All Questions

Let $L/\mathbb{Q}$ be a finite extension and $f_{1},\dotsc,f_{n}\in L[x_{1},\dotsc,x_{k}]$ be degree $d$ homogeneous polynomials. Is there a way to find homogenous degree $d’$ polynomials $g_{1},\...

Is there any way or algorithm to find generators of an ideal over number field? (A algorithm that can be implemented and not expensive)

What are some good references for Lattice Sieving in Number Field Sieve? Could someone suggest some research papers in this area?(Theoretical and Computational Perspective)

The ring of integers $\mathcal{O}_K$ of a number field $K$ is always isomorphic to some ring of the form $\mathbb{Z}[x_1, ..., x_r]/\mathfrak{p}$, where $\mathfrak{p} \subset \mathbb{Z}[x_1, ..., x_r]$...