RegularChains[MatrixTools] - Maple Programming Help

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RegularChains[MatrixTools]

 IsZeroMatrix
 check whether a matrix is null modulo a regular chain

 Calling Sequence IsZeroMatrix(A, rc, R)

Parameters

 A - square Matrix with coefficients in the ring of fractions of R rc - regular chain of R R - polynomial ring

Description

 • The command IsZeroMatrix(A, rc, R) returns true if and only if A is null modulo the saturated ideal of rc.
 • It is assumed that rc is strongly normalized.
 • This command is part of the RegularChains[MatrixTools] package, so it can be used in the form IsZeroMatrix(..) only after executing the command with(RegularChains[MatrixTools]).  However, it can always be accessed through the long form of the command by using RegularChains[MatrixTools][IsZeroMatrix](..).

Examples

 > with(RegularChains): with(ChainTools): with(MatrixTools):
 > R := PolynomialRing([y, z]);
 ${R}{≔}{\mathrm{polynomial_ring}}$ (1)
 > rc := Empty(R);
 ${\mathrm{rc}}{≔}{\mathrm{regular_chain}}$ (2)
 > rc := Chain([z^4+1, y^2-z^2], rc, R):
 > Equations(rc, R);
 $\left[{{y}}^{{2}}{-}{{z}}^{{2}}{,}{{z}}^{{4}}{+}{1}\right]$ (3)
 > m := Matrix([[1, y+z], [0, y-z]]);
 ${m}{≔}\left[\begin{array}{cc}{1}& {y}{+}{z}\\ {0}& {y}{-}{z}\end{array}\right]$ (4)
 > IsZeroMatrix(m, rc, R);
 ${\mathrm{false}}$ (5)