MaplePrimes - answers and comments on Question, Why can't VectorCalculus[Jacobian] take vectors?

Jacobian(Fvector,Xvector) workaround

PatrickT — Thu, 04 Nov 2010 13:40:52 Z

The following is a modified version of a trick shown by Robert Israel on MUG:

MyJacobian := (F,X) -> Matrix([seq([seq(diff(f,x),x=X)], f=F)]);
MyJacobian(Fvec,Xvec);

It seems to work and takes vectors. Any reason not to go down that road?

umm

pagan — Thu, 04 Nov 2010 21:24:03 Z

Are you sure that you haven't got it backwards, with it working for Vectors but not for lists?

Reference

PatrickT — Thu, 04 Nov 2010 13:44:57 Z

Reference to Robert's suggestion and context:

http://www.math.rwth-aachen.de/mapleAnswers/html/1603.html

> MyJacobian:= (F::list, V::list) ->
     Matrix([seq([seq(diff(f,v),v=V)], f=F)]);

don't think so

PatrickT — Thu, 04 Nov 2010 21:35:09 Z

An improved presentation:

#List,List
VectorCalculus[Jacobian]([x[1]*x[2],3*x[3]],[x[1],x[2]]);
                    Matrix(%id = 153334860)
#Vector,List
VectorCalculus[Jacobian](Vector([x[1]*x[2],3*x[3]]),[x[1],x[2]]);
                    Matrix(%id = 153334988)
#List,Vector
VectorCalculus[Jacobian]([x[1]*x[2],3*x[3]],Vector([x[1],x[2]]));
Error, invalid input: too many and/or wrong type of arguments passed to VectorCalculus:-Jacobian; first unused argument is Vector(2, {(1) = x[1], (2) = x[2]})
#Vector,Vector
VectorCalculus[Jacobian](Vector([x[1]*x[2],3*x[3]]),Vector([x[1],x[2]]));
Error, invalid input: too many and/or wrong type of arguments passed to VectorCalculus:-Jacobian; first unused argument is Vector(2, {(1) = x[1], (2) = x[2]})

where it has Matrix(%id=... it worked, where it has an Error message it didn't.

sorry

pagan — Thu, 04 Nov 2010 22:02:42 Z

@PatrickT Sorry, I misunderstood entirely. I misread and thought that you were talking about the first argument (which doesn't allow for lists).

VectorCalculus[Hessian] is even less flexible

PatrickT — Thu, 04 Nov 2010 22:46:32 Z

No worries, above all, thanks for your interest pagan. All this is accurately documented, by the way, I just wonder why the limitations. Hessian is even less versatile as it can only take algebraic expressions. With LISTS as arguments, what works with VectorCalculus[Jacobian] doesn't work with VectorCalculus[Hessian]. Is there a good reason, some fool-proof restriction?

VectorCalculus[Hessian](Flst,Xlst);
Error, invalid input: VectorCalculus:-Hessian expects its 1st argument, f, to be of type algebraic, but received [x[1]*x[2], 3*x[3]]

Edit: To be perfectly honest, I haven't looked into it and there may be a special package to deal with tensors.