ha! damn. of course. ah well...
On Thursday, 6 March 2014 23:04:27 UTC-3, Jameson wrote:
>
> Alternatively and without any need for trickery:
>
> julia> using Polynomial
>
> julia> x=Poly([1,0],:x)
> Poly(x)
>
> julia> 2x^2 + 1
> Poly(2x^2 + 1)
>
>
> On Thu, Mar 6, 2014 at 8:53 PM, andrew cooke <and...@acooke.org<javascript:>
> > wrote:
>
>> ...possibly offensive to some.
>>
>> i wanted a nice syntax for people to define polynomials. the code below
>> lets you write things like
>>
>> 2X^2 + 3X + 1
>> X+1
>>
>>
>>
>> and packages the coefficients into a nice format for a constructor (an
>> array of (coeff, power)).
>>
>> this kind of thing is common in haskell where because of the lovely
>> syntax you can "hide" function application in expressions. i haven't seen
>> anything similar in julia, but i haven;t read a lot of julia code.
>>
>> type Terms{I<:Integer}
>> terms::Array{(I, Int)}
>> end
>>
>> type Power
>> exp::Int
>> end
>>
>> type X end
>>
>> +{I<:Integer}(p1::Terms{I}, p2::Terms{I}) = Terms{I}(vcat(p1.terms, p2.
>> terms))
>> +{I<:Integer}(::Type{X}, p2::Terms{I}) = Terms{I}(vcat([(one(I),1)], p2.
>> terms))
>> +{I<:Integer}(p1::Terms{I}, ::Type{X}) = Terms{I}(vcat(p1.terms, [(one(I
>> ),1)]))
>> +{I<:Integer}(p1::Power, p2::Terms{I}) = Terms{I}(vcat([(one(I),p1.exp)],p2
>> .te\
>> rms))
>> +{I<:Integer}(p1::Terms{I}, p2::Power) = Terms{I}(vcat(p1.terms, [(one(I
>> ),p2.ex\
>> p)]))
>> +{I<:Integer}(n::I, p2::Terms{I}) = Terms{I}(vcat([(n,0)], p2.terms))
>> +{I<:Integer}(p1::Terms{I}, n::I) = Terms{I}(vcat(p1.terms, [(n,0)]))
>>
>> +{I<:Integer}(n::I, ::Type{X}) = Terms{I}([(n, 0),(one(I),1)])
>> +{I<:Integer}(::Type{X}, n::I) = Terms{I}([(one(I),1), (n, 0)])
>>
>> ^(::Type{X}, exp::Int) = Power(exp)
>> *{I<:Integer}(n::I, ::Type{X}) = Terms{I}([(n,1)])
>> *{I<:Integer}(n::I, p::Power) = Terms{I}([(n,p.exp)])
>>
>> println(2X^2 + 3X + 1)
>> println(X+1)
>>
>> which prints:
>>
>> Terms{Int64}([(2,2),(3,1),(1,0)])
>> Terms{Int64}([(1,1),(1,0)])
>>
>> there are some issues. X alone, for example, doesn't have enough info to
>> define the subtype of Integer, which i need. defining additional methods
>> for that case to give a nice "syntax error" resulted in an explosion of
>> ambiguous methods, so i dropped it an will try again later.
>>
>> also, you might hope to use promotion to avoid defining so much, but it
>> turns out to be harder than i thought.
>>
>> anyway, i thought someone might find it amusing,
>> andrew
>>
>>
>
