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 <dimp...@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.benja...@gmail.com>
> wrote:
> >On Wed, 29 Nov 2023 at 12:40, Eric Gourgoulhon <egourgoul...@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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