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RegularChains[MatrixTools][IsZeroMatrix] - check whether a matrix is null modulo a regular chain
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Calling Sequence
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IsZeroMatrix(A, rc, R)
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Parameters
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A
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square Matrix with coefficients in the ring of fractions of R
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rc
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regular chain of R
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R
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polynomial ring
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Description
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The command IsZeroMatrix(A, rc, R) returns true if and only if A is null modulo the saturated ideal of rc.
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It is assumed that rc is strongly normalized.
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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](..).
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Examples
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![R := PolynomialRing([y, z])](/support/helpjp/helpview.aspx?si=5676/file06503/math97.png)
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![rc := Chain([z^4+1, y^2-z^2], rc, R)](/support/helpjp/helpview.aspx?si=5676/file06503/math111.png)
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![[y^2-z^2, z^4+1]](/support/helpjp/helpview.aspx?si=5676/file06503/math118.png)
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![m := Matrix([[1, y+z], [0, y-z]])](/support/helpjp/helpview.aspx?si=5676/file06503/math122.png)
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![m := Matrix([[1, y+z], [0, y-z]])](/support/helpjp/helpview.aspx?si=5676/file06503/math125.png)
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| (5) |
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See Also
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Chain, Empty, Equations, IsStronglyNormalized, JacobianMatrix, LowerEchelonForm, MatrixInverse, MatrixMultiply, MatrixOverChain, MatrixTools, NormalForm, PolynomialRing, RegularChains
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Download Help Document
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