DOCUMENTATION CENTER SEARCH
Mathematica
>
Complex Numbers
>
Built-in
Mathematica
Symbol
Integer and Number Theoretic Functions
Polynomials over Algebraic Number Fields
Tutorials »
|
Extension
ComplexExpand
Modulus
I
See Also »
|
Complex Numbers
Number Theory
Polynomial Algebra
Polynomial Factoring & Decomposition
More About »
GaussianIntegers
GaussianIntegers
is an option for
FactorInteger
,
PrimeQ
,
Factor
and related functions which specifies whether factorization should be done over Gaussian integers.
MORE INFORMATION
With
GaussianIntegers->
False
, factorization is done over the ordinary ring of integers
.
With
GaussianIntegers->
True
, factorization is done over the ring of integers with
i
adjoined
.
The Gaussian primes used when
GaussianIntegers->
True
are chosen to have both real and imaginary parts positive.
The first entry in the list given by
FactorInteger
with
GaussianIntegers->
True
may be
-1
or
-
I
.
EXAMPLES
CLOSE ALL
Basic Examples
(1)
Factor a polynomial over
:
In[1]:=
Out[1]=
Factor an integer over
:
In[2]:=
Out[2]=
Scope
(3)
Properties & Relations
(1)
SEE ALSO
Extension
ComplexExpand
Modulus
I
TUTORIALS
Integer and Number Theoretic Functions
Polynomials over Algebraic Number Fields
MORE ABOUT
Complex Numbers
Number Theory
Polynomial Algebra
Polynomial Factoring & Decomposition
New in 2
© 2008 Wolfram Research, Inc.
. ![Z[i]](Files/GaussianIntegers.en/2.gif "Z[i]"){kind=small}
.
EXAMPLES
Basic Examples ![Q[ⅈ]](Files/GaussianIntegers.en/3.gif "Q[ⅈ]"){kind=small}
![Z[ⅈ]](Files/GaussianIntegers.en/4.gif "Z[ⅈ]"){kind=small}
Scope 