Possibility/ease of doing some vector ops in Maxima
Subject: Possibility/ease of doing some vector ops in Maxima
From: Neilen
Date: 23 Sep 2002 04:21:31 +0200
Hi Barton
On Thu, 2002-09-19 at 03:00, willisb@unk.edu wrote:
>
>
> Instead of grad, try using diff without a second argument.
> Used this way, diff works like a total derivative operator:
>
> diff(f(x,y)) = diff(f(x,y),x) * del(x) + diff(f(x,y),y) * del(y).
>
> First, tell Maxima that del(p) is zero.
>
> (C1) tellsimpafer(del(p),0);
> (D1) tellsimpafer(DEL(p),0)
>
> Second, compute the total derivative
>
> (C2) f : diff(L_1*L_2*(L_1-L_2)^(p-1));
> (D2) (L_1*(L_1-L_2)^(p-1)-(p-1)*L_1*(L_1-L_2)^(p-2)*L_2) * DEL(L_2)
> +((L_1-L_2)^(p-1)*L_2+(p-1)*L_1*(L_1-L_2)^(p-2)*L_2)*DEL(L_1)
When I try this, I get the following:
(C309) tellsimpafer(del(p),0);
(D309) tellsimpafer(DEL(p), 0)
(C310) f : diff(L_1*L_2*(L_1-L_2)^(p-1));
L_1*LOG(L_1-L_2)*(L_1-L_2)^(p-1)*L_2*DEL(p)+(L_1*(L_1-L_2)^(p-1)-
L_1*(L_1-L_2)^(p-2)*L_2*(p-1))*DEL(L_2)+(L_1*(L_1-L_2)^(p-2)*L_2*(p-1)+
(L_1-L_2)^(p-1)*L_2)*DEL(L_1)
I assume the tellsimpafer command is not doing quite the right thing?
Thanks
Neilen
>
> If you want grad instead of del, use subst
>
> (C3) f : subst(grad,del,f);
> (D3) (L_1*(L_1-L_2)^(p-1)-(p-1)*L_1*(L_1-L_2)^(p-2)*L_2) * GRAD(L_2)
> +GRAD(L_1)*((L_1-L_2)^(p-1)*L_2 +(p-1)*L_1*(L_1-L_2)^(p-2)*L_2)
>
> To extract the coefficients of grad(L_1), etc, use expand followed
> by coeff
>
> (C4) f : expand(f);
> (D4) -p*L_1*(L_1-L_2)^(p-2)*L_2*GRAD(L_2)
> +L_1*(L_1-L_2)^(p-2)*L_2*GRAD(L_2)
> +L_1*(L_1-L_2)^(p-1)*GRAD(L_2)
> +GRAD(L_1)*(L_1-L_2)^(p-1)*L_2
> +p*L_1*GRAD(L_1)*(L_1-L_2)^(p-2)*L_2
> -L_1*GRAD(L_1)*(L_1-L_2)^(p-2)*L_2
> (C5) [coeff(f, grad(L_1)), coeff(f,grad(L_2))];
>
> (D5) [(L_1-L_2)^(p-1)*L_2+p*L_1*(L_1-L_2)^(p-2)*L_2
> -L_1*(L_1-L_2)^(p-2)*L_2,
> -p*L_1*(L_1-L_2)^(p-2)*L_2+L_1*(L_1-L_2)^(p-2)*L_2
> +L_1*(L_1-L_2)^(p-1)]
> (C6)
>
>
> Maybe this helps?
>
> Barton
>
>
>
>
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