## 24 Citations

### Algorithmic transformation of multi-loop Feynman integrals to a canonical basis

- Mathematics, Physics
- 2018

The evaluation of multi-loop Feynman integrals is one of the main challenges in the computation of precise theoretical predictions for the cross sections measured at the LHC. In recent years, the…

### Transforming differential equations of multi-loop Feynman integrals into canonical form

- MathematicsJournal of High Energy Physics
- 2017

The method of differential equations has been proven to be a powerful tool for the computation of multi-loop Feynman integrals appearing in quantum field theory. It has been observed that in many…

### Transforming differential equations of multi-loop Feynman integrals into canonical form

- Physics
- 2016

A bstractThe method of differential equations has been proven to be a powerful tool for the computation of multi-loop Feynman integrals appearing in quantum field theory. It has been observed that in…

### Reduction of Feynman integrals in the parametric representation

- PhysicsJournal of High Energy Physics
- 2020

In this paper, the reduction of Feynman integrals in the parametric representation is considered. This method proves to be more efficient than the integration-by-part (IBP) method in the momentum…

### Reduction of Feynman integrals in the parametric representation

- PhysicsJournal of High Energy Physics
- 2020

In this paper, the reduction of Feynman integrals in the parametric representation is considered. This method proves to be more efficient than the integration-by-part (IBP) method in the momentum…

### Symmetries of Feynman integrals and the Integration By Parts method

- Mathematics, Physics
- 2015

Integration By Parts (IBP) is an important method for computing Feynman integrals. This work describes a formulation of the theory involving a set of differential equations in parameter space, and…

### Results and techniques for higher order calculations within the gradient-flow formalism

- PhysicsJournal of High Energy Physics
- 2019

A bstractWe describe in detail the implementation of a systematic perturbative approach to observables in the QCD gradient-flow formalism. This includes a collection of all relevant Feynman rules of…

### Fully massive vacuum integrals at 5 loops

- Physics
- 2015

Massive vacuum integrals with a single mass scale are a class of Feynman integrals that appear in many precision calculations within the Standard Model of particle physics and have been calculated to…

## 29 References

### Automatic integral reduction for higher order perturbative calculations

- Computer Science
- 2004

This paper implements the algorithm for the reduction of large systems of integrals to master integrals in MAPLE and develops two new features which keep the size of intermediate expressions relatively small throughout the calculation.

### HIGH-PRECISION CALCULATION OF MULTILOOP FEYNMAN INTEGRALS BY DIFFERENCE EQUATIONS

- Computer Science
- 2000

### Algorithm FIRE—Feynman Integral REduction

- Computer Science
- 2008

The recently developed algorithm FIRE performs the reduction of Feynman integrals to master integrals. It is based on a number of strategies, such as applying the Laporta algorithm, the s-bases…

### Critical points and number of master integrals

- Mathematics
- 2013

A bstractWe consider the question about the number of master integrals for a multiloop Feynman diagram. We show that, for a given set of denominators, this number is totally determined by the…

### FIRE4, LiteRed and accompanying tools to solve integration by parts relations

- Computer ScienceComput. Phys. Commun.
- 2013

### The Exact Solution of Systems of Linear Equations with Polynomial Coefficients

- Computer Science, MathematicsJACM
- 1973

An algorithm for computing exactly a general solution to a system of linear equations with coefficients that are polynomials over the integers by applying interpolation and the Chinese Remainder Theorem is presented.