RE: Rebuilding polygon from CoefficientList?

• To: mathgroup at smc.vnet.net
• Subject: [mg20191] RE: [mg20164] Rebuilding polygon from CoefficientList?
• From: "Ersek, Ted R" <ErsekTR at navair.navy.mil>
• Date: Tue, 5 Oct 1999 04:04:21 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```Holger Strauss wrote:
------------------------

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).
-----------------------------

My solution is given below.  It should work quite well.

In[1]:=
terms[coeff_,expon_List,vars_List]:=

CoefficientsToPolynomial[coeffs_,vars_]/;
Length[Dimensions[coeffs]]===Length[vars]:=
Plus@@Flatten[MapIndexed[terms[#1,#2-1,vars]&,coeffs,{-1}]]

In[3]:=
cl=CoefficientList[(2+3x-2y+z)^3, {x,y,z}]

Out[3]=
{{{8, 12, 6, 1}, {-24, -24, -6, 0}, {24, 12, 0, 0}, {-8, 0, 0, 0}},
{{36, 36, 9, 0}, {-72, -36, 0, 0}, {36, 0, 0, 0}, {0, 0, 0, 0}},
{{54, 27, 0, 0}, {-54, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}},
{{27, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}}

In[4]:=
poly=CoefficientsToPolynomial[cl,{a,b,c}];
Factor[poly]

Out[4]=
(2 + 3*a - 2*b + c)^3

You might want to read about CoefficientList, MapIndexed at my web page.
The URL is given below.
--------------------

Regards,
Ted Ersek

For Mathematica tips, tricks see
http://www.dot.net.au/~elisha/ersek/Tricks.html

```

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