Intersection (and quotient) of ideals in a single variable polynomial ring

[Luis Garcia-Puente]

The following code does not run in a Jupyter notebook inside cocalc 

R.<x> = PolynomialRing(QQ) 

f = x^3+6*x^2+12*x+8;

g = x^2+x-2;

I = R.ideal([f]);

J = R.ideal([g]);

I.intersection(J)

This produces an error that ends with the line:

AttributeError: 'Ideal_1poly_field' object has no attribute 'intersection'

Similarly,  we get an error in the following line

I.quotient(J)

AttributeError: 'Ideal_1poly_field' object has no attribute 'quotient'

However, if we use the ring on 2 variables

R.<x,y> = PolynomialRing(QQ) 

all computations execute.

[William]

  Hi Luis,

It's actually not a bug, but a missing feature.   The problem is that in the first case R is a *univariate* polynomial ring, and in the second case it is a multivariate polynomial ring and different functionality is available in each case.  Read the docs for PolynomialRing (via PolynomialRing?) for more details.  To fix your code, just use the implementation="singular" option to get a multivariate polynomial ring in 1 variable:

     R.<x> = PolynomialRing(QQ, implementation="singular")

-William

[William]

Link:  https://share.cocalc.com/share/df81e09e5b8f16f28b3a2e818dcdd4560e7818ae/support/2020-08-18-mpoly.ipynb?viewer=share