# jacobian(Ideal) -- the Jacobian matrix of the generators of an ideal

## Synopsis

• Function: jacobian
• Usage:
jacobian I
• Inputs:
• I, an ideal, in a polynomial ring
• Outputs:
• , the Jacobian matrix of partial derivatives of the generators of I

## Description

This is identical to jacobian generators I. See jacobian(Matrix) for more information.
 i1 : R = QQ[x,y,z]; i2 : I = ideal(y^2-x*(x-1)*(x-13)) 3 2 2 o2 = ideal(- x + 14x + y - 13x) o2 : Ideal of R i3 : jacobian I o3 = {1} | -3x2+28x-13 | {1} | 2y | {1} | 0 | 3 1 o3 : Matrix R <--- R
If the ring of I is a polynomial ring over a polynomial ring, then indeterminates in the coefficient ring are treated as constants.
 i4 : R = ZZ[a,b,c][x,y,z] o4 = R o4 : PolynomialRing i5 : jacobian ideal(a*y*z+b*x*z+c*x*y) o5 = {1, 0} | cy+bz | {1, 0} | cx+az | {1, 0} | bx+ay | 3 1 o5 : Matrix R <--- R

## Ways to use this method:

• jacobian(Ideal) -- the Jacobian matrix of the generators of an ideal
• "jacobian(MonomialIdeal)"