Solving Polynomial Systems with phcpy

Otto, Jasmine; Forbes, Angus G.; Verschelde, Jan

doi:10.25080/majora-7ddc1dd1-009

Cited by 6 publications

(4 citation statements)

References 33 publications

(35 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Many different implementations of the PHC method can be found in the literature, such as phcpy [133], StringVacua [134], and Bertini [135]. In this work, we have used Paramotopy 22 [110], a highly efficient PHC-based algorithm specially suited for polynomial systems like (B.1) which depend on parameter tuples.…”

Section: Jhep04(2021)149mentioning

confidence: 99%

Towards a complete mass spectrum of type-IIB flux vacua at large complex structure

Sousa

Urkiola

Wachter

2021

J. High Energ. Phys.

View full text Add to dashboard Cite

The large number of moduli fields arising in a generic string theory compactification makes a complete computation of the low energy effective theory infeasible. A common strategy to solve this problem is to consider Calabi-Yau manifolds with discrete symmetries, which effectively reduce the number of moduli and make the computation of the truncated Effective Field Theory possible. In this approach, however, the couplings (e.g., the masses) of the truncated fields are left undetermined. In the present paper we discuss the tree-level mass spectrum of type-IIB flux compactifications at Large Complex Structure, focusing on models with a reduced one-dimensional complex structure sector. We compute the tree-level spectrum for the dilaton and complex structure moduli, including the truncated fields, which can be expressed entirely in terms of the known couplings of the reduced theory. We show that the masses of this set of fields are naturally heavy at vacua consistent with the KKLT construction, and we discuss other phenomenologically interesting scenarios where the spectrum involves fields much lighter than the gravitino. We also derive the probability distribution for the masses on the ensemble of flux vacua, and show that it exhibits universal features independent of the details of the compactification. We check our results on a large sample of flux vacua constructed in an orientifold of the Calabi-Yau $$ {\mathbbm{W}\mathrm{\mathbb{P}}}_{\left[1,1,1,1,4\right]}^4 $$ W ℙ 1 1 1 1 4 4 . Finally, we also discuss the conditions under which the spectrum derived here could arise in more general compactifications.

show abstract

Section: Jhep04(2021)149mentioning

confidence: 99%

Towards a complete mass spectrum of type-IIB flux vacua at large complex structure

Sousa

Urkiola

Wachter

2021

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…The new methods are illustrated with computational experiments on two well known examples in the literature, with ad hoc tools, using test procedures in version 2.4.85 PHCpack [39] (with QDlib [16] and CAMPARY [19] for multiple double arithmetic), version 1.1.1 of phcpy [28], version 1.4 of sympy [20], and version 1.1.0 of mpmath [18], in Python 3.7.3. The computations were done on a CentOS 6.10 Linux computer with 23.4GB of memory and a 12-core Intel Xeon X5690 at 3.47Ghz.…”

Section: Computational Experimentsmentioning

confidence: 99%

Locating the Closest Singularity in a Polynomial Homotopy

Verschelde¹,

Viswanathan²

2022

Preprint

Self Cite

View full text Add to dashboard Cite

A polynomial homotopy is a family of polynomial systems, where the systems in the family depend on one parameter. If for one parameter we know a regular solution, then what is the nearest value of the parameter for which the solution in the polynomial homotopy is singular? Applying the ratio theorem of Fabry on the solution paths defined by the homotopy, extrapolation methods can accurately locate the nearest singularity. Once the radius of convergence is known, then via a transformation of the continuation parameter, the series expansions of the solution curves will have convergence radius equal to one. To compute all coefficients of the series we propose the quaternion Fourier transform.

show abstract

“…As a demonstration to a large scale project, GPRbuild is applied to make share objects for PHCpack, a free and open source software package to solve polynomial systems with homotopy continuation. The python interface to PHCpack is phcpy [7]. Written mainly in Ada, PHCpack contains MixedVol [2] and DEMiCs [6] to count bounds on the number of isolated solutions fast.…”

Section: Building Phcpackmentioning

confidence: 99%

Exporting Ada Software to Python and Julia

Verschelde¹

2022

Preprint

Self Cite

View full text Add to dashboard Cite

The objective is to demonstrate the making of Ada software available to Python and Julia programmers using GPRbuild. GPRbuild is the project manager of the GNAT toolchain. With GPRbuild the making of shared object files is fully automated and the software can be readily used in Python and Julia. The application is the build process of PHCpack, a free and open source software package to solve polynomial systems by homotopy continuation methods, written mainly in Ada, with components in C ++ , available at github at https://github.com/janverschelde/PHCpack. Language Agnostic ComputingThis paper describes interface development from the perspective of an Ada programmer, aimed to export the functionality of a software package to Python [8] and Julia [1] computational environments, available through Jupyter notebooks [5]. The Jupyter notebook is the interface to SageMath [9], a free open source system for mathematical computing.In order to export all functionality the interface passes through C, which may be regarded as a least common multiple of programming languages, as Ada, Python, and Julia share enough common ground to enable language agnostic computing, as Jupyter stands for Julia, Python, R, and many others.

show abstract

Solving Polynomial Systems with phcpy

Cited by 6 publications

References 33 publications

Towards a complete mass spectrum of type-IIB flux vacua at large complex structure

Towards a complete mass spectrum of type-IIB flux vacua at large complex structure

Locating the Closest Singularity in a Polynomial Homotopy

Exporting Ada Software to Python and Julia

Contact Info

Product

Resources

About