RegularChains[MatrixTools]
JacobianMatrix
Jacobian matrix of a polynomial system modulo a regular chain
Calling Sequence
Parameters
Description
Examples
JacobianMatrix(sys, rc, R)
sys
-
system of polynomials in R
rc
strongly normalized regular chain
R
polynomial ring
The command JacobianMatrix(sys, rc, R) returns the Jacobian matrix of sys modulo the saturated ideal of rc.
This command is part of the RegularChains[MatrixTools] package, so it can be used in the form JacobianMatrix(..) 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][JacobianMatrix](..).
withRegularChains:
withMatrixTools:
R≔PolynomialRingx,y,z
R≔polynomial_ring
sys≔x+y+z2−1,x+y2+z−1,x2+y+z−1
sys≔z2+x+y−1,y2+x+z−1,x2+y+z−1
dec≔Triangularizesys,R
dec≔regular_chain,regular_chain,regular_chain,regular_chain
mapEquations,dec,R
x−z,y−z,z2+2z−1,x,y,z−1,x,y−1,z,x−1,y,z
seqJacobianMatrixsys,deci,R,i=1..nopsdec
112z12z12z11,112101011,110121011,110101211
withLinearAlgebra:
seqDeterminantJacobianMatrixsys,deci,R,i=1..nopsdec
−8z3+6z−2,0,0,0
See Also
Equations
IsStronglyNormalized
LowerEchelonForm
MatrixInverse
MatrixMultiply
MatrixOverChain
MatrixTools
NormalForm
PolynomialRing
RegularChains
Triangularize
Download Help Document