isAction(I,actionList)
Let S be the homogeneous coordinate ring of P^N, and x_0,...,x_N be the coordinates. Let \pi:X\to P^n be a Noether normalization. Note that giving a coherent sheaf F on X is equivalent to giving a sheaf G (=\pi_{*}F) on P^n together with multiplication maps X_i (=\pi_{*} (\cdot x_i)) : G\to G(1) such that X_i X_j = X_j X_i for every i, j, and f(X_0, ..., X_n)=0 for every f \in I. In other words, \{X_0,...,X_N\} \, gives an action which makes G into an O_Xmodule.
This method checks first that actionList is composed of commuting matrices, and then checks whether f(X_0,...,X_n)=0 for each generator f of I.
The following is an example when C is a conic, F=O_C, and \pi\, is a linear projection at the coordinate point [0:0:1]. In the case, the pushforward \pi_{*}F = O_{P^1} \oplus O_{P^1}(1).







The object isAction is a method function.