(sin(x)/cos(x)).rewrite(tan(x)) should give tan(x)

[oscarbenjamin]

Rewrite tan could be improved here:

In [39]: expr = sin(x)/cos(x)                                                                                                                  

In [40]: expr                                                                                                                                  
Out[40]: 
sin(x)
──────
cos(x)

In [41]: expr.rewrite(tan)                                                                                                                     
Out[41]: 
       ⎛x⎞ 
  2⋅tan⎜─⎟ 
       ⎝2⎠ 
───────────
       2⎛x⎞
1 - tan ⎜─⎟
        ⎝2⎠

I would like that to be just tan(x).

[sylee957]

I see the rewriting works first by rewriting its elements

sympy/sympy/core/basic.py

Lines 1641 to 1644 in a7e6f09

	if hints.get('deep', True):
	args = [a._eval_rewrite(pattern, rule, **hints)
	if isinstance(a, Basic) else a
	for a in self.args]

because deep=True by default.
And besides the fact that there is no individual rewriting method implemented in Mul, this may prevent any strategies to be implemented in top level.

I have one trivial example using pattern matching though,

>>> from sympy import *

>>> a = Symbol('a')
>>> expr = cos(a)/sin(a)

>>> x = Wild('x')
>>> expr = expr.replace(sin(x)/cos(x), tan(x))
>>> expr = expr.replace(cos(x)/sin(x), 1/tan(x))
>>> pprint(expr, use_unicode=False)
  1   
------
tan(a)

But I suppose they are already handled better in simplify, if whatever we can introduce for rewriting, can have possibility to be computationally expensive.

[oscarbenjamin]

Maybe a high-level Expr._eval_rewrite(tan) can call replace like that before recursing down.

[oscarbenjamin]

Also:

In [44]: e                                                                                                                                     
Out[44]: 
cos(x)
──────
sin(x)

In [45]: e.rewrite(cot)                                                                                                                        
Out[45]: 
   2⎛x⎞    
cot ⎜─⎟ - 1
    ⎝2⎠    
───────────
       ⎛x⎞ 
  2⋅cot⎜─⎟ 
       ⎝2⎠