mixedMultiplicity (W1, W2)
Given the ideals $I_0,...,I_r$ in a polynomial ring $R$ and the tuple $a = (a_0,...,a_r) \in \mathbb{N}^{r+1}$ such that $I_0$ is primary to the maximal homogeneous ideal of $R$, $I_1,...,I_r$ have positive height and $a_0+...+a_r = dim R -1$, the command computes the mixed multiplicity $e_a$ of the ideals.
|
|
|
|
The function computes the Hilbert polynomial of the graded ring $\oplus I_0^{u_0}I_1^{u_1}...I_r^{u_r}/I_0^{u_0+1}I_1^{u_1}...I_r^{u_r}$ to calculate the mixed multiplicity. This setup enforces $a_0 \neq 0.$ Due to the same reason, to compute the $(a_0+1, a_1,..., a_r)$-th mixed multiplicity, one needs to enter the sequence ${a_0,a_1,...,a_r}$ in the function. The same is illustrated in the following example.
|
|
|
|
|
|
The object mixedMultiplicity is a method function with options.