Comment #6 on issue 3544 by asmeu...@gmail.com: binomial should not get
expanded except when expand(func=True) is called on it
http://code.google.com/p/sympy/issues/detail?id=3544
The point of the issue is that the *default* should be to not evaluate. In
generally, it may be possible to make something that usually evaluates not
evaluate or visa-versa, but the default should aim for what will be most
desirable. I can give several arguments why binomial(n, 5) should not
auto-expand (by default):
- As described in the OP, it makes dealing with things like that summation.
- The size of the expression grows linearly with the value of the second
argument. That means that binomial(n, 10) might be manacle, but
binomial(n, 100) is quite large, and binomial(n, 1000) is huge. (By the
way, if we document this, we should recommend expand_func, not
expand(func=True), as the latter will also expand the polynomial in n
itself)
So basically, it violates rules, 2, 3, and 4 from
https://github.com/sympy/sympy/wiki/Automatic-Simplification. n*(n - 4)*(n
- 3)*(n - 2)*(n - 1)/120 is definitely not simpler than binomial(n, 5).
The size issue means that it will not be cheap even for relatively small
arguments to binomial. And the OP clearly gives a case where this would not
want to be done.
And going back to what I said in the first paragraph of this comment, if
there's ever ambiguity between whether something should evaluate to
something else automatically or not, I would say, when in doubt, don't
evaluate. Not evaluating is much easier to deal with than evaluating. To
evaluate later, one just has to call the relevant function (in this case,
expand_func). These functions generally work recursively, so one can even
call it on a larger expression containing the object and it will still be
evaluated. To not evaluate, on the other hand, one usually has to resort
to hacks like evaluate=False, and even if they are implemented in a way
that isn't hacky, it isn't easy to "unevaluate" something later on,
especially if it's part of a larger expression.
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