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](..).