Revision history [back]

You can also explicotely use the fact that the ring of congruences modulo 4 is a field :

sage: R.<x>=Zmod(4)[]
sage: Q.<a>=R.quotient(2*x)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

[ Snip... ]

TypeError: polynomial must have unit leading coefficient

But :

sage: R.<x>=GF(4)[]
sage: Q.<a>=R.quotient(2*x)
sage: Q
Univariate Polynomial Ring in x over Finite Field in z2 of size 2^2

HTH,

EDIT : this answer is FALSE : see John Palmieri's comment. I leave it for the edification of future ask.sagemath.org (per-)users.

You can also ~~explicotely~~ explicitely use the fact that the ring of congruences modulo 4 is a field :

sage: R.<x>=Zmod(4)[]
sage: Q.<a>=R.quotient(2*x)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)

[ Snip... ]

TypeError: polynomial must have unit leading coefficient

But :

sage: R.<x>=GF(4)[]
sage: Q.<a>=R.quotient(2*x)
sage: Q
Univariate Polynomial Ring in x over Finite Field in z2 of size 2^2

HTH,