linalg(deprecated)/ffgausselim - Maple Help

linalg(deprecated)

 ffgausselim
 fraction-free Gaussian elimination on a matrix

 Calling Sequence ffgausselim(A) ffgausselim(A, 'r') ffgausselim(A, 'r', 'd') ffgausselim(A, rmar)

Parameters

 A - rectangular matrix 'r' - (optional) for returning the rank of A 'd' - (optional) for returning the determinant of A rmar - (optional) non-negative integer

Description

 • Important: The linalg package has been deprecated. Use the superseding command LinearAlgebra[GaussianElimination], instead.
 - For information on migrating linalg code to the new packages, see examples/LinearAlgebraMigration.
 • Fraction-free Gaussian elimination with row pivoting is performed on A, an n by m matrix of multivariate polynomials over the rationals. The result is an upper triangular matrix of multivariate polynomials.
 • If an optional second parameter is specified, and it is a name, it is assigned the rank of A. The rank of A is the number of non-zero rows in the resulting matrix.
 • If an optional third parameter is also specified, and the rank of A = n, then it is assigned the determinant of $\mathrm{submatrix}\left(A,1..n,1..n\right)$.
 • If an optional second parameter is specified, and it is an integer, the elimination is terminated at this column position.
 • The command with(linalg,ffgausselim) allows the use of the abbreviated form of this command.

Examples

Important: The linalg package has been deprecated. Use the superseding command LinearAlgebra[GaussianElimination], instead.

 > $\mathrm{with}\left(\mathrm{linalg}\right):$
 > $A≔\mathrm{matrix}\left(3,3,\left[x,1,0,0,0,1,1,y,1\right]\right)$
 ${A}{≔}\left[\begin{array}{ccc}{x}& {1}& {0}\\ {0}& {0}& {1}\\ {1}& {y}& {1}\end{array}\right]$ (1)
 > $\mathrm{ffgausselim}\left(A,'r','d'\right)$
 $\left[\begin{array}{ccc}{x}& {1}& {0}\\ {0}& {y}{}{x}{-}{1}& {x}\\ {0}& {0}& {y}{}{x}{-}{1}\end{array}\right]$ (2)
 > $\mathrm{rank}\left(A\right)$
 ${3}$ (3)
 > $\mathrm{det}\left(A\right)$
 ${-}{y}{}{x}{+}{1}$ (4)