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The Maxima on-line user's manual

Algebra Calculator

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Jacobian Calculator

Jacobian

Function: jacobian (<f>, <x>) Returns the Jacobian matrix of the list of functions <f> with respect to the list of variables <x>. The (i, j)-th element of the Jacobian matrix is diff(<f>[i], <x>[j]).

Examples:

          (%i1) jacobian ([sin (u - v), sin (u * v)], [u, v]);
                            [ cos(v - u)  - cos(v - u) ]
          (%o1)             [                          ]
                            [ v cos(u v)   u cos(u v)  ]
          (%i2) depends ([F, G], [y, z]);
          (%o2)                  [F(y, z), G(y, z)]
          (%i3) jacobian ([F, G], [y, z]);
                                     [ dF  dF ]
                                     [ --  -- ]
                                     [ dy  dz ]
          (%o3)                      [        ]
                                     [ dG  dG ]
                                     [ --  -- ]
                                     [ dy  dz ]

(%o1)                                true
(%i2) 

Jacobian Example

Related Examples

jacobian

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jacobian

a(x,y,z)=(1+x*y)^2 + ...

f(x,y,z)=x^4/a(x,y,z);

g(x,y,z)=x^3/a(x,y,z);

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jacobian

jacobian ([v, u/v], [...

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jacobian-sin

jacobian ([(z*sin (x)...

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jacobian-sqrt

jacobian ([2*x*z+2*y*...

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jacobian

f(x,y,z,w) := [y/x/(x...

dpf(x,y,z,w) = jacobi...

dpf(1,1,1,1);

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jacobian

f(x,y,z,w) := [y/x/(x...

jacobian (f(x,y,z,w),...

jacobian (f(x,y,z,w),...

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jacobian

jacobian ([C0+C1*U^r]...

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jacobian

h(x,y):=x^2*(3*x-3)-y...

jacobian(h(x,y),[x,y]);

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