Paramotopy swMATH ID: 8781 Software Authors: Daniel Bates; D. Brake; M. Niemerg Description: Paramotopy: Software for parameter homotopies. It has long been known in the numerical algebraic geometry community that parameter homotopies provide a powerful tool for solving parametrized polynomial systems at a large number of parameter values. Paramotopy is a new software package dedicated to the efficient, parallel processing of a large number of parameter homotopies. Paramotopy makes use of Bertini’s implementation of user-defined homotopies, paired with Boost and other libraries for the efficient handling of large numbers of parameter values and solutions. It was initially developed to solve problems from redundant kinematics - see joint work with D. Brake (North Carolina State University), A. Maciejewski (Colorado State University), and V. Putkaradze (University of Alberta). This talk will include a brief introduction to parameter homotopies, a short tutorial on Paramotopy, and details about an application from biochemistry. In particular, the number of equilibria of a biochemical reaction network depends on the choice of a number of parameter values. With D. Brake, J. Gunawardena (Harvard Medical School), B. Gyori (National University of Singapore), and K-M Nam (Swarthmore College), we have devised a number of methods for better understanding the geography of the parameter space for such problems, with Paramotopy as a key ingredient. Homepage: http://www.paramotopy.com/ Related Software: Bertini; PHCpack; HOM4PS; alphaCertified; NumericalAlgebraicGeometry; Macaulay2; MATCONT; Bertini_real; SageMath; PyTorch; Scikit; MESSI; ProjectionCAD; REDLOG; RegularChains; QEPCAD; Maple; 3BA; ATAME; Axl Cited in: 13 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Paramotopy: parameter homotopies in parallel. Zbl 1396.65179Bates, Dan; Brake, Danielle; Niemerg, Matt 2018 all top 5 Cited by 42 Authors 5 Bates, Daniel J. 5 Niemerg, Matthew E. 2 Davenport, James Harold 2 Hauenstein, Jonathan D. 2 Mehta, Dhagash 2 Newell, Andrew J. 1 Bates, Dan 1 Bernal, Edgar A. 1 Bradford, Russell J. 1 Brake, Daniel A. 1 Brake, Danielle A. 1 Cicoli, Michele 1 Davis, Brent R. 1 Eklund, David 1 England, Matthew 1 Errami, Hassan 1 Gerdt, Vladimir Petrovich 1 Griffin, Zachary A. 1 Grigor’ev, Dmitriĭ Yur’evich 1 Hao, Wenrui 1 He, Yang-Hui Evariste 1 Hoyt, Charles Tapley 1 Kauers, Manuel 1 Klevers, Denis 1 Košta, Marek 1 Krippendorf, Sven 1 Labahn, George 1 Maciejewski, Anthony A. 1 Mayrhofer, Christoph 1 Peterson, Chris 1 Putkaradze, Vakhtang 1 Quevedo Rodriguez, Fernando 1 Radulescu, Ovidiu 1 Regan, Margaret H. 1 Rummel, Markus 1 Sturm, Thomas 1 Tang, Tingting 1 Urban, Josef 1 Valandro, Roberto 1 Valeanu, Alexandru 1 Weber, Andreas Günter 1 Zheng, Chunyue all top 5 Cited in 8 Serials 3 Journal of Symbolic Computation 2 Journal of High Energy Physics 1 Applied Mathematics and Computation 1 Journal of Scientific Computing 1 Numerical Algorithms 1 Advances in Geometry 1 Lecture Notes in Computer Science 1 Mathematics in Computer Science all top 5 Cited in 10 Fields 9 Numerical analysis (65-XX) 5 Computer science (68-XX) 4 Commutative algebra (13-XX) 4 Algebraic geometry (14-XX) 1 General and overarching topics; collections (00-XX) 1 Mechanics of particles and systems (70-XX) 1 Optics, electromagnetic theory (78-XX) 1 Quantum theory (81-XX) 1 Relativity and gravitational theory (83-XX) 1 Biology and other natural sciences (92-XX) Citations by Year