q = G.quotient(J, 'x')
sage: a = Q(I)
sage: (7*a + 5) * (13*a - 2)
-4*I
Which is not exactly what you get via your function
sage: modGI(complex(7*I + 5) * complex(13*I - 2), complex(3*I+5))
(2+4j)
But these are the same thing in the quotient
sage: sage: Q(2 + 4*I)
-4*I
Asked: 2020-01-20 22:36:40 +0100
Seen: 590 times
Last updated: Jan 21 '20
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