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### Equivalent to Singular's minpoly?

Hello everyone

In Singular, one can define a ring such as

ring r = (0,i),(x,y),dp;
minpoly = i2+1;


in order to specify that the parameter i verifies i²+1=0. Can I do this, or is it at all needed to work with Q(i), in Sage?

As of now, I have defined a ring

K.<x,y,I>=QQ[]


but I don't know if defining I as a parameter of the ring in Sage is needed, neither how could I define the minimal polynomial for K.

Thank you.

### Equivalent to Singular's minpoly?

Hello everyone

In Singular, one can define a ring such as

ring r = (0,i),(x,y),dp;
minpoly = i2+1;


in order to specify that the parameter i verifies i²+1=0. Can I do this, or is it at all needed to work with Q(i), in Sage?

As of now, I have defined a ring

K.<x,y,I>=QQ[]


but I don't know if defining I as a parameter of the ring in Sage is needed, neither how could I define the minimal polynomial for K.

Thank you.

Edit: I discovered I can simplify each polynomial using .mod(I^2+1) but I guess there has to be a more general solution that applies this to the ring itself.