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GraphicalModelsMLE :: jacobianMatrixOfRationalFunction

jacobianMatrixOfRationalFunction -- Jacobian matrix of a rational function

Synopsis

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 :

For the programmer

The object jacobianMatrixOfRationalFunction is a method function.