P Adic Groebner Fans

Let $f=2x+3y+z \in \mathbb{Q}[x,y,z]$.

• Compute $\mathrm{in}_{(0,0,0)}(f)$ when $\mathbb{Q}$ has the $p$-adic valuation for all primes $p$.
• Draw the Gröbner complex of $I=\langle f \rangle$ when $\mathbb{Q}$ has the 7-adic evaluation. Repeat for all other primes $p$ (including $p=2$ and $p=3$).