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LinearAlgebra[Modular]

  

ZigZag

  

in place conversion of mod m Matrix to ZigZag form

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

ZigZag(m, A)

Parameters

m

-

modulus

A

-

square mod m Matrix

Description

• 

The ZigZag function applies a sequence of similarity transformations to the nxn mod m Matrix A to obtain the ZigZag form of A.

  

A ZigZag form is an almost block diagonal structure having fewer than 2n nonzero entries.

• 

A ZigZag form can be used to obtain the Smith normal form and the Frobenius form of a Matrix. The Frobenius form of a Matrix is the same as the Frobenius form of its ZigZag form.

• 

This command is part of the LinearAlgebra[Modular] package, so it can be used in the form ZigZag(..) only after executing the command with(LinearAlgebra[Modular]).  However, it can always be used in the form LinearAlgebra[Modular][ZigZag](..).

Examples

withLinearAlgebra[Modular]:

p97

p:=97

(1)

AModp,Matrix5,5,i,j→ifijthenrandelse0end if,integer[]

A:=7796108658036802244003960390004312000055

(2)

A2Copyp,A:

ZigZagp,A2:

A2

77100000100000100000104483676

(3)

FrobeniusA2modp,FrobeniusAmodp

0000710001001004900104000156,0000710001001004900104000156

(4)

See Also

Frobenius

LinearAlgebra/Details

LinearAlgebra[Modular]

LinearAlgebra[Modular][Copy]

LinearAlgebra[Modular][Mod]

 


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