(* Beispiel 7.4 *)
ω=2
2
n=4
4
m=5
5
p=a0+a1*x+a2*x^2+a3*x^3
2 3 a0 + a1 x + a2 x + a3 x
(* a0=0 a1=1 a2=2 a3=3 *)
(* qlm=x^(2^m)-ω^rev(l/(2^m)) *)
q02=x^4-1 (* =x^2^2-ω^rev(0/4)=x^4-2^rev(00) *)
4 -1 + x
q01=x^2-1 (* =x^2^1-ω^rev(0/2)=x^2-2^rev(00) *)
2 -1 + x
q21=x^2-4 (* =x^2^1-ω^rev(2/2)=x^2-2^rev(01) *)
2 -4 + x
q00=x-1 (* =x^2^0-ω^rev(0/1)=x-2^rev(00) *)
-1 + x
q10=x-4 (* =x^2^0-ω^rev(1/1)=x-2^rev(01) *)
-4 + x
q20=x-2 (* =x^2^0-ω^rev(2/1)=x-2^rev(10) *)
-2 + x
q30=x-3 (* =x^2^0-ω^rev(3/1)=x-2^rev(11) *)
-3 + x
p=a0+a1*x+a2*x^2+a3*x^3
2 3 a0 + a1 x + a2 x + a3 x
r01=PolynomialRemainder[p,q01,x]
a0 + a2 + (a1 + a3) x
r21=PolynomialRemainder[p,q21,x]
a0 + 4 a2 + (a1 + 4 a3) x
r00=PolynomialRemainder[r01,q00,x]
a0 + a1 + a2 + a3
r10=PolynomialRemainder[r01,q10,x]
a0 + 4 a1 + a2 + 4 a3
r20=PolynomialRemainder[r21,q20,x]
a0 + 2 a1 + 4 a2 + 8 a3
r30=PolynomialRemainder[r21,q30,x]
a0 + 3 a1 + 4 a2 + 12 a3
Converted by Mathematica (July 7, 2003)