Identifies true equation as FALSE

[theauditor]

The following equation returns 'False'
Equation : ((sin(x) - cos(x))(sin(x) + cos(x))) == (1 - 2 (cos(x)**2))

How ever individually the RHS and LHS produce the right results
(1 - 2 (cos(x)**2)) = -cos(2x)
((sin(x) - cos(x))(sin(x) + cos(x))) = -cos(2x)

[aktech]

This is correct. The == is used for structural comparison, not mathematical. http://docs.sympy.org/latest/tutorial/gotchas.html#equals-signs

[theauditor]

Hmmm. Works but not at all intuitive. Feels like it should have been solved with a simple operator. Doesn't feel right :(

[ashutoshsaboo]

@aktech @asmeurer @certik @hargup . How about if we change the structural comparison == to mathematical comparison just for SymPy Gamma? As, in we can modify the input of the user (using simple string manipulation) to simplify(a-b)==0 or a.equals(b) and then pass it ahead to the SymPy functions, for evaluating the modified result?

Details about this described here - https://groups.google.com/d/msg/sympy/kiCMquuqC2s/q9RVhPC8AAAJ .

Any opinions on this?

[asmeurer]

Yes, I agree that for SymPy Gamma == should be more mathematical. It also could mean "solve", as in, if someone writes x^2 - 1 = 0, they probably want to solve for x. So = (and ==) should have a card for determining of the two sides are equal, and for solving the equation.

[asmeurer]

It's obviously impossible to do this perfectly, but in general, SymPy Gamma should aim to do what the user expects it to do, and work around some of the idiosyncrasies of SymPy the library.

[ashutoshsaboo]

@asmeurer Yes exactly I agree with you. I'll try mapping the == in SymPy Gamma to a.equals(b) and then correspondingly calling the solve() function as well.

But what would you suggest would be better the simplify(a-b)==0 or a.equals(b)? AFAIK, a.equals(b) must be much more efficient and less in complexity than simplify(a-b)==0?

[asmeurer]

I think equals is fine.

[ashutoshsaboo]

@asmeurer Please review PR #75 ! Thanks! 😃