\\ (C) 2007 Marco Bodrato <http://marco.bodrato.it/>
\\ This code is released under GNU-GPL 2.0 licence.

U = U2*x^2 + U1*x*y + U0*y^2
V = V2*x^2 + V1*x*y + V0*y^2

\\ P(x,y): P0=(0,1); P1=(2,1); P2=(1,1); P3=(-1,1); P4=(1,0)
\\ Evaluation[1]: 5*2 add/sub, 2 shift; 5mul (n)
W0 = U0 + U2         ; W4 = V0 + V2
W3 = W0 - U1         ; W2 = W4 - V1
W0 = W0 + U1         ; W4 = W4 + V1


W1 = W3 * W2         ; W2 = W0 * W4

W0 =(W0 + U2)<<1 - U0; W4 =(W4 + V2)<<1 - V0


W3 = W0 * W4
W0 = U0 * V0         ; W4 = U2 * V2
\\ Interpolation[1,2]: 8 add/sub, 3 shift, 1 Sdiv (2n)
W3 =(W3 - W1)/3
W1 =(W2 - W1)>>1
W2 = W2 - W0
W3 =(W3 - W2)>>1 - W4<<1
W2 = W2 - W1 - W4
W1 = W1 - W3
\\ Recomposition:
W  = W4*x^4+ W3*x^3*y+ W2*x^2*y^2+ W1*x*y^3 + W0*y^4
W == U*V

\\ References: http://bodrato.it/papers/#Toom-Cook
\\ [1] Marco BODRATO,"Towards Optimal Toom-Cook Multiplication
\\ for Univariate and Multivariate Polynomials in Characteristic
\\ 2 and 0"; "WAIFI'07 proceedings" (C.Carlet and B.Sunar, eds.)
\\ LNCS#4547, Springer, Madrid, Spain, June 2007, pp. 116-133.

\\ [2] M. BODRATO, A. ZANONI, "Integer and Polynomial
\\ Multiplication: Towards Optimal Toom-Cook Matrices";
\\ "Proceedings of the ISSAC 2007 conference", pp. 17-24
\\ ACM press, Waterloo, Ontario, Canada, July 29-August 1, 2007