The MultigradedImplicitization package provides methods for computing the maximal $\mathbb{Z}^k$ grading in which the kernel of a polynomial map $F$ is homogeneous and exploiting it to find generators of $\ker(F)$. This package is particularly useful for problems from algebraic statistics which often involve highly structured maps $F$ which are often naturally homogeneous in a larger multigrading than the standard $\mathbb{Z}$-multigrading given by total degree. For more information on this approach see the following:
References:
[1] Cummings, J., & Hollering , B. (2023). Computing Implicitizations of Multi-Graded Polynomial Maps. arXiv preprint arXiv:2311.07678.
[2] Cummings, J., & Hauenstein, J. (2023). Multi-graded Macaulay Dual Spaces. arXiv preprint arXiv:2310.11587.
[3] Cummings, J., Hollering, B., & Manon, C. (2024). Invariants for level-1 phylogenetic networks under the cavendar-farris-neyman model. Advances in Applied Mathematics, 153, 102633.
This documentation describes version 1.1 of MultigradedImplicitization, released May 15, 2025.
If you have used this package in your research, please cite it as follows:
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The object MultigradedImplicitization is a package, defined in MultigradedImplicitization.m2.
The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/MultigradedImplicitization.m2:413:0.