Hi,

I am preparing patches that will resolve

http://trac.sagemath.org/sage_trac/ticket/6465

and will also move symbolic integration as a sub-class
of SFunction into new symbolics.


Currently, Sage allows omitting variable of integration for convenience.
However, this convenience comes at a hefty price by making Sage
syntax highly inconsistent. On top of this, it mask genuine typing error
as a valid input.

For example: "integrate(f(x), x, a, )" is treated as "integrate(f(x), x, x, a)"
where user may have wanted to type "integrate(f(x), x, a, b)" but
missed the "b".

Given we are moving to a new settings, I am proposing that we make
integration syntax bit stricter and consistent now. In particular, we allow only
following inputs as valid

(1) integrate( f(x), x)
(2) integrate( f(x), (x,a,b) )
(3) integrate( f(x), x, a, b)


Cheers,
Golam

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