## Examples of Tr

from PyM import *

def Tr(x,K='',L=''):
    k = prime_field(K_(x))
    if K=='': K = k
    Cx = conjugates(x,K)
    if L=='': s = 1
    else: s = dim(L,K)//len(Cx)
    return s * sum(Cx)
    
k = Zn(3); u = 1>>k
[K,a] = extension(k,[1,0,1],'a')
[L,b] = extension(K,[1,0,-1,1],'b')

show( Tr(u), Tr(a), Tr(b), Tr(a*b), Tr(b**2), Tr(a*b**2))

show( Tr(u,K), Tr(a,K))

show( Tr(u,k,K), Tr(a,k,K))

show( Tr(u,L=L), Tr(a,L=L), Tr(b,L=L), Tr(a*b,L=L), Tr(b**2,L=L), Tr(a*b**2,L=L))

show( Tr(u,k,L), Tr(a,k,L), Tr(b,k,L), Tr(a*b,k,L), Tr(b**2,k,L), Tr(a*b**2,k,L))

show( Tr(u,K,L), Tr(a,K,L), Tr(b,K,L), Tr(a*b,K,L), Tr(b**2,K,L), Tr(a*b**2,K,L))