# jacobianMatrixOfRationalFunction -- Jacobian matrix of a rational function

## Synopsis

• Usage:
jacobianMatrixOfRationalFunction(F)
• Inputs:
• Outputs:
• , the Jacobian matrix of a rational function

## Description

This function computes the Jacobian matrix of a rational function. The input is an element in a fraction field.

 i1 : R=QQ[x,y]; i2 : FR=frac R; i3 : F=1/(x^2+y^2); i4 : jacobianMatrixOfRationalFunction(F) o4 = {1} | (-2x)/(x4+2x2y2+y4) | {1} | (-2y)/(x4+2x2y2+y4) | 2 1 o4 : Matrix FR <--- FR
 i5 : R=QQ[t_1,t_2,t_3]; i6 : FR=frac R; i7 : jacobianMatrixOfRationalFunction( (t_1^2*t_2)/(t_1+t_2^2+t_3^3) ) o7 = {-2} | (2t_1t_2t_3^3+2t_1t_2^3+t_1^2t_2)/(t_3^6+2t_2^2t_3^3+t_2^4+2t_1t_ {-2} | (t_1^2t_3^3-t_1^2t_2^2+t_1^3)/(t_3^6+2t_2^2t_3^3+t_2^4+2t_1t_3^3+ {-2} | (-3t_1^2t_2t_3^2)/(t_3^6+2t_2^2t_3^3+t_2^4+2t_1t_3^3+2t_1t_2^2+t_ ------------------------------------------------------------------------ 3^3+2t_1t_2^2+t_1^2) | 2t_1t_2^2+t_1^2) | 1^2) | 3 1 o7 : Matrix FR <--- FR

## Ways to use jacobianMatrixOfRationalFunction :

• "jacobianMatrixOfRationalFunction(RingElement)"

## For the programmer

The object jacobianMatrixOfRationalFunction is .