Fixing integral subs

[MechCoder]

First attempt at fixing integral subs.

1. If old, new in eq.subs(old, new) are both functions of the integration variables, then substitution takes place irrespective of whether eq is a definite or indefinite integral.
2. If it is a indefinite integral, then this is followed, https://code.google.com/p/sympy/issues/detail?id=3829
3. If it is definite, and there is a linear transformation, then it is xreplaced.

[jrioux]

SymPy Bot Summary: 🔴 Failed after merging Manoj-Kumar-S/Integralfix (aaa1eab) into master (90fc660).
@manoj-kumar-s: Please fix the test failures.
🔴 PyPy 2.0.0-beta-1; 2.7.3-final-42: fail
🔴 Python 2.7.2-final-0: fail
🔴 Python 3.2.1-final-0: fail
✅ Sphinx 1.1.3: pass
Doc Coverage: unchanged
35.931% of functions have doctests (compared to 35.931% in master)
41.310% of functions are imported into Sphinx (compared to 41.310% in master)

[MechCoder]

@asmeurer : Could you review this? There are a lot of test failures.

[asmeurer]

First, please add tests for the new behavior, so that I can easily see what it does and verify that it is correct.

[MechCoder]

@asmeurer : I added tests. Could you have a look now?

[asmeurer]

Include the integration variable.

[asmeurer]

Add tests for substituting against integrals with only the upper limit.

[asmeurer]

I think it would be better to do the substitution so that it results in a definite integral again if possible. So for example Integral(f(x), x).subs(x, y) should give Integral(f(y), y).

[MechCoder]

@asmeurer : And that would be possible only if the transformation is linear right?

[jrioux]

I disagree with most of the tests here. The only test that makes sense to me is

expr = Integral(x**log(x)*exp(x)) 
assert expr.subs(x, y) == Integral(x**log(x)*exp(x), (x, y))

.subs has a mathematical meaning whereas the type of replacement implemented in this PR (besides the above) should IMHO be the function of .replace or .xreplace (or yet a fourth function). See the discussion at #2198, especially about @asmeurer's comment about the 1, 2, 3's of subs scope.

[zanzibar7]

I don't think "eq.subs" is the function that's supposed to do this. My under is that subs is supposed to preserve mathematical equality, and this doesn't.

[asmeurer]

@manoj-kumar-s I think it would be fine if it only worked for subs(x, y) where x is one of the integration variables and y is a Symbol.

[asmeurer]

You should also add tests for multiple integrals, especially multiple integrals of varying types (definite and indefinite). Let's also make sure that it works correctly for things like Integral(f(x), (x, 0, x)) where the integration variable is both bound and free.

[asmeurer]

@jrioux @zanzibar7 thanks for helping review this. @raoulb we discussed this issue a few times on IRC. Do you want to help out here as well?

[MechCoder]

@jrioux , @zanzibar7 , @asmeurer : I'm still a bit confused. So do you mean to say only this should work?

`eq = Integral(f(x), x).subs(x, y)` should give `eq = Integral(f(x)., (x, y))`

and what to do abput stuff like eq = Integral(f(x), x).subs(f(x), g(x)) , it should just return a ValueError?

and for a definite integral say eq = Integral(f(x), (x, 1, 2)).subs(x, y) what should it return? and for Integral(f(x), (x, 0, x)).subs(x, y) it should return Integral(f(x), (x, 0, y)). I'm sorry but I read through the discussion on that PR and it has got me slighly more confused.

[MechCoder]

So that means bascially subs should work for a definite integral only when the old in subs is an integration variable and the new in subs can be anything? And for indefinite integrals it should raise a ValueError?

[MechCoder]

Okay, I'm preparing a gist of rules that have to be followed, so that I can become clear.

[MechCoder]

@jrioux , @zanzibar7 , @asmeurer : Could you please have a look at this, and say if my interpretation is right? https://gist.github.com/Manoj-Kumar-S/6277258

[jrioux]

I disagree with your point 1: this subs should return Integral(f(x), (x, y)); the operation Integral(f(x), x) -> Integral(f(y), y) should be done by some integral transformation method (which probably already exists but I don't know its name), but not by .subs, IMHO.

I agree with point 2, which is what issue 3829 is about.

I disagree with your point 3 and all its subpoints. Basically, anything that's bound inside Integral isn't free for substitution with .subs (but other method such as .replace and .xreplace might accomplish this). When a .subs finds nothing to substitute, it returns the original expression unchanged and does not raise an exception.

I think you should concentrate on issue 3829 and nothing more, and maybe even hold off a bit, as #2198 looks in good shape to fix up the rest.

[MechCoder]

Okay, great.

[jrioux]

SymPy Bot Summary: 🔴 Failed after merging Manoj-Kumar-S/Integralfix (95bf661) into master (905dd3e).
@manoj-kumar-s: Please fix the test failures.
🔴 PyPy 2.0.0-beta-1; 2.7.3-final-42: fail
🔴 Python 2.7.2-final-0: fail
🔴 Python 3.2.1-final-0: fail
✅ Sphinx 1.1.3: pass
Doc Coverage: unchanged
35.931% of functions have doctests (compared to 35.931% in master)
41.310% of functions are imported into Sphinx (compared to 41.310% in master)

[asmeurer]

But isn't Integral(f(x), (x, y)) essentially equivalent to Integral(f(y), y) when y is a Symbol?

[asmeurer]

Manoj, maybe move that to the wiki, so that we can edit it.

[jrioux]

Logic for things like Integral(f(x), (x, y)) replaced by Integral(f(y), y) should go in the class constructor, IMHO (and better make sure to check the assumptions on x and y).

[asmeurer]

SymPy Bot Summary: 🔴 Failed after merging Manoj-Kumar-S/Integralfix (95bf661) into master (5e2ea80).
@manoj-kumar-s: Please fix the test failures.
🔴 Python 2.6.8-final-0: fail
🔴 Python 2.7.3-final-0: fail
🔴 PyPy 1.8.0-final-0; 2.7.2-final-42: fail
🔴 Python 3.2.3-final-0: fail
🔴 Sphinx 1.1.3: fail

[MechCoder]

@asmeurer Is anyone working on this right now, in a simultaneous PR. I don't think I have the bandwidth to work on this right now. So closing.