normal form of a matrix with respect to a regular chain
MatrixOverChain(A, rc, R)
Matrix with coefficients in the field of fractions of R
regular chain of R
The command MatrixOverChain(A, rc, R) returns the normal form of A with respect to rc. In broad terms, this is obtained by mapping RegularChains[NormalForm] on the coefficients of A.
The result is viewed as a matrix with coefficients in the total ring of fractions of R/I where I is 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 MatrixOverChain(..) 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][MatrixOverChain](..).
R ≔ PolynomialRing⁡x,y,z
R ≔ polynomial_ring
T ≔ Empty⁡R:
T ≔ Chain⁡z+1⁢z+2,y2+z,x−z⁢x−y,T,R
T ≔ regular_chain
m ≔ Matrix⁡x,y,z,x2,y2,z2,x3,y5,z6
m ≔ xyzx2y2z2x3y5z6
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