       Re: Rebuilding polygon from CoefficientList?

• To: mathgroup at smc.vnet.net
• Subject: [mg20193] Re: [mg20164] Rebuilding polygon from CoefficientList?
• From: BobHanlon at aol.com
• Date: Tue, 5 Oct 1999 04:04:23 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```Holger,

reconstructPolynomial[coefMatrix_List, vars_List] :=
Module[{maxPwrs = Dimensions[coefMatrix] - 1, factors, k},
factors =
Table[#[]^k, {k, 0, #[]}] & /@ Transpose[{vars, maxPwrs}];
Flatten[coefMatrix].Flatten[Outer[Times, Apply[Sequence, factors]]]];

poly =  a*x^3*y + b*x^2*y^2*z + c*x*y^3*z^2 + d*z^2 + e*t*x*y*z;

var = {x, y, z};

coef = CoefficientList[poly, var];

reconstructPolynomial[coef, var] == poly

True

var = {t, x, y, z};

coef = CoefficientList[poly, var];

reconstructPolynomial[coef, var] == poly

True

Bob Hanlon

In a message dated 10/4/1999 3:10:53 AM, strauss at ika.ruhr-uni-bochum.de
writes:

>I have a mixed polynomial poly in several variables vars.
>
>cl = CoefficientList[poly, vars]
>
>gives a multi-dimensional matrix of coefficients.
>
>Can anyone help with an algorithm/expression that
>re-constructs the original poly given cl and vars?
>(In practice, I'd like to manipulate the coefficients before
>reconstructing the polynomial; otherwise this wouldn't
>make sense).
>The algorithm must be able to handle any number of vars.
>I've found a solutions for a small and fixed number of vars
>using some ugly nested For loops. However, I suppose
>that there must be a more efficient solution using some cute
>matrix operations.
>

```

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