[RFC] real roots

[Chris Smith]

In PR 8814 I write, 

Something has to be done to allow one to compute real_root(float, odd) as real. At first I thought to handle this in real_root, but then I thought it might be better to catch it in _eval_power itself. Which do you think is better:

# This is how a negative rational base behaves:

>>> root(S('-1/10'),3)
(-1)**(1/3)*10**(2/3)/10

# Now, for a negative float...

>>> root(S('-.1'),3)
0.464158883361278*(-1)**(1/3)  # <-- should a negative float give this (a)
>>> _.n()
0.232079441680639 + 0.401973384383085*I  # <-- or this (b)?

The SymPy  trend is to fully evaluate an expression if args are numbers, but by selecting the principle root in the case of Pow, the user looses the option to select the real branch post-calc. (Hence, I favor not fully evaluating in this case, selecting behavior (a).) If the power is not an odd rational, the usual, fully evaluated result is obtained.

/c

[Aaron Meurer]

Without commenting on your proposal, I'd like to point out that point of the principal nths root is that all other nth roots are the powers of that root. 

Aaron Meurer

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[Chris Smith]

By allowing the (-1)**(1/3) to remain we leave open (as with Rational bases) the option of getting to the real root with real_root. I wish we had a good mechanism to check if something like root(x, 3) + 2 == 0 when substituting in -8 for x. It is for this reason that the following returns no solution:

>>> solve(root(x,3)+2)

[]

[Aaron Meurer]

On Wed, Jan 14, 2015 at 12:02 AM, Chris Smith <smi...@gmail.com> wrote:

By allowing the (-1)**(1/3) to remain we leave open (as with Rational bases) the option of getting to the real root with real_root. I wish we had a good mechanism to check if something like root(x, 3) + 2 == 0 when substituting in -8 for x. It is for this reason that the following returns no solution:

>>> solve(root(x,3)+2)

[]

I suppose this is right. There is no x that when plugged in to that equation, gives 0. Maybe 8*exp_polar(3*pi*I) could be considered a solution. 

Aaron Meurer

 

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