A field-theory motivated approach to symbolic computer algebra

@article{Peeters2006AFM,
  title={A field-theory motivated approach to symbolic computer algebra},
  author={Kasper Peeters},
  journal={ArXiv},
  year={2006},
  volume={abs/cs/0608005}
}
  • K. Peeters
  • Published 1 August 2006
  • Computer Science
  • ArXiv

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References

SHOWING 1-10 OF 33 REFERENCES

Introducing Cadabra: a symbolic computer algebra system for field theory problems

The present paper is an introduction to the Cadabra program using several concrete problems from gravity, supergravity and quantum field theory.

An algorithm to simplify tensor expressions

Parsing TEX into mathematics

A program is developed that can handle 43% of 10,740 TEX formulas in a well-known table of integrals and it is expected that a higher success rate can be achieved easily.

STL tutorial and reference guide - C++ programming with the standard template library

This second edition of the STL Tutorial and Reference Guide is fully updated to reflect all of the changes made to STL for the final ANSI/ISO C++ language standard and has been expanded with new chapters and appendices.

A system for automatic generation of tensor algorithms

APassivating agent is added to a cracking catalyst by mixing the untreated cracking catalyst with a refractory material which has been previously treated with a passivating agent.

New features of FORM

Version 3 of FORM is introduced. It contains many new features that are inspired by current developments in the methodology of computations in quantum field theory. A number of these features is

Superfield integrals in high dimensions

An efficient, covariant, graph-based method to integrate superfields over fermionic spaces of high dimensionality and has applications to the construction of higher-derivative supergravity actions as well as the computation of string and membrane vertex operator correlators.

GAMMA: A Mathematica package for performing gamma-matrix algebra and Fierz transformations in arbitrary dimensions

We have developed a Mathematica package capable of performing gamma-matrix algebra in arbitrary (integer) dimensions. As an application we can compute Fierz transformations.

MathTensor - a system for doing Tensor analysis by computer

The mathtensor a system for doing tensor analysis by computer that will be your best choice for better reading book that will not spend wasted by reading this website.

Algorithmic simplification of tensor expressions

The canonical form of a single tensor is defined and it is shown that the problem of finding the canonical formof a generic tensor expression reduces to finding thecanon form of single tensors.