Robert Dodier wrote:
> On Feb 2, 9:16 pm, kcrisman <kcris...@gmail.com> wrote:
>
>> sage: integrate(sin(x),[x],[var('y')]) # double integral, x first
>> sage: integrate(sin(x),[x,0,pi],[y]) # one definite, one indefinite
>> sage: integrate(sin(x),(x,),(x,)) # double integral, using tuples
>> instead of lists if you like parentheses
>> sage: integrate(sin(x),(x,),(var('y'),),(var('z'),)) # or more
>> integrals
>
> Since the Sage project does not have the burden of history
> (relatively speaking) I think you guys should go nuts and try
> to do it "right".
>
> I'll leave it to you to decide what's right but to me it means
> trying to directly represent general integrals, so the syntax is:
> integrate(F, R) or integrate(F, R, mu) where F is a function,
> R is a region, and mu is an optional measure.
Wow, you've really opened up possibilities here. This is a very
intriguing idea.
We can define a function so that it knows what the variables and
constants are, i.e.,
sage: var('y')
sage: f(x) = sin(x)*y
So integrating this function should be okay with the below
sage: integrate(f, [0, pi])
In fact, the following general form
sage: integrate(expression, (x, a, b), (y, c, d))
could be a shortcut for
sage: integrate((x,y) |--> expression, set( (x,y) s.t. a<=x<=b and c<=y<=d))
and we would still have the familiar syntax while supporting much more
powerful statements. (Note that I use Sage functions instead of Python
lambda functions, so they can be sped up using fast_float easily).
Robert, please keep contributing to the conversation. You've obviously
thought a lot more about this than we have. I'd like to hear you
elaborate on this if you have time.
Jason
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