HELP: how to create a quotient of ZZ[x] or ZZ[x,y]?

[JohnAAbbott]

I wanted to create the quotient ring ZZ[x]/ideal(6,(x+1)*(x+2)*(x+3)) but failed to find the correct approach in Oscar:

P,alpha = polynomial_ring(ZZ, "alpha");
I = ideal(P, [P(6),(alpha+1)*(alpha+2)*(alpha+3)]);  # <--- FAILS
k = quo(P,I);

I also tried another method:

ZZ6,_ = quo(ZZ,6);
P,alpha = polynomial_ring(ZZ6, "alpha");
I = ideal(P, [(alpha+1)*(alpha+2)*(alpha+3)]);  # <--- FAILS

What is the correct way to proceed?

[thofma]

It does not exist.

[thofma]

Or try residue_ring(P, (alpha+1)*(alpha+2)*(alpha+3)) if it is a principal ideal.

[JohnAAbbott]

Thanks: that is a useful short-cut for principal ideals (but my ideal is not principal).

[ederc]

Well, if you define it as multivariate ring it works.

P,(alpha,) = polynomial_ring(ZZ, ["alpha"]);

[JohnAAbbott]

OK, thanks. That works also for me... very odd that it baulks if I use the "univariate" constructor. I suppose that makes it a bug.

[thofma]

Sounds more like a feature request.

[fieker]

or do it in 2 steps as a quotient of Z/6Z[t] - that can be constructed. We don't have ideals in ZZ[x]