       Re: Recombining CoefficientList

• To: mathgroup at smc.vnet.net
• Subject: [mg2531] Re: [mg2501] Recombining CoefficientList
• From: Allan Hayes <hay at haystack.demon.co.uk>
• Date: Thu, 16 Nov 1995 01:46:38 -0500

```sherod at boussinesq.Colorado.EDU (Scott Herod)
in mathgroup at smc.vnet.net
writes

> CoefficientList[poly, {x1,x2,...,xn}] returns an array of
> coefficients of the various powers of the xi in poly.  Has someone
> got a code segment to recreate poly from the list of xi and the
>output?

Here is a slight modification of tmj  5.3 p24 (In[] and Out[])

ToPolynomial[cl_, vars_] :=
Plus@@Flatten[
MapIndexed[#1 Times@@(vars^(#2-1))&,cl,{Depth[cl]-1}]
]

Example:

poly = a x^3 + b x^4 y + c x y + d y^2 + e

3              4        2
e + a x  + c x y + b x  y + d y

cl = CoefficientList[poly, {x,y}]

{{e, 0, d}, {0, c, 0}, {}, {a, 0, 0}, {0, b, 0}}

ToPolynomial[cl, {x,y}]

3              4        2
e + a x  + c x y + b x  y + d y

Allan Hayes
hay at haystack.demon.co.uk

```

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