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The Maxima on-line user's manual

Algebra Calculator

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Hessian Calculator

Hessian

Function: hessian (<f>, <x>) Returns the Hessian matrix of <f> with respect to the list of variables <x>. The (i, j)-th element of the Hessian matrix is diff(<f>, <x>[i], 1, <x>[j], 1).

hessian (y + x^2/(x*y-1), [x, y]);
derivative (y + x^2/(x*y-1), x);

Examples:

          (%i1) hessian (x * sin (y), [x, y]);
                               [   0       cos(y)   ]
          (%o1)                [                    ]
                               [ cos(y)  - x sin(y) ]
          (%i2) depends (F, [a, b]);
          (%o2)                       [F(a, b)]
          (%i3) hessian (F, [a, b]);
                                  [   2      2   ]
                                  [  d F    d F  ]
                                  [  ---   ----- ]
                                  [    2   da db ]
                                  [  da          ]
          (%o3)                   [              ]
                                  [   2      2   ]
                                  [  d F    d F  ]
                                  [ -----   ---  ]
                                  [ da db     2  ]
                                  [         db   ]

(%o1)                                true
(%i2) 

Hessian Example

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