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CoReLG

Computing with real Lie algebras

Version 1.52

30 September 2019

Heiko Dietrich
Email: heiko.dietrich@monash.edu
Homepage: http://users.monash.edu.au/~heikod/
Address:
School of Mathematics
Monash University
Wellington Road 1
VIC 3800, Melbourne, Australia

Paolo Faccin
Email: paolofaccin86@gmail.com
Address:
Dipartimento di Matematica
Via Sommarive 14
I-38050 Povo (Trento), Italy

Willem de Graaf
Email: degraaf@science.unitn.it
Homepage: http://www.science.unitn.it/~degraaf
Address:
Dipartimento di Matematica
Via Sommarive 14
I-38050 Povo (Trento), Italy

Abstract

This package provides functions for computing with various aspects of the theory of real simple Lie algebras.

Copyright

Acknowledgements

The research leading to this package has received funding from the European Union's Seventh Framework Program FP7/2007-2013 under grant agreement no 271712, and from the Australian Research Council, grantor code DE140100088 and DP190100317.

1 Introduction

1.1 The simple real Lie algebras

1.2 Cartan subalgebras and more

1.3 Nilpotent orbits

1.4 On base fields

2 The field SqrtField

2.1 Definition of the field

2.1-1 SqrtFieldIsGaussRat

2.2 Construction of elements

  2.2-1 Sqroot
  2.2-2 CoefficientsOfSqrtFieldElt
  2.2-3 SqrtFieldEltByCoefficients
  2.2-4 SqrtFieldEltToCyclotomic
  2.2-5 SqrtFieldEltByCyclotomic

2.3 Basic operations

  2.3-1 SqrtFieldMakeRational
  2.3-2 SqrtFieldPolynomialToRationalPolynomial
  2.3-3 SqrtFieldRationalPolynomialToSqrtFieldPolynomial
  2.3-4 Factors