Consider using Mathematica syntax for integration

[certik]

I think we should use this syntax for integration:

>>> integrate(x**3, (x, -1, 1))
0
>>> integrate(sin(x), (x, 0, pi/2))
1
>>> integrate(cos(x), (x, -pi/2, pi/2))
2

instead of

sage: integral(x/(x^2+1), x, 0, 1)
     log(2)/2

as in SAGE currently, to be close to Mathematica. Because then you can
use the syntax:

integrate(cos(x*y), (x, -pi/2, pi/2), (y, 0, pi))

for multiple integrals.

See also [1], how we discussed this in SymPy.

[1] http://code.google.com/p/sympy/issues/detail?id=25

CC: @jasongrout

Component: calculus

Issue created by migration from https://trac.sagemath.org/ticket/1221

[williamstein]

comment:1

I changed this to sage-2.9, since it will be very easy to implement.

[williamstein]

comment:2

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chris@seberino.org	
W. Stein I wanted to commend you for leading Sage. I think it is a great idea...
	
Nov 19 (2 days ago)
William Stein	
On Nov 20, 2007 11:10 AM, seberino@spawar.navy.mil So do I. I think we should...
	
11:17 AM (20 hours ago)
Ondrej Certik to sage-devel
	
show details 2:22 PM (17 hours ago)
	
	
	
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On Nov 20, 2007 8:17 PM, William Stein <wstein@gmail.com> wrote:
>
> On Nov 20, 2007 11:10 AM, seberino@spawar.navy.mil
> <seberino@spawar.navy.mil> wrote:
> > > As to syntax, I think in Python we could use:
> > > >>> integrate(cos(x), (x, -pi/2, pi/2))
> > >  Because then you can
> > > use the syntax:
> > >
> > > integrate(cos(x*y), (x, -pi/2, pi/2), (y, 0, pi))
> > >
> > > for multiple integrals. But anyway, it's just a cosmetic issue.
> >
> > When I commended Sage's syntax I was assuming you were using this
> > Mathematica like syntax already.  I agree with Ondrej and think his
> > suggestion above is the way to go.
>
> So do I.  I think we should change that functions as suggested.  Anybody
> want to submit a patch?  Ondrej, could you create a trac ticket making precise
> what you want, etc.?

http://sagetrac.org/sage_trac/ticket/1221

Ondrej
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Stephen Forrest to sage-devel
	
show details 2:44 PM (17 hours ago)
	
	
	
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On Nov 20, 2007 2:10 PM, seberino@spawar.navy.mil
<seberino@spawar.navy.mil> wrote:

[snip]
> >  Because then you can
> > use the syntax:
> >
> > integrate(cos(x*y), (x, -pi/2, pi/2), (y, 0, pi))
> >
> > for multiple integrals. But anyway, it's just a cosmetic issue.
>
> When I commended Sage's syntax I was assuming you were using this
> Mathematica like syntax already.  I agree with Ondrej and think his
> suggestion above is the way to go.

This probably goes without saying, but presumably after the change one
will still be able to use the syntax 'integrate(sin(x),x) ' for
indefinite integration?  That is, the second argument may be a triple
or a symbol?

Steve
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Ondrej Certik to sage-devel
	
show details 5:11 PM (14 hours ago)
	
	
	
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On Nov 20, 2007 11:44 PM, Stephen Forrest <stephen.forrest@gmail.com> wrote:
>
> On Nov 20, 2007 2:10 PM, seberino@spawar.navy.mil
> <seberino@spawar.navy.mil> wrote:
>
> [snip]
> > >  Because then you can
> > > use the syntax:
> > >
> > > integrate(cos(x*y), (x, -pi/2, pi/2), (y, 0, pi))
> > >
> > > for multiple integrals. But anyway, it's just a cosmetic issue.
> >
> > When I commended Sage's syntax I was assuming you were using this
> > Mathematica like syntax already.  I agree with Ondrej and think his
> > suggestion above is the way to go.
>
> This probably goes without saying, but presumably after the change one
> will still be able to use the syntax 'integrate(sin(x),x) ' for
> indefinite integration?  That is, the second argument may be a triple
> or a symbol?

Exactly as you say.

Ondrej
- Show quoted text -

[sagetrac-mabshoff]

comment:4

This will break backward compatibility in a massive way, so I would suggest setting it to "won't fix".

Cheers,

Michael

[certik]

comment:5

Well, I haven't replied here when you suggested won't fix, as I was thinking about this.

I understand that breaking code is bad.

But still consistency is consistency. There are ways to improve the API in a non compatible way, e.g. introduce both versions and raise python warning for the old API. and after couple releases, remove it.

Also this was agreed on the sage-devel, so if you seek a different conclusion, you should (imho) advocate that on the list.

[jicama]

comment:6

See also #2787.

[burcin]

comment:8

I suggest we close this ticket since we now support the suggested syntax:

----------------------------------------------------------------------
| Sage Version 4.4.1.alpha2-patched, Release Date: 2010-04-29        |
| Type notebook() for the GUI, and license() for information.        |
----------------------------------------------------------------------
**********************************************************************
*                                                                    *
* Warning: this is a prerelease version, and it may be unstable.     *
*                                                                    *
**********************************************************************
sage: integrate(x**3, (x, -1, 1))
0
sage: integrate(sin(x), (x, 0, pi/2))
1
sage: integrate(cos(x), (x, -pi/2, pi/2))
2

The docstring for sage.misc.functional.integrate() and sage.symbolic.integration.integral.integral() contains plenty of doctests to test the tuple syntax.

Further discussion on

• implementing multiple integrals with integrate(cos(x*y), (x, -pi/2, pi/2), (y, 0, pi)) and
• replacing the examples in the docstrings with the tuple syntax and deprecating the old one
  can be continued in make the interface to integrate() like the (new consistent) interface to diff() #2787.

Comments?

[robert-marik]

comment:9

I think so, the one-variable issue is resolved and the double integrals are covered in #2787

[burcin]

comment:10

I'm closing this as fixed. See comment:8 for more info.