GaussInt
GIfactor
Gaussian integer factorization
Calling Sequence
Parameters
Description
Examples
GIfactor(c)
c
-
Gaussian integer, a list or a set of Gaussian integers
The GIfactor function returns the Gaussian integer factorization of c.
The answer is in the form: uf1e1⋅…⋅fnen such that c=u⋅f1e1⋅…⋅fnen where u is one of four units, f1,...,fn are the distinct primary prime factors of c, and e1,...,en are their multiplicities.
The number x+Iy of the four associated primes a+Ib, −a−Ib, −b+Ia, b−Ia is singled out as primary in which we have simultaneously either (x=1mod4andy=0mod4) or (x=−1mod4andy=2mod4).
The expand function may be applied to cause the factors to be multiplied together again.
withGaussInt:
GIfactor−72−100I
I1+I4−3−2I−3+8I
expand
−72−100I
GIfactor12101−15295I
−11+I1+4I5+8I9+16I−7−18I
12101−15295I
See Also
expand
GaussInt[GIfacset]
GaussInt[GIfactors]
GaussInt[GIprime]
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