Polyint

[jverzani]

Add definite integral interface to polyint, as mentioned in #110 .

[stevengj]

LGTM.

Note that the docstring formatting here is nonstandard for Julia. If you follow the format of Base, it would be, for example:

"""
    polyint(p::Poly, k::Number=0)

Indefinite integral of a polynomial: integrate the polynomial `p` term
by term, optionally adding constant term `k`. The degree of the
resulting polynomial is one higher than the degree of `p`.


Examples:

polyint(Poly([1, 0, -1])) # Poly(x - 0.3333333333333333x^3)
polyint(Poly([1, 0, -1]), 2) # Poly(2.0 + x - 0.3333333333333333x^3)

See also `polyint(p, a, b)` for a definite integral over `[a,b]`.
"""

[stevengj]

In principle, you could probably write a recurrence for P(b) - P(a) in terms of b-a, but I'm not sure it's worth it here.

[jverzani]

Thanks for your help! I'll leave this as is. I'll open a separate issue about updating docstrings.

[stevengj]

Basically, one would want to work out the polynomial P(x + δ) in δ = b - a. See: http://math.stackexchange.com/questions/694565/polynomial-shift