The documented effect is usually of most impact:
https://maxima.sourceforge.io/docs/manual/maxima_46.html#index-domain
there may be other undocumented effects, but the one above tends to explain
a lot already.
On Sunday 3 December 2023 at 06:26:20 UTC-8 Oscar Benjamin wrote:
> What does "set domain to complex" mean in terms of Maxima's settings?
>
> Maxima's solve seems to compute complex solutions by default:
>
> (%i21) solve(x^2 + 1);
> (%o21) [x = - %i, x = %i]
>
> On Sun, 3 Dec 2023 at 13:37, Dima Pasechnik <dim...@gmail.com> wrote:
> >
> > Yes, Sage modifies the defaults of Maxima, in particular we set domain
> to complex.
> >
> > On 3 December 2023 12:28:45 GMT, Oscar Benjamin <oscar.j....@gmail.com>
> wrote:
> > >On Wed, 29 Nov 2023 at 12:40, Eric Gourgoulhon <egourg...@gmail.com>
> wrote:
> > >>
> > >> Le mardi 28 novembre 2023 à 18:25:04 UTC+1, kcrisman a écrit :
> > >>
> > >> Yes. Maxima's attitude is that the square root of negative one is an
> expression which might have multiple values, rather than just picking one
> you hope might be consistent over branch points.
> > >>
> > >> To enforce Maxima to work in the real domain, avoiding to play too
> much with complex square roots, one can add at the beginning of the Sage
> session:
> > >>
> > >> maxima_calculus.eval("domain: real;")
> > >>
> > >> Then the second example in the initial message of this thread yields
> > >>
> > >> [[x == 2/5*sqrt(6)*sqrt(5), y == 16, l == 1/9*18750^(1/6)], [x ==
> -2/5*sqrt(6)*sqrt(5), y == 16, l == -1/9*18750^(1/6)]]
> > >>
> > >> instead of an empty list.
> > >
> > >When using Maxima (5.45.1) directly I get this result with default
> settings:
> > >
> > >(%i1) f: 10*x^(1/3)*y^(2/3)$
> > >
> > >(%i2) g: 5*x^2 + 6*y$
> > >
> > >(%i3) solve([diff(f,x)=l*diff(g,x), diff(f,y)=l*diff(g,y), g=120],
> [x,y,l]);
> > > 1/6
> > > 2 sqrt(6) 18750
> > >(%o3) [[x = ---------, y = 16, l = --------],
> > > sqrt(5) 9
> > > 1/6
> > > 2 sqrt(6) 18750
> > > [x = - ---------, y = 16, l = - --------]]
> > > sqrt(5) 9
> > >
> > >Does Sage modify some Maxima settings related to this or does it call
> > >something other than solve?
> > >
> > >--
> > >Oscar
> > >
> >
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