How to tell sympy to simplify or change between minimums and absolute values?

For example, how can we make this simplify to zero (or show me where I’ve made a dumb mistake and then it just works)

import sympy
sympy.var('s t', real=True)
(s - 2 * sympy.Min(s, t) - sympy.Abs(s - t)).simplify()  # should be zero?

I see evidence that sympy knows about these kind of relations but I’m not clear what triggers it to go from $|t – s|$ to a representation involving min or max.

>Solution :

You can use rewrite(Piecewise):

In [239]: e
Out[239]: s - │s - t│ - 2⋅Min(s, t)

In [240]: e.rewrite(sympy.Piecewise)
Out[240]: 
      ⎛⎧s  for s ≤ t⎞   ⎛⎧s - t   for s - t ≥ 0⎞
s - 2⋅⎜⎨            ⎟ - ⎜⎨                     ⎟
      ⎝⎩t  otherwise⎠   ⎝⎩-s + t    otherwise  ⎠

In [241]: e.rewrite(Piecewise).simplify()
Out[241]: -t