Re: Multiplying Polynomials
- To: mathgroup at smc.vnet.net
- Subject: [mg117897] Re: Multiplying Polynomials
- From: Daniel Lichtblau <danl at wolfram.com>
- Date: Sat, 2 Apr 2011 17:06:20 -0500 (EST)
----- Original Message -----
> From: "TBone" <TBone at yahoo.com>
> To: mathgroup at smc.vnet.net
> Sent: Saturday, April 2, 2011 2:41:16 AM
> Subject: [mg117863] Multiplying Polynomials
> This is very simple and I freely confess my ingnorance.
>
> I'm trying to set up a generating function to count some letters of
> the
> alphabet. Specifically, I need to multiply two polynomials in the
> variable x, do some surgery on the result, and continue with another
> letter.
>
> Here is my problem.
>
> I start with:
>
> expand[(1+ax+a^2x^2+...)*(1+bx+b^2x^2+...)]
>
> and continue with:
>
> expand[(1+ax+bx+abx^2+...)*(1+cx+c^2x^2+...)]
>
> Howerver, it chokes on the following:
>
> expand[(1 + a x + b x + c x + a^2 x^2 + a b x^2 + b^2 x^2 + a c x^2 +
> b
> c x^2 +
> c^2 x^2 + a^2 b x^3 + a b^2 x^3 + a^2 c x^3 + a b c x^3 + b^2 c x^3 +
> a c^2 x^3 + b c^2 x^3 + a^2 b^2 x^4 + a^2 b c x^4 + a b^2 c x^4 +
> a^2 c^2 x^4 + a b c^2 x^4 + b^2 c^2 x^4 + a^2 b^2 c x^5 + a^2 b c^2
> x^5 +
> a b^2 c^2 x^5 + a^2 b^2 c^2 x^6)*(1 + dx + d^2 x^2)]
>
> What gives?
>
> TIA!!
>
> --TB
Dunno, from this description. No idea what you expected. Mathematica
is case sensitive. Is the issue that you have expand instead of Expand?
Or is your dx meant to be d x (more clearly done as d*x)?
I would suggest code that makes it less easy to mess up variables
vs products.
pgenerator = 1 + x + x^2;
letteredpolys = pgenerator /. x -> {a*x, b*x, c*x, d*x}
Out[12]= {1 + a*x + a^2*x^2, 1 + b*x + b^2*x^2, 1 + c*x + c^2*x^2,
1 + d*x + d^2*x^2}
Now you could do, say,
FoldList[Expand[#1*#2] &, 1, polys]
Daniel Lichtblau
Wolfram Research