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.
Leaving aside mu for the moment, F is specifically a function
(named or unnamed, and not a general expression) and R is an
interval or product of intervals or some more general set.
1-d integrals would be like integrate(lambda([x], sin(x)), [0, pi])
(sorry, I don't know the python lambda notation)
or integrate(sin, [0, pi]). 2-d like
integrate(lambda([x, y], x*y), [0, 1] cross [0, 1]),
more general region like integrate(lambda([u, v], exp(u - v)),
set((u, v) s.t. u - v < 0)).
I've imagined some notations such as cartesian product
and so-called "set builder" which may not yet exist in Sage.
The existing notation integrate(a, b, c, d) could be preserved
as a convenience function equivalent to integrate(lambda([b], a), [c,
d]).
I've left out many details but the general point is that I think
you guys (= Sage project) should aim high.
FWIW
Robert Dodier
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