Software

GluCat: Clifford algebra templates

The Australian National University
Dr. Paul Leopardi (Associated with)
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ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rfr_id=info%3Asid%2FANDS&rft_id=info:doi10.25911/5fc71f84e5c01&rft.title=GluCat: Clifford algebra templates&rft.identifier=10.25911/5fc71f84e5c01&rft.publisher=The Australian National University&rft.description=GluCat is a library of C++ template classes for calculations with the universal Clifford algebras over the real field. The dimension of the algebras you can use is limited only by computer word size. Unlike some software packages for Clifford algebras, the maximum signature is fixed by default or by user defined template parameter values, and calculations are performed in the appropriate subalgebra. GluCat classes are meant to be used as numeric classes with other template libraries. To do this, GluCat classes need to look and behave like floating point numeric types such as float and double. The GluCat classes do this by providing a definition for std::numeric_limits, most or all the expected operators like +, -, *, /, and functions like sqrt(). In use with other template libraries, you will need to look out for the differences between GluCat classes and floating point numeric types. Two key differences are that Clifford algebras do not have a total ordering, and that multiplication in Clifford algebras is not necessarily commutative. A third difference is that not all non-zero elements of a Clifford algebra have a multiplicative inverse. PyClical is a Python extension module that is designed to make it easy for you to use Python to perform computations in Clifford algebras, and to implement algorithms and programs that use these computations. The syntax and semantics of the main index_set and clifford classes in PyClical is designed to be as similar as possible to that of the GluCat template classes index_set and matrix_multi, so that you should be able to use PyClical to teach yourself how to use calculations in Clifford algebras, and then transfer that knowledge to your ability to use GluCat template classes in C++. &rft.creator=Anonymous&rft.date=2020&rft_rights=GNU LESSER GENERAL PUBLIC LICENSE Version 3, 29 June 2007 https://github.com/penguian/glucat/blob/master/COPYING https://www.gnu.org/licenses/lgpl-3.0.en.html&rft_rights=GNU LESSER GENERAL PUBLIC LICENSE Version 3, 29 June 2007 http://www.gnu.org/licenses/gpl.html&rft_subject=Algebra and Number Theory&rft_subject=MATHEMATICAL SCIENCES&rft_subject=PURE MATHEMATICS&rft_subject=Algebraic Structures in Mathematical Physics&rft_subject=MATHEMATICAL PHYSICS&rft_subject=Numerical Computation&rft_subject=INFORMATION AND COMPUTING SCIENCES&rft_subject=COMPUTATION THEORY AND MATHEMATICS&rft_subject=Clifford algebras, numerical linear algebra&rft.type=Computer Program&rft.language=English Access the software

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GNU LESSER GENERAL PUBLIC LICENSE Version 3, 29 June 2007

http://www.gnu.org/licenses/gpl.html

GNU LESSER GENERAL PUBLIC LICENSE Version 3, 29 June 2007
https://github.com/penguian/glucat/blob/master/COPYING
https://www.gnu.org/licenses/lgpl-3.0.en.html

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Contact Information

Postal Address:
56 Mills Road, Leonard Huxley Building The Australian National University ACT 2600 Australia

Street Address:
Ph: 0405197804

paul.leopardi@anu.edu.au

Full description

GluCat is a library of C++ template classes for calculations with the universal Clifford algebras over the real field. The dimension of the algebras you can use is limited only by computer word size. Unlike some software packages for Clifford algebras, the maximum signature is fixed by default or by user defined template parameter values, and calculations are performed in the appropriate subalgebra. GluCat classes are meant to be used as numeric classes with other template libraries. To do this, GluCat classes need to look and behave like floating point numeric types such as float and double. The GluCat classes do this by providing a definition for std::numeric_limits<>, most or all the expected operators like +, -, *, /, and functions like sqrt(). In use with other template libraries, you will need to look out for the differences between GluCat classes and floating point numeric types. Two key differences are that Clifford algebras do not have a total ordering, and that multiplication in Clifford algebras is not necessarily commutative. A third difference is that not all non-zero elements of a Clifford algebra have a multiplicative inverse. PyClical is a Python extension module that is designed to make it easy for you to use Python to perform computations in Clifford algebras, and to implement algorithms and programs that use these computations. The syntax and semantics of the main index_set and clifford classes in PyClical is designed to be as similar as possible to that of the GluCat template classes index_set<> and matrix_multi, so that you should be able to use PyClical to teach yourself how to use calculations in Clifford algebras, and then transfer that knowledge to your ability to use GluCat template classes in C++.

Created: 2002

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