Comment #24 on issue 51 by asmeurer: RootOf for polynomial equations
http://code.google.com/p/sympy/issues/detail?id=51
Three things I just thought of relating to RootOf:
1. I wonder if RootOf when given an index should be unevaluated by default
and require .doit() to convert into a closed form (if it exists).
For example, if RootOf.evalf() is implemented, RootOf(Poly,
index=0).evalf() would evaluate the first root by bisection methods,
whereas RootOf(Poly, index=0).doit().evalf() would evaluate the closed-form
radical.
2. The behavior of RootOf when not given an index.
In [11]: RootOf(x**2 - 1)
Out[11]: [-1, 1]
In [12]: RootOf(x**5 + x + 3,)
Out[12]:
⎡ ⎛ 5 ⎞⎤
⎣RootOf⎝x + x + 3, 0⎠⎦
The first one gives both roots as a list, the second only gives the first
one. Assumedly this is because it is only giving the real roots. So two
questions:
- Why does it only give the real roots when no index is given?
- Is index=None indented to act as RootsOf once did? Otherwise, I don't
see much use for not requiring the index argument always.
3. While we are on the subject of arguments, why not require the variable
as an argument? I know that right now only numerical coefficients are
supported, but I don't see why something like RootOf(x**2 + b*x + c, x, 0)
shouldn't be supported in the future.
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