changes to core/power

[smichr]

This patch tries to get power's eval_power and as_numer_denom() to do more with separation of fractional bases.

Original issue for #5062: http://code.google.com/p/sympy/issues/detail?id=1963
Original author: https://code.google.com/u/117933771799683895267/
Original owner: https://code.google.com/u/117933771799683895267/

[smichr]

It's branch 1963 (single commit over master) at smichr's acct at github.

Original comment: http://code.google.com/p/sympy/issues/detail?id=1963#c1
Original author: https://code.google.com/u/117933771799683895267/

[asmeurer]

I'm not particularly fond of 

eq=eqn(npos, dpos, pow);assert eq.is_Pow and eq.as_numer_denom() == (npos**pow, dpos**pow)
eq=eqn(npos, dneg, pow);assert eq.is_Pow and eq.as_numer_denom() == (eq, 1)
eq=eqn(nneg, dpos, pow);assert eq.is_Pow and eq.as_numer_denom() == (nneg**pow, dpos**pow)
eq=eqn(nneg, dneg, pow);assert eq.is_Pow and eq.as_numer_denom() == (eq, 1)

I prefer 

eq = eqn(npos, dpos, pow)
assert eq.is_Pow and eq.as_numer_denom() == (npos**pow, dpos**pow)
eq = eqn(npos, dneg, pow)
assert eq.is_Pow and eq.as_numer_denom() == (eq, 1)
eq = eqn(nneg, dpos, pow)
assert eq.is_Pow and eq.as_numer_denom() == (nneg**pow, dpos**pow)
eq = eqn(nneg, dneg, pow)
assert eq.is_Pow and eq.as_numer_denom() == (eq, 1)

or 
eq1 = eqn(npos, dpos, pow)
eq2 = eqn(npos, dneg, pow)
eq3 = eqn(nneg, dpos, pow)
eq4 = eqn(nneg, dneg, pow)

assert eq1.is_Pow and eq1.as_numer_denom() == (npos**pow, dpos**pow)
assert eq2.is_Pow and eq2.as_numer_denom() == (eq2, 1)
assert eq3.is_Pow and eq3.as_numer_denom() == (nneg**pow, dpos**pow)
assert eq4.is_Pow and eq4.as_numer_denom() == (eq4, 1)

Either way, there should be a space on either side of =.  

As far as the changes go, can you explain why (-1/(2 - 3**(1/2)))**(-2*any) behaves different than (-1/(1 - 3**(1/2)))**(-2*any)?

**Labels:** -NeedsReview NeedsBetterPatch  

Original comment: http://code.google.com/p/sympy/issues/detail?id=1963#c2
Original author: https://code.google.com/u/asmeurer@gmail.com/

[smichr]

I will make those changes.

Regarding the behavior, it's (neg/neg)**x vs (neg/pos)**x. Unless sign simplification is done to change the (neg/neg)**x to (pos/pos)**x one can't break up the numerator and denominator...and as_numer_denom isn't attempting simplification. Perhaps it should at least attempt sign simplification? What do you think?

Original comment: http://code.google.com/p/sympy/issues/detail?id=1963#c3
Original author: https://code.google.com/u/117933771799683895267/

[smichr]

Both changes have been made and repushed. (A little clean-up was also done in test_expr.py.) If both num and den are negative they are negated. That seems like the right thing to do since a request is being made for the numrator and denominator...the fraction should be returned separated if possible.

**Labels:** -NeedsBetterPatch NeedsReview  

Original comment: http://code.google.com/p/sympy/issues/detail?id=1963#c4
Original author: https://code.google.com/u/117933771799683895267/

[asmeurer]

**Labels:** smichr  

Original comment: http://code.google.com/p/sympy/issues/detail?id=1963#c5
Original author: https://code.google.com/u/asmeurer@gmail.com/

[smichr]

https://github.com/sympy/sympy/pull/55

Original comment: http://code.google.com/p/sympy/issues/detail?id=1963#c6
Original author: https://code.google.com/u/117933771799683895267/

[smichr]

**Status:** Fixed  

Original comment: http://code.google.com/p/sympy/issues/detail?id=1963#c7
Original author: https://code.google.com/u/117933771799683895267/