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# Floating-point numbers

Version 1.0.3

15/02/2023

Integration of mpfr, mpfi, mpc, fplll and cxsc in GAP

Laurent Bartholdi
Email: laurent.bartholdi@gmail.com
Homepage: https://www.math.uni-sb.de/ag/bartholdi/

Address:
FR Mathematik
D-66041 Saarbrücken
Germany

### Abstract

This document describes the package Float, which implements in GAP arbitrary-precision floating-point numbers.

The computer algebra system GAP is available at https://gap-system.org.

This documentation for Float is available at https://www.gap-system.org/Manuals/pkg/float-1.0.3/doc/manual.pdf in PDF format, and may be accessed online at https://gap-packages.github.io/float/.

The latest release of the package may be downloaded as https://github.com/gap-packages/float/releases/download/v1.0.3/float-1.0.3.tar.gz (tar, gzipped). The latest repository version (possibly unstable) may be downloaded as https://github.com/gap-packages/float/tarball/master (tar, gzipped), https://github.com/gap-packages/float.git (git repository), https://packages.debian.org/search?keywords=gap-float&searchon=names&suite=all§ion=all (debian package), or explored at https://github.com/gap-packages/float/tree/master/.

For comments or questions on Float please contact the author.

### Copyright

© 2011-2021 by Laurent Bartholdi

### Acknowledgements

Part of this work was supported by the "Swiss National Fund for Scientific Research (SNF)", the "German National Science Foundation (DFG)", and the Courant Research Centre "Higher Order Structures" of the University of Göttingen.

### Contents

1 Licensing
2 Float package
2.1 A sample run
3 Polynomials
3.1 The Floats pseudo-field
3.1-1 FLOAT_PSEUDOFIELD
3.2 Roots of polynomials
3.3 Finding integer relations
3.3-1 PSLQ
3.4 LLL lattice reduction
4 Implemented packages
4.1 MPFR
4.1-1 IsMPFRFloat
4.2 MPFI
4.2-1 IsMPFIFloat
4.3 MPC
4.3-1 IsMPCFloat
4.4 CXSC
4.4-1 IsCXSCReal
4.5 FPLLL
4.5-1 FPLLLReducedBasis
4.5-2 FPLLLShortestVector
References
Index
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