1 | initial version |
You have (X+1)^2k = X^2k + 1 + 2(...) so ( X+1 )^2k = 0 mod ( X^2k +1 , 2 )
In other words (X^n+1) is nilpotent in any ring F2[X]/(X^n+1) where n is even, so it remains to concentrate on odd values of n
try something like for i in range(2,10): A=R.quo(x^(2*i+1)+1);j=2 while A((x+1)^j)<>A(x+1): j=j+1
2 | No.2 Revision |
You have (X+1)^2k = X^2k + 1 + 2(...) so ( X+1 )^2k = 0 mod ( X^2k +1 , 2 )
In other words (X^n+1) is nilpotent in any ring F2[X]/(X^n+1) where n is even, so it remains to concentrate on odd values of n
try something like
like this (N rather small...)
for i in range(2,10):
range(2,10):
A=R.quo(x^(2*i+1)+1);j=2
while A((x+1)^j)<>A(x+1):
A=R.quo(x^(2*i+1)+1);j=2
while A((x+1)^j)<>A(x+1):
j=j+1j=j+1
3 | No.3 Revision |
You have (X+1)^2k = X^2k + 1 + 2(...) so ( X+1 )^2k = 0 mod ( X^2k +1 , 2 )
In other words (X^n+1) is nilpotent in any ring F2[X]/(X^n+1) where n is even, so it remains to concentrate on odd values of n
try something like this (N rather small...)
for i in range(2,10):
4 | No.4 Revision |
You have (X+1)^2k = X^2k + 1 + 2(...) so ( X+1 )^2k = 0 mod ( X^2k +1 , 2 )
In other words (X^n+1) is nilpotent in any ring F2[X]/(X^n+1) where when n is even, so it remains to concentrate on odd values of n
try something like this (N rather small...)
for i in range(2,10):
A=R.quo(x^(2*i+1)+1);j=2 while A((x+1)^j)<>A(x+1): j=j+1
5 | No.5 Revision |
You have (X+1)^2k = X^2k + 1 + 2(...) so ( X+1 )^2k = 0 mod ( X^2k +1 , 2 )
In other words (X^n+1) (X+1)^n is nilpotent in any ring F2[X]/(X^n+1) when n is even, so it remains to concentrate on odd values of n
try something like this (N rather small...)
for i in range(2,10):
A=R.quo(x^(2*i+1)+1);j=2 while A((x+1)^j)<>A(x+1): j=j+1