An Implementation of Exact Mixed Volume Computation

TY - GEN

T1 - An Implementation of Exact Mixed Volume Computation

AU - Jensen, Anders Nedergaard

N1 - Conference code: 5

PY - 2016

Y1 - 2016

N2 - Mixed volumes of lattice polytopes play a central role in numerical and tropical algebraic geometry. We present an implementation of a new algorithm for their computation based on tropical homotopy continuation, which is a combinatorial procedure using ideas from numerical algebraic geometry. While the mathematical aspects of the algorithm are presented elsewhere, here we mainly address technical details of the implementation, in particular how it was made fast and reliable. The implementation is distributed as part of the library gfanlib.

AB - Mixed volumes of lattice polytopes play a central role in numerical and tropical algebraic geometry. We present an implementation of a new algorithm for their computation based on tropical homotopy continuation, which is a combinatorial procedure using ideas from numerical algebraic geometry. While the mathematical aspects of the algorithm are presented elsewhere, here we mainly address technical details of the implementation, in particular how it was made fast and reliable. The implementation is distributed as part of the library gfanlib.

KW - Mixed volumes

KW - Numerical algebraic geometry

KW - Tropical geometry

UR - http://www.scopus.com/inward/record.url?scp=84978792894&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-42432-3_25

DO - 10.1007/978-3-319-42432-3_25

M3 - Article in proceedings

SN - 978-3-319-42431-6

VL - 9725

T3 - Lecture Notes in Computer Science (LNCS)

SP - 198

EP - 205

BT - Mathematical Software - 5th International Conference, ICMS 2016, Proceedings

A2 - Greuel, Gert-Martin

A2 - Koch, Thorsten

A2 - Paule, Peter

A2 - Sommese, Andrew

PB - Springer

T2 - International Congress on Mathematical Software

Y2 - 11 July 2016 through 14 July 2016

ER -