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Mathematics Calculus Wolfram Language

How to calculate Stokes' determinant?

Zhenyu Zeng

Posted 22 days ago

Hello, I need to calculate the Stokes' determinant in Mathematica, such as What should I do in Mathematica? I can't image the right code in Mathematica.

POSTED BY: Zhenyu Zeng

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Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 21 days ago

Determinants are complicated. One more approach: stokes[{f1_, f2_, f3_}, {x_, y_, z_}] := Sum[{d[y, z], d[z, x], d[x, y]}[[perm[[1]]]]* D[{f1, f2, f3}[[perm[[3]]]], {x, y, z}[[perm[[2]]]]]* Signature[perm], {perm, Permutations[Range[3]]}]; stokes[{y^2, x, z^2}, {x, y, z}]

Determinants are complicated. One more approach:

stokes[{f1_, f2_, f3_}, {x_, y_, z_}] :=
  Sum[{d[y, z], d[z, x], d[x, y]}[[perm[[1]]]]*
    D[{f1, f2, f3}[[perm[[3]]]], {x, y, z}[[perm[[2]]]]]*
    Signature[perm],
   {perm, Permutations[Range[3]]}];
stokes[{y^2, x, z^2}, {x, y, z}]

POSTED BY: Gianluca Gorni