giac(2)
R=PolynomialRing(QQ,x,5)
t=sum(R.gens())
gt=giac(str(t))
w=walltime();cpug=giac.cputime();walltime(w)
w=walltime();cpug=giac.cputime();ez=(gt^15).normal();giac.cputime()-cpug;walltime(w)
w=walltime();cpus=cputime();z=(t^15);cputime()-cpus;walltime(w)


R=PolynomialRing(QQ,x,3)
t=sum(R.gens())
n=17;
w=walltime();cpug=giac.cputime();ez=(giac(t+1)^n+1).normal();giac.cputime()-cpug;walltime(w)
w=walltime();cpus=cputime();z=((t+1)^n+1);cputime()-cpus;walltime(w)
w=walltime();cpug=giac.cputime();f1=(ez*(ez+1)).normal();giac.cputime()-cpug;walltime(w)
w=walltime();cpus=cputime();f2=(z*(z+1));cputime()-cpus;walltime(w)
w=walltime();cpug=giac.cputime();l1=f1.factor();giac.cputime()-cpug;walltime(w)
w=walltime();cpus=cputime();l2=f2.factor();cputime()-cpus;walltime(w)



R=PolynomialRing(QQ,x,4)
t=sum(R.gens())
n=17;
w=walltime();cpug=giac.cputime();ez=(giac(t+1)^n+1).normal();giac.cputime()-cpug;walltime(w)
w=walltime();cpus=cputime();z=((t+1)^n+1);cputime()-cpus;walltime(w)
w=walltime();cpug=giac.cputime();f1=(ez*(ez+1)).normal();giac.cputime()-cpug;walltime(w)
w=walltime();cpus=cputime();f2=(z*(z+1));cputime()-cpus;walltime(w)




n=10;
w=walltime();cpug=giac.cputime();ez=(giac(t+1)^n+1).normal();giac.cputime()-cpug;walltime(w)
w=walltime();cpus=cputime();z=((t+1)^n+1);cputime()-cpus;walltime(w)
w=walltime();cpug=giac.cputime();f1=(ez*(ez+1)).normal();giac.cputime()-cpug;walltime(w)
w=walltime();cpus=cputime();f2=(z*(z+1));cputime()-cpus;walltime(w)
w=walltime();cpug=giac.cputime();l1=f1.factor();giac.cputime()-cpug;walltime(w)
w=walltime();cpus=cputime();l2=f2.factor();cputime()-cpus;walltime(w)



R=PolynomialRing(QQ,x,5)
t=sum(R.gens())
n=10;
w=walltime();cpug=giac.cputime();ez=(giac(t+2)^n+3).normal();giac.cputime()-cpug;walltime(w)
w=walltime();cpus=cputime();z=((t+2)^n+3);cputime()-cpus;walltime(w)
w=walltime();cpug=giac.cputime();f1=(ez*(ez+1)).normal();giac.cputime()-cpug;walltime(w)
w=walltime();cpus=cputime();f2=(z*(z+1));cputime()-cpus;walltime(w)

w=walltime();cpug=giac.cputime();l1=f1.factors();giac.cputime()-cpug;walltime(w)
w=walltime();cpus=cputime();l2=f2.factor();cputime()-cpus;walltime(w)