On Oct 1, 5:58 pm, kcrisman <kcris...@gmail.com> wrote:
[Snip]
> Still, this idea is worth trying for others to play with. Especially
> if it were first implemented with a 1 or 2 level recursion, it would
> help out with a lot of integrals and limits which just need to know
> x>,<,==0. How efficient is Mma's Reduce for this sort of thing?
>
> - kcrisman
Not sure if this answers your question, but here is an example from
MMA. I tried including a few assumptions to reduce the length of the
output of Reduce[], but it didn't help. Basically, every solution is a
set of conditions linked by '&&', while different solutions are
separated by '||'. I find this kind of output pretty helpful, as it
allows simple tests and then picking the right solution for each case.
Note also that MMA's Reduce[] also solves inequalities. Not sure if
maxima can do this, but it would be great.
Cheers,
Stan
Reduce[wv == (wv1 /. wb -> wb1) && p > 0 && veloc > 0 && mort > 0 &&
lwat > 0 && jbiom > 0 && rwat > 0 && av >= 0, wv, Reals]
(veloc > 0 && av > 1 && lwat == veloc/(-av + av^2) && rwat > 0 &&
p > 0 && mort > 0 &&
jbiom > 0 && (bv == -Sqrt[((
av^2 lwat^2 - av^3 lwat^2 + av lwat veloc)/(-lwat rwat +
av lwat rwat - rwat veloc))] ||
bv == Sqrt[(
av^2 lwat^2 - av^3 lwat^2 + av lwat veloc)/(-lwat rwat +
av lwat rwat - rwat veloc)])) || (veloc >
0 && ((av == 0 && lwat > 0 &&
rwat > 0 && ((bv < 0 && p > 0 && mort > 0 &&
jbiom > 0) || (bv > 0 && p > 0 && mort > 0 &&
jbiom > 0))) || (0 < av <= 1 && lwat > 0 && rwat > 0 &&
p > 0 && mort > 0 &&
jbiom > 0) || (av >
1 && ((0 < lwat < veloc/(-av + av^2) && rwat > 0 && p > 0 &&
mort > 0 && jbiom > 0) || (lwat == veloc/(-av + av^2) &&
rwat > 0 && ((bv < 0 && p > 0 && mort > 0 &&
jbiom > 0) || (bv > 0 && p > 0 && mort > 0 &&
jbiom > 0))) || (veloc/(-av + av^2) < lwat <
veloc/(-1 + av) &&
rwat > 0 && ((bv < -Sqrt[((
av^2 lwat^2 - av^3 lwat^2 +
av lwat veloc)/(-lwat rwat + av lwat rwat -
rwat veloc))] && p > 0 && mort > 0 &&
jbiom >
0) || (-Sqrt[((
av^2 lwat^2 - av^3 lwat^2 +
av lwat veloc)/(-lwat rwat + av lwat rwat -
rwat veloc))] < bv < Sqrt[(
av^2 lwat^2 - av^3 lwat^2 +
av lwat veloc)/(-lwat rwat + av lwat rwat -
rwat veloc)] && p > 0 && mort > 0 &&
jbiom > 0) || (bv > Sqrt[(
av^2 lwat^2 - av^3 lwat^2 +
av lwat veloc)/(-lwat rwat + av lwat rwat -
rwat veloc)] && p > 0 && mort > 0 &&
jbiom > 0))) || (lwat > veloc/(-1 + av) && rwat > 0 &&
p > 0 && mort > 0 && jbiom > 0)))) &&
wv == (-av^3 lwat p + av^4 lwat p - av^2 p veloc)/(-av^2 lwat^2 +
av^3 lwat^2 - bv^2 lwat rwat + av bv^2 lwat rwat -
av lwat veloc - bv^2 rwat veloc))
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