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](..).