#2787: make the interface to integrate() like the (new consistent) interface to
diff()
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Reporter: jason | Owner: was
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.4
Component: calculus | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Comment (by nbruin):
I would say that deprecating `integral(f(x),x,a,b)` for a definite
integral will be too large a backward incompatible change to pull of.
The gain for multiple integrals is also a little tricky: The proposed
order for integral(f(x,y),x,y) where x is inner and y is outer is
definitely consistent with mathematical notation `int int f(x,y) dx dy`
but it's opposite to python's iteration order `[ (i,j) for i in range(3)
for j in range(3) ]`, where j iterates in the inner loop.
Also, the proposed notation is for multiple integrals, which in
mathematics are usually written as multiple (nested) integrals anyway.
Single integral notation is usually reserved for higher dimensional
integrals (Lebesgue, usually), in which case no particular "integration
order" is implies, and indeed the domain of integration might not allow
for a direct translation into nested integrals.
The fact that integral has to both accommodate definite integrals and
taking antiderivatives breaks the complete symmetry with the `diff`
interface. It would be nice if the interface were more symmetrical, but I
think there are good reasons why it's not. If a complete converse to
`diff()` is required, perhaps we need `antiderivative()`, which doesn't
need to accommodate definite integrals (although of course no-one would
find its existence).
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Ticket URL: <http://trac.sagemath.org/ticket/2787#comment:12>
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