Ability to Integrate?

[jeffreyshen19]

From what I can see, there doesn't seem to be an ability to integrate math functions. Is this a desired feature? If so, I can put in a pull request.

Cheers,
Jeffrey

[josdejong]

Do you mean like building support for integration (opposite of differentiation)? Or do you mean importing new functions? For the latter case, there already is a function import available.

[jeffreyshen19]

I meant the former (opposite of differentiation).

[josdejong]

Having support for integration would indeed be great!

It's complicated to implement integration though. Do you have concrete plans how you would go ahead?

[jeffreyshen19]

I was thinking of implementing integration similar to how differentiation is done (manually inputing integration rules).

[ericman314]

Integration is a completely different problem than differentiation. In terms of difficulty, differentiation is like computing a hash, and integration is like reversing it. But it's definitely on our wish list, so we can use all the help we can get.

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[jeffreyshen19]

Agreed. However, many common functions can be integrated using simple integration rules + reverse chain rule. This, unfortunately, is not general and can not be applied to every function. Another possibility is to have a function which calculates the numeric value of an integral using a Riemannian approximation.

Thoughts?

[josdejong]

A numeric integration (and differentiation) function would be interesting too, that's not that hard to implement. It's completely different from symbolic computations though :)

[bjodah]

FWIW: As far as I know the best CAS implementation of integration is RUBI. There was a Google summer of code project last year in the sympy organization which aimed to port these rules into SymPy. They didn't quite finish, but once (if) that ends up working, then it shouldn't be too hard writing another export function for mathjs (since the approach they ended up taking was generating Python code).

[ericman314]

Fascinating idea, @bjodah. I think it's worth a look.

[bjodah]

If you are interested in the status of that effort I would recommend reading up/reaching out on SymPy's mailing list: https://groups.google.com/forum/m/#!searchin/sympy/rubi

[josdejong]

@joelhoover what you you think about that? (See #1015)

[Schnark]

BTW: Numeric integration is actually one of the examples in the documentation: http://mathjs.org/examples/advanced/custom_argument_parsing.js.html

[cshaa]

Let's continue the discussion in #1015