incorrect dot methods

[stevengj]

The module defines three dot methods:

dot{T<:Number,S}(p::Poly{S}, c::T) = p * c
dot{T<:Number,S}(c::T, p::Poly{S}) = c * p
dot(p1::Poly, p2::Poly) = p1 * p2

which make no sense to me.

dot should define an inner product, which means that it should return a number (or whatever the coefficient type of the polynomial is). For polynomials, you would normally define the dot product to be some kind of integral. But since there are many such definitions and no single canonical choice, it would be better to leave this undefined.

[jverzani]

That's my fault. I wanted a unicode operation for printing, so I could copy and paste the printed output of polynomials. I noticed, \cdot could be used if I overloaded these. I'll fix to print with * and drop these, I don't think they are used otherwise.

[stevengj]

Thanks! I noticed this in my class when we were covering orthogonal polynomials, and I wanted to show some examples with Polynomials.jl by defining a proper dot product.

[stevengj]

Another thing I noticed is that it would be nice to have a polyint(p, a, b) method to compute the definite integral on [a,b].

[jverzani]

I put in a PR with a simple minded implementation. If you know of a more performant approach, can you let me know?

…

On Tue, Mar 21, 2017 at 4:52 PM, Steven G. Johnson ***@***.*** > wrote: Another thing I noticed is that it would be nice to have a polyint(p, a, b) method to compute the definite integral on [a,b]. — You are receiving this because you modified the open/close state. Reply to this email directly, view it on GitHub <#110 (comment)>, or mute the thread <https://github.com/notifications/unsubscribe-auth/AAZvTMktEY4ohmVHB0kpAOhEEywavUtZks5roDiEgaJpZM4MiVHp> .

-- John Verzani Chair, Department of Mathematics College of Staten Island, CUNY verzani@math.csi.cuny.edu