The Gausselim and Gaussjord functions are placeholders for representing row echelon forms of the rectangular matrix A.

The commands Gausselim(A,...) mod p and Gassjord(A,...) mod p apply Gaussian elimination with row pivoting to A, a rectangular matrix over a finite ring of characteristic p. This includes finite fields, GF(p), the integers mod p, and GF(p^k) where elements of GF(p^k) are expressed as polynomials in RootOfs.

The result of the Gausselim command is a an upper triangular matrix B in row echelon form.  The result of the Gaussjord command is also an upper triangular matrix B but in reduced row echelon form.

If an optional second parameter is specified, and it is a name, it is assigned the rank of the matrix A.

If A is an  by  matrix with  and if an optional third parameter is also specified, and it is a name, it is assigned the determinant of the matrix A[1..m,1..m].