jacobianMatrixOfRationalFunction -- Jacobian matrix of a rational function

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