HEPAComp - Hermite-Padé Approximant Computation
This software application computes a rational approximant to a function, given by its Taylor expansion at the origin. Then the zeros of the polynomials of the rational approximant are plotted on the complex plane. This is achieved by using two applications, PARI/GP and gnuplot.
Java user interface - requires installation of Oracle Java LTS.
Qt user interface - requires installation of Visual C++ Redistributable for 64-bit.
- Hotfix for HEPAComp v1.8 for cubic equation Ax^3 + Bx^2 + Cx + D = 0, where B=0 and C=0 at the same time. Extract and replace pari/eqn3.gp and pari/eqnCubic.gp with the new files. This fixes the case where A=1, B=0, C=0, D=polynomial of z. Now it works. 6 Jan 2026
- HEPAComp v1.8 | Windows | Linux | Mac | 1 Oct 2025
- HEPAComp v1.7 | Windows | Linux | 7 Jul 2025
- HEPAComp v1.6 | Windows | Linux | 20 Oct 2024
- HEPAComp v1.5 | Windows | Linux | 5 Feb 2023
- HEPAComp v1.4 | Windows | Linux | 24 May 2021
- HEPAComp v1.3 | Windows | Linux | 15 Oct 2020
- HEPAComp v1.2 | Windows | Linux | 30 Jul 2017
- HEPAComp v1.1 | Windows | Linux | 28 May 2017
- HEPAComp v1.0.0 | Windows | Linux | 20 Mar 2016
- HEPAComp v0.9.9 | Windows | Linux | 31 Dec 2014
- HEPAComp v0.9.7 | Windows | 6 Apr 2014
- HPAComp v0.9.5 | Windows | 23 Feb 2014
- HPAComp v0.9 | Windows | 18 Feb 2014
- HPAcomp v0.7 | Windows | 9 Jan 2014
- HPAcomp v0.5 | Windows | 15 Dec 2013
Base functionality
- Input a function that a has a Taylor expansion at the origin in the field funF. Select all options that are desirable.
- Press Start, which invokes PARI/GP, and after completion it creates files with the zeros of the resulting polynomials.
- Press Create plot, which invokes gnuplot, and creates a plot from all sessions from the list. Finally, SumatraPDF displays the PDF result file.
Optional functionality from v1.8
- Press 1 to input polynomials of z (A,B,C,D,E) that represent an equation of the form Ax^4 + Bx^3 + Cx^2 + Dx + E = 0, where x=F(z)=funF. The solution of the equation is an anonymous function of z, internally represented by power series, that is the input for funF.
History of the project
- 2025 Aug/Sep - New functionality: Input of equations quadratic/cubic/quartic instead of explicit function. The solution of the equation is an anonymous function represented by power series, that is the input for the algorithms. New user interface on Qt.
- 2024 Oct - MHEPA Discriminant, known as MHEPAD, with both algorithms.
- 2023 Feb - New functionality: Loading of external vector file instead of explicit function.
- 2021 Apr/May - New Viskovatov algorithm for MHEPA/MHEPAS.
- 2020 May/Oct - New Viskovatov algorithm for PADE/HEPA/HEPAD/HEPAS. Second rewrite of the user interface to allow for panel resize and flexibility of the application.
- 2017 May/Jul - MHEPA Determinant 2x2 and 3x3, known as MHEPAS.
- 2016 Mar - Complete rewrite of the user interface to allow multiple approximations to be displayed in a single plot. HEPA Discriminant and HEPA Determinant 2x2, known as HEPAD/HEPAS.
- 2014 Dec - Non-diagonal versions for PADE/HEPA/MHEPA.
- 2014 Apr - Two-point Pade approximant of F,G, known as TPPA/TPPB.
- 2014 Feb - I found about PARI/GP matsolve function, which is faster than manual matrix solving.
- 2014 Jan - Hermite-Pade approximant of [1,F,G,H], known as MHEPA.
- 2013 Nov/Dec - First version of the software with Pade approximant of F(z) and Hermite-Pade approximant of [1,F,G], known as PADE/HEPA.
- 2013 Feb - Fortran code experiments, until I found about PARI/GP.
- 2012 Sep - Initial idea for the project:
The task is to extend Pade approximant of F(z) with one more function, by using the generalization Hermite-Pade approximant of [A,B,C,...], in which it is equivalent to Hermite-Pade approximant of [-1,F]; therefore our goal is to investigate Hermite-Pade approximant of [1,F,G].
We want to solve Hermite-Pade approximant of [1,F,G] ourselves, instead of using proprietary mathematical software. All software in the package is open-source, and there is no cost for using it.