Given a list $\{v_1,...,v_d\}$ of vectors in $\mathbb Z^n$ this function computes the toric ring $R/I$ where $R$ is the polynomial ring $\mathbb{Q}[x_1,\dots,x_d]$ with $x_i$ having degree $v_i$ and $I$ is the associated toric ideal. In particular $I$ is the kernel of the map $R \to \mathbb{Q}[y_1,\dots,y_n]$ defined by $x_i \mapsto \mathbb y^{v_i}$.
i1 : L = {{2,0},{1,1},{0,2}};
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i2 : X = affineToricRing L; -- The singular quadric in A^3 |
i3 : I = ideal X
2
o3 = ideal(x - x x )
1 0 2
o3 : Ideal of QQ[x ..x ]
0 2
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i4 : hilbertSeries I
2 2
1 - T T
0 1
o4 = --------------------------
2 2
(1 - T )(1 - T T )(1 - T )
1 0 1 0
o4 : Expression of class Divide
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The object affineToricRing is a method function.