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SqrtFinField := function(x,z,q)
local T,c,e,i,k,me,mu,s,sigma,t,tau,xl,xs,xsm1d2,xsp1d2,y;
e := One(x);
me := -e;
s := q-1;
T := -1;
while IsEvenInt(s) do
s := s / 2;
T := T + 1;
od;
Print("T=",T,"\n");
Print("s=",s,"\n");
c := [z^s];
for i in [1..T] do Add(c,c[i]^2); od;
Print(c,"\n");
xsm1d2 := x^((s-1)/2);
Print("x^((s-1)/2)",xsm1d2,"\n");
xsp1d2 := xsm1d2*x;
Print("x^((s+1)/2)",xsp1d2,"\n");
xs := xsm1d2*xsp1d2;
Print("x^s=",xs,"\n");
if xs = e then return xsp1d2; fi;
xl := [xs];
y := xs;
t := 0;
while y <> me do
y := y^2;
Add(xl,y);
t := t + 1;
od;
if t = T then return fail; fi;
tau := [T-1];
mu := 1;
for k in [1..t] do
sigma := xl[t-k+1];
for i in [0..mu-1] do
sigma := sigma * c[tau[i+1]+1];
od;
Print("sigma=",sigma,"\n");
tau := tau - 1; # increase all tau values
if sigma = me then
Add(tau,T-1);
mu := mu + 1;
fi;
od;
sigma := xsp1d2;
for i in [0..mu-1] do
sigma := sigma * c[tau[i+1]+1];
od;
return sigma;
end;
[ Dauer der Verarbeitung: 0.34 Sekunden
(vorverarbeitet)
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