Singular

ring r1 = (2^3,a),x,dp;
is generated by a3+a+1 working as maximal ideal and it is a known fact and also stored in Singular CAS,
https://github.com/Singular/Sources/tre ... y/gftables

Dear all:

I am learning using singular , and I run the following script in singular
> ring A1=(2^3,a),x,dp;
> minpoly ;
1*a^3+1*a^1+1*a^0
> ring A2=(2,a),x,dp;
// ** redefining A2 **
> minpoly ;
0


I am confused by it,
I have not specified a monopoly for both A1 and A2 rings, but the A1 have a monopoly already, but not the A2.

Does this means that the A1 have only 1 monopoly so we don't need to specify it?

Shengyu Shen