Comment #21 on issue 3560 by [email protected]: solve() is a giant mess
http://code.google.com/p/sympy/issues/detail?id=3560
I think that's a good idea. We often confuse properties of the individual
solutions and the properties of the whole set of solutions that we might
want to put on this object. For example
Solution:
- Is it a real solution (sometimes solve() returns partially solved
results, like solve(f(x) - x, x) => [f(x)])?
SolutionSet:
- Are all solutions guaranteed to be included?
(I know there are more, but I can't think of them off the top of my head)
Two questions:
- How should it work if solutions are parameterized? One example is
solve(sin(x), x). The solution set is {n*pi | n integer}. Another example
is solving a linear system that has free variables (or more generally, a
positive dimensional system). Is this formalism part of Solution or
SolutionSet? I don't like your example, because it doesn't give the general
form of the solution, n*pi. Just iterating is not enough. If you have a
scheme like
* solve f(x) = 0
* plug the solutions into g(x)
* do something
You should be able to easily plug the general solution into g(x) (e.g.,
n*pi, where n = Dummy('n', integer=True)).
- What should happen for inequalities? In this case, solve() returns a
boolean expression.
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