JacobianMatrix - Maple Help
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RegularChains[MatrixTools]

  

JacobianMatrix

  

Jacobian matrix of a polynomial system modulo a regular chain

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

JacobianMatrix(sys, rc, R)

Parameters

sys

-

system of polynomials in R

rc

-

strongly normalized regular chain

R

-

polynomial ring

Description

• 

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](..).

Examples

withRegularChains:

withMatrixTools:

RPolynomialRingx,y,z

Rpolynomial_ring

(1)

sysx2+y+z1,x+y2+z1,x+y+z21

sysz2+x+y1,y2+x+z1,x2+y+z1

(2)

decTriangularizesys,R

decregular_chain,regular_chain,regular_chain,regular_chain

(3)

mapEquations,dec,R

xz,yz,z2+2z1,x,y,z1,x,y1,z,x1,y,z

(4)

seqJacobianMatrixsys,deci,R,i=1..nopsdec

112z12z12z11,112101011,110121011,110101211

(5)

withLinearAlgebra:

seqDeterminantJacobianMatrixsys,deci,R,i=1..nopsdec

8z3+6z2,0,0,0

(6)

See Also

Equations

IsStronglyNormalized

LowerEchelonForm

MatrixInverse

MatrixMultiply

MatrixOverChain

MatrixTools

NormalForm

PolynomialRing

RegularChains

Triangularize