RegularChains[MatrixTools][MatrixInverse] - compute the inverse of a matrix modulo a regular chain
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Calling Sequence
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MatrixInverse(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 MatrixInverse(A, rc, R) returns two lists.
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All the returned regular chains form a triangular decomposition of rc (in the sense of Kalkbrener).
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It is assumed that rc is strongly normalized.
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The algorithm is an adaptation of the algorithm of Bareiss.
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This command is part of the RegularChains[MatrixTools] package, so it can be used in the form MatrixInverse(..) 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][MatrixInverse](..).
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Examples
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Automatic case discussion.
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Assume we have two variables y and z that have the same square and z is a 4th root of -1. Suppose we need to compute modulo this relation.
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We want to compute the inverse of the previous matrix.
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Let us check the first result.
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Consider now this other matrix.
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Get a generic answer that would hold both cases.
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Check.
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See Also
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Chain, Empty, Equations, IsStronglyNormalized, IsZeroMatrix, JacobianMatrix, LowerEchelonForm, MatrixCombine, MatrixMultiply, MatrixOverChain, MatrixTools, NormalForm, PolynomialRing, RegularChains
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