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GaussInt

  

GIfactor

  

Gaussian integer factorization

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

GIfactor(c)

Parameters

c

-

Gaussian integer, a list or a set of Gaussian integers

Description

• 

The GIfactor function returns the Gaussian integer factorization of c.

• 

The answer is in the form: uf1e1fnen such that c=uf1e1fnen 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, aIb, b+Ia, bIa 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.

Examples

withGaussInt:

GIfactor72100I

I1+I432I3+8I

(1)

expand

72100I

(2)

GIfactor1210115295I

11+I1+4I5+8I9+16I718I

(3)

expand

1210115295I

(4)

See Also

expand

GaussInt[GIfacset]

GaussInt[GIfactors]

GaussInt[GIprime]

 


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