Re: [Maxima-discuss] sqrt(1-sin(t)^2) -> sqrt(1-sin(t))*sqrt(sin(t)+1)

[Michel T. <ta...@lp...>]

Something like that:

(%i10) ex1: changevar(ex0, s=sin(t), t, s);
              /
              [
(%o10)       I cos(t) sqrt(1 - sin(t)) sin(t) sqrt(sin(t) + 1) dt
              ]
              /
(%i11) map(rootscontract,%);
                      /
                      [                           2
(%o11)               I cos(t) sin(t) sqrt(1 - sin (t)) dt
                      ]
                      /
(%i12) map(trigsimp,%);
                         /
                         [
(%o12)                  I cos(t) sin(t) abs(cos(t)) dt
                         ]
                         /
(%i13) assume(cos(t) > 0);
(%o13)                           [cos(t) > 0]
(%i14) ev(%o12);
                               /
                               [    2
(%o14)                        I cos (t) sin(t) dt
                               ]
                               /
(%i15) ex2: changevar(ex1, u=cos(t), u, t);

etc.  Several times one is bothered by sign questions.


Le 02/07/2022 à 08:54, Eduardo Ochs a écrit :
> Hi list,
>
> if I execute this
>
>    display2d : false;
>    ex0 : 'integrate(s*sqrt(1-s^2), s);
>    ex1 : changevar(ex0, s=sin(t), t, s);
>
> what I get is:
>
>    (%i1) display2d : false;
>    (%o1) false
>    (%i2) ex0 : 'integrate(s*sqrt(1-s^2), s);
>    (%o2) 'integrate(s*sqrt(1-s^2),s)
>    (%i3) ex1 : changevar(ex0, s=sin(t), t, s);
>    (%o3) 'integrate(cos(t)*sqrt(1-sin(t))*sin(t)*sqrt(sin(t)+1),t)
>
> but I am trying to prepare material for a course on basic integration
> techniques, so the style of simplification that I need is different...
> this factorization is "bad":
>
>     sqrt(1-sin(t)^2)
>     ->  sqrt(1-sin(t))*sqrt(sin(t)+1)
>
> Questions:
>
>    1) how do I tell Maxima to not factor that sqrt?
>    2) how do I tell Maxima to do this instead?
>
>       sqrt(1-sin(t)^2)
>       ->  cos(t)
>
> Thanks in advance!
>    Eduardo Ochs
>    http://angg.twu.net/eev-maxima.html
>
>
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-- 
Michel Talon