Well, I think it would be an abuse of subs to make it work with your
autoupdating dictionary. If I understand mul_dict, it doesn't contain any
entries at the start -- it becomes populated as you request ei*ej values.
What about using Transform:
# a rule that all Muls get multiplied by 2
>>> m = {} # the dictionary that keeps track of the rule
>>> (x+x*y+z*a).xreplace(Transform(lambda k: m.setdefault(k, 2*k), lambda
w: w.is_Mul))
2*a*z + 2*x*y + x
>>> m
{x*y: 2*x*y, a*z: 2*a*z}
But that is not the right way to benefit from the dictionary since the
argument to setdefault is called every time. Instead (and I verify by using
the `ok` function that delays the number of seconds equal to its argument)
this is how it should be done:
>>> def ok(i):
... t=time()
... while time()-t<i:pass
... return i
...
>>> (3*x+3*x*y+3*z*a).xreplace(Transform(lambda k: m[k] if k in m else
m.setdefault(k, ok(k)), lambda w: w.is_Integer))
3*a*z + 3*x*y + 3*x
That only takes 3 seconds to run, not 9.
/c
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