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Multiplying Polynomials

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  Multiplying Polynomials TBone <TBone@yahoo.com> - 2011-04-02 07:51 +0000
    Re: Multiplying Polynomials Gary Wardall <gwardall@gmail.com> - 2011-04-02 22:06 +0000

#1407 — 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

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#1433

On Apr 2, 2:51 am, TBone <TB...@yahoo.com> wrote:
> 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

Try:

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)]

For:
(1 + dx + d^2 x^2)

do you want:?

(1 + d*x + d^2 x^2)

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