Each of these functions creates a new ring of the form $R[X_0,\ldots, X_r]$ or $k[X_0,\ldots, X_r]$, where $R$ is the ring of the input ideal and $k$ is the coefficient ring of the output ideal. This option allows the user to change the base names of the new variables in this ring. The default variable is X.
i1 : S = QQ[x_0..x_3] o1 = S o1 : PolynomialRing |
i2 : C = trim monomialCurveIdeal(S,{2,3,5}) 3 2 3 2 o2 = ideal (x x - x x , x - x x , x - x x ) 1 2 0 3 2 1 3 1 0 2 o2 : Ideal of S |
i3 : multiReesIdeal ({C}, VariableBaseName => "T") 2 2 3 2 3 2 o3 = ideal (x T - x T - x T , x T - x T - x T , (x - x x )T + (- x + x x )T ) 2 1 1 2 3 3 1 1 0 2 2 3 1 0 2 2 2 1 3 3 o3 : Ideal of S[T ..T ] 1 3 |
i4 : homIdealPolytope ({(0,1),(1,0),(2,1),(1,2)}, VariableBaseName => "T") 2 2 2 2 o4 = ideal (T T , T T , T T , T T ) 1 2 1 2 1 3 2 3 o4 : Ideal of QQ[T ..T ] 1 3 |