FiniteFieldSolve: Exactly Solving Large Linear Systems in High-Energy Theory
arXiv:2311.01671 · doi:10.1016/j.cpc.2024.109171
Abstract
Large linear systems play an important role in high-energy theory, appearing in amplitude bootstraps and during integral reduction. This paper introduces FiniteFieldSolve, a general-purpose toolkit for exactly solving large linear systems over the rationals. The solver interfaces directly with Mathematica, is straightforward to install, and seamlessly replaces Mathematica's native solvers. In testing, FiniteFieldSolve is approximately two orders of magnitude faster than Mathematica and uses an order of magnitude less memory. The package also compares favorably against other public solvers in FiniteFieldSolve's intended use cases. As the name of the package suggests, solutions are obtained via well-known finite field methods. These methods suffer from introducing an inordinate number of modulo (or integer division) operations with respect to different primes. By automatically recompiling itself for each prime, FiniteFieldSolve converts the division operations into much faster combinations of instructions, dramatically improving performance. The technique of compiling the prime can be applied to any finite field solver, where the time savings will be solver dependent. The operation of the package is illustrated through a detailed example of an amplitude bootstrap.
arXiv comment29 pages, v2 updated to match published version
References in corpus (49)
- New Relations for Gauge-Theory Amplitudes
- Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
- Perturbative Quantum Gravity as a Double Copy of Gauge Theory
- Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills
- Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
- Black Hole Binary Dynamics from the Double Copy and Effective Theory
- From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion
- FIRE6: Feynman Integral REduction with Modular Arithmetic
- Integral Reduction with Kira 2.0 and Finite Field Methods
- TikZ-Feynman: Feynman diagrams with TikZ
- A novel approach to integration by parts reduction
- Scattering amplitudes over finite fields and multivariate functional reconstruction
- Scattering Amplitudes and Conservative Binary Dynamics at
- Effective Field Theories from Soft Limits
- Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
- Reconstructing Rational Functions with
- A Periodic Table of Effective Field Theories
- The Ultraviolet Properties of N=4 Supergravity at Four Loops
- Enhanced Ultraviolet Cancellations in N = 5 Supergravity at Four Loop
- Ultraviolet Properties of N = 8 Supergravity at Five Loops
- Absence of Three-Loop Four-Point Divergences in N=4 Supergravity
- Basics of Generalized Unitarity
- Symmetry and Action for Flavor-Kinematics Duality
- The Five-Loop Four-Point Integrand of N=8 Supergravity as a Generalized Double Copy
- Ultraviolet Cancellations in Half-Maximal Supergravity as a Consequence of the Double-Copy Structure
- Vector Effective Field Theories from Soft Limits
- Locality and Unitarity from Singularities and Gauge Invariance
- Kinematic Hopf Algebra for BCJ Numerators in Heavy-Mass Effective Field Theory and Yang-Mills Theory
- Double-Copy Constructions and Unitarity Cuts
- Scattering Amplitudes from Soft Theorems and Infrared Behavior
- Off-Shell Color-Kinematics Duality for Chern-Simons
- AdS Virasoro-Shapiro from single-valued periods
- On Effective Field Theories with Celestial Duals
- AdS Virasoro-Shapiro from dispersive sum rules
- Simple encoding of higher derivative gauge and gravity counterterms
- Amplitudes and Ultraviolet Behavior of N=8 Supergravity
- Overcoming Obstacles to Colour-Kinematics Duality at Two Loops
- UV considerations on scattering amplitudes in a web of theories
- Composing Effective Prediction at Five Points
- Generalizations of the Double-Copy: the KLT Bootstrap
- 10D Super-Yang-Mills Scattering Amplitudes From Its Pure Spinor Action
- New Flavor-Kinematics Dualities and Extensions of Nonlinear Sigma Models
- Double Copy in Higher Derivative Operators of Nambu-Goldstone Bosons
- Non-perturbative Double Copy in Flatland
- The Color-Dual Fates of , , and Supergravity
- Amplitude/Operator Basis in Chiral Perturbation Theory
- Hidden Conformal Invariance of Scalar Effective Field Theories
- Scattering amplitude annihilators
- On the Virasoro-Shapiro Amplitude