I am going to respond to all of your (Martin RUBEY's) issues at once:
This problem has been discussed at various times, under the name
'warting problem' among others. This is a issue that has to be resolved
somehow,
as more code gets written in maxima, instead of lisp where its easier to work
around.
(C8) solver([u-t*(u^(k+1)+1)=0,1-(k+1)*t*u^k=0],[u,t],[k]);
k
1 Enter SOLVE [(- k - 1) t u + 1, t]
1
1 Exit SOLVE [t = ----------]
k
(k + 1) u
Here is where k is 2, and the results are wrong, the commercial macsyma
has the same problem.
3
2 u - 1
1 Enter SOLVE [--------, u]
2
3 u
SQRT(3) %I - 1 SQRT(3) %I + 1 1
1 Exit SOLVE [u = --------------, u = - --------------, u = ----]
1/3 1/3 1/3
2 2 2 2 2
4 k
---
3
>
> (C9) solver([u-t*(u^(l+1)+u+1) = 0,1-t*((l+1)*u^l+1) = 0],[u,t],[l]);
>
> 1 Enter SOLVE [(-l-1)*t*u^l-t+1,u]
> Is l an integer?
>
> y;
> 1 Exit SOLVE [u = (1/(l*t+t)-t/(l*t+t))^(1/l)]
> 1 Enter SOLVE
> [-((l*((-(t-1)/((l+1)*t))^(1/l)+1)+1)*t-l*(-(t-1)/((l+1)*t))^(1/l))/(l+1),t]
> 1 Exit SOLVE [t =
> l*(-(t-1)/((l+1)*t))^(1/l)/(l*(-(t-1)/((l+1)*t))^(1/l)+l+1)]
> (D9) [[u = (-(t-1)/((l+1)*t))^(1/l),
> [-((l*((-(t-1)/((l+1)*t))^(1/l)+1)+1)*t-l*(-(t-1)/((l+1)*t))^(1/l))
> /(l+1)]]]
>
> The second item of the solution does not make t explicit, although solve
> did...
>
No, t is still implicitly defined. The solve of the commercial macsyma cannot
solve this either.
>
> 2. second bug (I think this is known, but I'm not sure)
>
> the second time solver is invoked, it is silently assumed that l is an
> integer. I think this assumption should be removed...
>
This has to do with solve setting the integer property of L, when it asked.
It is the way maxima works. You can remove this property with remove.
>
> I'll post all three as a bug report
>
> Martin
>
> Unfortunately, maxima starts to become unusable for me now. I'm unhappy.
Is there something you cant work around for now?
Dan
>
>
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