GaussInt - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Group Theory : Numbers : Integer Functions : Gaussian Integers : GaussInt/GIhermite

GaussInt

  

GIhermite

  

Gaussian-integer-only Hermite Normal Form

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

GIhermite(A)

GIhermite(A, U)

Parameters

A

-

Matrix of Gaussian integers

U

-

name

Description

• 

The function GIhermite computes the Hermite Normal Form (reduced row echelon form) of a Matrix of Gaussian integers.

• 

The Hermite normal form of A is an upper triangular Matrix H with rank(A) = the number of nonzero rows of H.

• 

The Hermite normal form is obtained by doing elementary row operations. This includes interchanging rows, multiplying through a row by a unit in Zi, and adding an integral multiple of one row to another.

• 

One can use transposes to obtain the column form of the Hermite Normal Form.

• 

In the case of two arguments, the second argument U will be assigned the transformation Matrix on output, such that the following holds: GIhermite(A) = U . A.

Examples

withGaussInt:

AMatrix37I,7+11I,11I,134I,17+12I,19

A:=37I7+11I11I134I17+12I19

(1)

BGIhermiteA,U

B:=1592I828I0198276+13I

(2)

U

1+4I2I413I7+3I

(3)

LinearAlgebra:-EqualU.A,B

true

(4)

See Also

GaussInt[GIsmith]

LinearAlgebra[HermiteForm]

LinearAlgebra[SmithForm]

 


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam