I was trying to solve the following equation over the complex numbers: sin(z) + cos(z) = 2
In Sage:
sage: z = var('z')
sage: solve(sin(z) + cos(z) == 2, z)
[sin(z) == -cos(z) + 2]
Obviously, that's not what I want. Wolfram|Alpha yields the two solutions in multiple forms: http://www.wolframalpha.com/input/?i=cos%28z%29+%2B+sin%28z%29+%3D%3D+2
Can this be done in Sage?
sage: solve(sin(x)+cos(x)==2,x,to_poly_solve=True)
[x == 1/4*pi + 2*pi*z6 - I*log(-1/2*(sqrt(2) - 2)*sqrt(2)), x == 1/4*pi + 2*pi*z8 - I*log(sqrt(2) + 1)]
Note that one gets a family of solutions because these are multi-valued inverses.
The to_poly_solve option still is not documented in the global solve?, but will show up if you do x.solve?. Apologies for not having done this.
@kcrisman, In addition to documenting the `to_poly_solve` option for the built-in `solve`, would it also make sense to have `solve` print a message to the user with the suggestion to try the option when an implicit solution is returned? I guess this depends on if it's easy to detect an implicit solution vs. an explicit one.
That wouldn't be too hard to do. We basically do this already with `to_poly_solve`, in order to make sure we don't use it and then miss "real" solutions that would get caught. You just check if the variable is on both sides :) Can you open a ticket for this and cc: me? We've gotten so many bug reports on this over the years it's insane.
In this context, `z6` refers to an integer parameter in the solution. There are infinitely many solutions to the equation and they all differ by integer multiples of 2*pi.
Asked: 2011-04-14 06:35:51 +0100
Seen: 2,550 times
Last updated: Apr 14 '11
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