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numtheory

  

sq2factor

  

integer factorization in Z(sqrt(2))

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

sq2factor(z)

Parameters

z

-

integer, list or set of integers in Z2

Description

• 

Important: The numtheory[sq2factor] command has been deprecated.  Use the superseding command NumberTheory[FactorNormEuclidean] instead.

• 

The sq2factor function returns the integer factorization of z.

• 

All integers of Z2 have the form a+b2, where a and b are rational integers.

• 

The answer is in the form: ±1uf1e1...fnen such that z=±1uf1e1fnen where f1,,fn are distinct prime factors of z, e1,,en are non-negative integer numbers, u is a unit in Z2 and is represented under the form wn or w&conjugate0;n or wn or w&conjugate0;n where w is the fundamental unit (i.e, w=1+2), and n is a non-negative integer.

• 

The expand function may be applied to cause the factors to be multiplied together again.

• 

The command with(numtheory,sq2factor) allows the use of the abbreviated form of this command.

Examples

withnumtheory:

sq2factor124

1+24

(1)

sq2factor83424959

9503+18552950318552

(2)

expand

83424959

(3)

sq2factor92329322

251+21+325+217+592

(4)

expand

92329322

(5)

See Also

expand

GaussInt[GIfactor]

ifactor

 


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