I don't understand everything that the Mathematica syntax is doing
there, but is this the same as
a = Wild('a', exclude=[x])
b = Wild('b', exclude=[x])
expr.replace(Integral(cos(a + b*x), x), sin(a + b*x)/b)
I guess what isn't supported so well is making x itself be a Wild
representing a Symbol.
What I would do is extend Wild to accept a callable, which can be used
to determine if an expression should match it. So for instance, you
could match only Symbols with Wild('x', param=lambda i: isinstance(i,
Symbol)) (what should "param" be called?). The exclude parameter would
be a special case of this with lambda i: not i.has(exclude). We could
also add a special case for isinstance to avoid having to type lambda
in the common case.
One could then do
x = Wild('x', isinstance=[Symbol])
a = Wild('a', exclude=[x])
b = Wild('b', exclude=[x])
expr.replace(Integral(cos(a + b*x), x), sin(a + b*x)/b)
and it would do the right thing, for instance, for expr =
Integral(cos(1 + 2*t), t).
The question is how hard it is to make this work with the pattern
matching algorithm that is currently implemented.
Aaron Meurer
On Thu, Sep 19, 2013 at 10:40 AM, F. B. <[email protected]> wrote:
> Mathematica has the ability to do pattern matching such as:
>
> Int[cos[a_.+b_.*x_], x_Symbol] := Sin[a+b*x] / b /; FreeQ[{a, b}, x]
>
> Here a and b are matched if they do not contain x.
>
> As far as I know, SymPy is unable to perform such a match. Are there any
> ideas to extend the pattern matching algorithm?
>
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