MatGcd - Maple Help
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LinearAlgebra[Modular]

  

MatGcd

  

compute mod m GCD from Matrix of coefficients

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

MatGcd(m, A, nrow)

Parameters

m

-

modulus

A

-

mod m Matrix; each row stores the coefficients of a polynomial

nrow

-

number of rows in A containing polynomial coefficients

Description

• 

The MatGcd function computes the GCD of the nrow polynomials formed by multiplication of the input Matrix A by the Vector . It is capable of computing the mod m GCD of more than two polynomials simultaneously.

• 

Each polynomial must be stored in a row of the input Matrix, in order of increasing degree for the columns. For example, the polynomial  is stored in a row as [3, 2, 1].

• 

On successful completion, the degree of the GCD is returned, and the coefficients of the GCD are returned in the first row of A.

  

Note: The returned GCD is not normalized to the leading coefficient 1, as the leading coefficient is required for some modular reconstruction techniques.

• 

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

Examples

(1)

An example of three polynomials with a known GCD.

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

An example of a trivial GCD.

(11)

(12)

(13)

(14)

(15)

See Also

coeff

Expand

LinearAlgebra/Details

LinearAlgebra[Modular]

LinearAlgebra[Modular][Mod]

randpoly

seq

trunc

 


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