Algorithms for computing mixed multiplicities, mixed volumes and sectional Milnor numbers
Goel, Kriti ; Roy, Sudeshna ; Verma, J. K.
arXiv, Tome 2019 (2019) no. 0, / Harvested from
We give Macaulay2 algorithms for computing mixed multiplicities of ideals in a polynomial ring. This enables us to find mixed volumes of lattice polytopes and sectional Milnor numbers of a hypersurface with an isolated singularity. The algorithms use the defining equations of the multi-Rees algebra of ideals. We achieve this by generalizing a recent result of David A. Cox, Kuei-Nuan Lin, and Gabriel Sosa in. One can also use a Macaulay2 command `reesIdeal' to calculate the defining equations of the Rees algebra. We compare the computation time of our scripts with the scripts already available.
Publié le : 2019-02-19
Classification:  Mathematics - Commutative Algebra,  Primary 13-04, 13A30, 13H15.} Primary 13-04, 13A30, 13H15.} 13A30, 13H15 
@article{1902.07384,
     author = {Goel, Kriti and Roy, Sudeshna and Verma, J. K.},
     title = {Algorithms for computing mixed multiplicities, mixed volumes and
  sectional Milnor numbers},
     journal = {arXiv},
     volume = {2019},
     number = {0},
     year = {2019},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1902.07384}
}

Goel, Kriti; Roy, Sudeshna; Verma, J. K. Algorithms for computing mixed multiplicities, mixed volumes and
  sectional Milnor numbers. arXiv, Tome 2019 (2019) no. 0, . http://gdmltest.u-ga.fr/item/1902.07384/