Sparse Polynomial Square

Author

Eric W. Weisstein
November 11, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Algebra/SparsePolynomialSquare.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/SparsePolynomialSquare.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Example

Rényi

p=Expand[(1+2x-2(x^2)+4(x^3)+4(x^4))(1+2(x^4)-2(x^8)+4(x^12)-10(x^16)+28(x^20)-84(x^24))]

Length/@{p,Expand[p^2]}

Choudhry

p=Expand[((x^2)+2x-2)((x^15)+4(x^12)-8(x^9)+32(x^6)-160(x^3)+896)]

Length/@{p,Expand[p^2]}

Coppersmith and Davenport (Subscript[P, 12])(x) = Trott, p. 276

p=Expand[(1+2x-2(x^2)+4(x^3)-10(x^4)+50(x^5)+125(x^6))(1-110(x^6))]

Length/@{p,Expand[p^2]}

p[α_]:=Expand[(1+2x-2(x^2)+4(x^3)-10(x^4)+50(x^5)+125(x^6))(1+α (x^6))]

15625/{-110,-253,-55/2}

Map[Length,({p[#],Expand[p[#]^2]}&/@{-110,-253,-55/2,-(3125/22),-(15625/253),-(6250/11)}),{2}]