how to correctly check that integration evaluated?

Integrate

asked 2018-06-20 17:23:42 +0200

Nasser
917 ●10 ●31 ●58

What is the correct way in sage to check that the result of integration has evaluated? I.e. the result has no unevaluated integrate remaining in it?

The way I am checking fail in some cases. For example

sage: var('x')
sage: anti=integrate((4*x - sqrt(-x^2 + 1))/(sqrt(-x^2 + 1) + 5), x)

sage: anti
-x - 4*sqrt(-x^2 + 1) + 5*integrate(1/(sqrt(x + 1)*sqrt(-x + 1) + 5), x) + 20*log(sqrt(-x^2 + 1) + 5)

The above did not fully evaluate, since there is an integrate inside the result returned. But when I do

sage: isinstance(anti.operator(), sage.symbolic.integration.integral.IndefiniteIntegral)
False

I was expecting to get True. It failed the check, because integrate was not the first operator. This one works

sage: anti=integrate(1/(sqrt(x + 1)*sqrt(-x + 1) + 5), x) 
sage: isinstance(anti.operator(), sage.symbolic.integration.integral.IndefiniteIntegral)
True

So what is the correct way to tell sage to scan the whole expression and if there is an instance of integrate any where, to return True

Thank you

--Nasser

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answered 2018-06-20 19:45:51 +0200

joaoff
220 ●1 ●6 ●21

Does this help? this is just an idea. You can improve it, of course.

var('x')
anti=integrate((4*x - sqrt(-x^2 + 1))/(sqrt(-x^2 + 1) + 5), x)
#anti=integrate(1/(sqrt(x + 1)*sqrt(-x + 1) + 5), x)
if str(anti).find("integrate") != -1:
    print("Result contains unevaluated integral!")
anti

Output:

Result contains unevaluated integral!
-x - 4*sqrt(-x^2 + 1) + 5*integrate(1/(sqrt(x + 1)*sqrt(-x + 1) + 5), x) + 20*log(sqrt(-x^2 + 1) + 5)

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answered 2018-06-20 23:30:27 +0200

Emmanuel Charpentier
7057 ●6 ●46 ●137

You must parse (recursively) the output expression, and tchack that tour tree does not contain any integrate call (i. e. a subexpression whose operator is sage.all.integrate. This must be recursive because integrate may return a sum or a product whose one term or factr is an unevaluated integrate call...

The implementation is Left As An Exercise (TM) to the reader (who may be wise to check if a general parsng function exists in Sage... or in some Python library...).

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