expand(trig=True) doesn't like difference of angles

[G B]

I'm still new to sympy, so I might be doing something stupid, but I think there's a problem here:

In [1]: from sympy import *

In [2]: x,y=symbols('x,y')

In [3]: cos(x+y).expand(trig=True)

Out[3]: -sin(x)*sin(y) + cos(x)*cos(y)

So far so good.  but then:

In [4]: cos(x-y).expand(trig=True)

Leads to a long traceback that culminates with: AttributeError: 'Mul' object has no attribute '_eval_expand_trig'

For giggles, I also tried:

In [5]: cos(x + (-y)).expand(trig=True)

Which fails in the same way.  I can post the full traceback if it helps.

[Aaron Meurer]

Ah, that is a bug. You should report that at
http://code.google.com/p/sympy/issues/. The reason it happens is that
it tries to do the expansion recursively, but sin(-x) becomes -sin(x).
The fix is not too hard either, if you want to give it a shot.

The work around is to do the expansion with +y and then do
expr.subs(y, -y) at the end.

By the way, x - y and x + -y are exactly the same thing in SymPy.
Both are represented internally as Add(x, Mul(-1, y)).

Aaron Meurer

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[G B]

Oh, so that's where the broken Mul comes from...  =)  Makes sense, of course, but I was looking at my code saying "there's no multiplication!".

I've submitted the issue.

[G B]

I seem to have fixed my problem by making changing in sympy/functions/elementary/trigonometric.py this definition in class sin (and making a corresponding change in class cos).  The change was to tell sin/cos not evaluate in their constructors.

I haven't run any tests on this except for my code where I found the problem.

    def _eval_expand_trig(self, **hints):

        from sympy import expand_mul

        arg = self.args[0]

        x = None

        if arg.is_Add: # TODO, implement more if deep stuff here

            # TODO: Do this more efficiently for more than two terms

            x, y = arg.as_two_terms()

#GCB 120920 added ",evaluate=False" to the next 4 lines

            sx = sin(x,evaluate=False)._eval_expand_trig()

            sy = sin(y,evaluate=False)._eval_expand_trig()

            cx = cos(x,evaluate=False)._eval_expand_trig()

            cy = cos(y,evaluate=False)._eval_expand_trig()

            return sx*cy + sy*cx

        else:

            n, x = arg.as_coeff_Mul(rational=True)

            if n.is_Integer: # n will be positive because of .eval

                # canonicalization

                # See http://mathworld.wolfram.com/Multiple-AngleFormulas.html

                if n.is_odd:

                    return (-1)**((n - 1)/2)*C.chebyshevt(n, sin(x))

                else:

                    return expand_mul((-1)**(n/2 - 1)*cos(x)*C.chebyshevu(n -

                        1, sin(x)), deep=False)

        return sin(arg)

On Wednesday, September 19, 2012 7:02:11 PM UTC-7, Aaron Meurer wrote:

[Aaron Meurer]

This was fixed at https://github.com/sympy/sympy/pull/1537 (using your fix).

Aaron Meurer

> https://groups.google.com/d/msg/sympy/-/u5JcmqrSlRoJ.

[G B]

Great! I'd seen the fixed notice on the issue, but wasn't sure what the patch was. Glad to hear that I was a bit of help.

Cheers—
Greg