`to_poly_solve` inconsistency of solutions for equivalent forms of goniometric equations
Subject: `to_poly_solve` inconsistency of solutions for equivalent forms of goniometric equations
From: Raymond Toy
Date: Wed, 18 Apr 2012 17:08:38 -0700
On 4/18/12 4:02 PM, Barton Willis wrote:
> Appending 'simpfuncs = ['expand] helps somewhat; try to_poly_solve(sin(x)/cos(x) = 1, x, 'simpfuncs = ['expand]);
>
> I made no particular effort to make to_poly_solve (usually) find syntactically identical solution sets to semantically identical equations. That simply
> wasn't a design goal. Although it might seem easy to do write a pre-processor that would do things such as sin(x)/cos(x) --> tan(x), it's not so
> easy to do this in a way that doesn't make some answers much much more complicated, or to do it without introducing spurious solutions.
I think it should be this way. Maxima doesn't automatically convert
sin(x)/cos(x) to tan(x). I don't think to_poly_solve should magically
do that either.
Although it would be nice for %union and %if were smarter so that %if
would know that cos(%pi/4*(8*%z40+1)) is never zero. Then we'd just
have %union of two values of x. And it would be nice to see that they
differ by just an integral multiple of %pi so that they could be
combined into one.
Ray