An Assessment of the Efficiency of Computer Algebra Systems in the Solution of Scientific Computing Problems

Abstract We discuss new ideas for consideration of loop diagrams and angular integrals in D-dimensions in QCD. In case of loop diagrams, we propose the covariant formalism of expansion of tensorial loop integrals into the orthogonal basis of linear combinations of external momenta. It gives a very simple representation for the final results and is more convenient for calculations on computer algebra systems. In case of angular integrals we demonstrate how to simplify the integration of differential cross sections over polar angles. Also we derive the recursion relations, which allow to reduce all occurring angular integrals to a short set of basic scalar integrals. All order ε-expansion is given for all angular integrals with up to two denominators based on the expansion of the basic integrals and using recursion relations. A geometric picture for partial fractioning is developed which provides a new rotational invariant algorithm to reduce the number of denominators.

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Computeralgebra - eine Säule* des Wissenschaftlichen Rechnens / Computer-Algebra - a Part of the Foundation of Scientific Computing

it - Information Technology ◽

10.1524/itit.1995.37.6.5 ◽

1995 ◽

Vol 37 (6) ◽

Author(s):

J. Grabmeier

Keyword(s):

Computer Algebra ◽

Scientific Computing

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The Fischer-Clifford Matrices and Character Table of a Maximal Subgroup of Fi24

Algebra Colloquium ◽

10.1142/s1005386710000386 ◽

2010 ◽

Vol 17 (03) ◽

pp. 389-414 ◽

Cited By ~ 4

Author(s):

Faryad Ali ◽

Jamshid Moori

Keyword(s):

Automorphism Group ◽

Conjugacy Class ◽

Maximal Subgroup ◽

Computer Algebra ◽

Character Table ◽

Computer Algebra Systems ◽

Split Extension ◽

Sporadic Group ◽

Local Subgroup ◽

Fischer Group

The Fischer group [Formula: see text] is the largest 3-transposition sporadic group of order 2510411418381323442585600 = 222.316.52.73.11.13.17.23.29. It is generated by a conjugacy class of 306936 transpositions. Wilson [15] completely determined all the maximal 3-local subgroups of Fi24. In the present paper, we determine the Fischer-Clifford matrices and hence compute the character table of the non-split extension 37· (O7(3):2), which is a maximal 3-local subgroup of the automorphism group Fi24 of index 125168046080 using the technique of Fischer-Clifford matrices. Most of the calculations are carried out using the computer algebra systems GAP and MAGMA.

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