clifford-package {clifford}

Arbitrary Dimensional Clifford Algebras

Description

A suite of routines for Clifford algebras, using the 'Map' class of the Standard Template Library. Canonical reference: Hestenes (1987, ISBN 90-277-1673-0, "Clifford algebra to geometric calculus"). Special cases including Lorentz transforms, quaternion multiplication, and Grassman algebra, are discussed. Conformal geometric algebra theory is implemented. Uses 'disordR' discipline.

Details

The DESCRIPTION file:

Package:	clifford
Type:	Package
Title:	Arbitrary Dimensional Clifford Algebras
Version:	1.0-8
Authors@R:	person(given=c("Robin", "K. S."), family="Hankin", role = c("aut","cre"), email="[e-mail]", comment = c(ORCID = "0000-0001-5982-0415"))
Maintainer:	Robin K. S. Hankin <[e-mail]>
Description:	A suite of routines for Clifford algebras, using the 'Map' class of the Standard Template Library. Canonical reference: Hestenes (1987, ISBN 90-277-1673-0, "Clifford algebra to geometric calculus"). Special cases including Lorentz transforms, quaternion multiplication, and Grassman algebra, are discussed. Conformal geometric algebra theory is implemented. Uses 'disordR' discipline.
License:	GPL (>= 2)
Suggests:	knitr,rmarkdown,testthat,onion,lorentz
VignetteBuilder:	knitr
Imports:	Rcpp (>= 0.12.5),mathjaxr,disordR (>= 0.0-8), magrittr, methods, partitions (>= 1.10-4)
LinkingTo:	Rcpp,BH
SystemRequirements:	C++11
URL:	https://github.com/RobinHankin/clifford
BugReports:	https://github.com/RobinHankin/clifford/issues
RdMacros:	mathjaxr
Author:	Robin K. S. Hankin [aut, cre] (<https://orcid.org/0000-0001-5982-0415>)

Index of help topics:

Ops.clifford            Arithmetic Ops Group Methods for 'clifford'
                        objects
[.clifford              Extract or Replace Parts of a clifford
allcliff                Clifford object containing all possible terms
antivector              Antivectors or pseudovectors
as.vector               Coerce a clifford vector to a numeric vector
cartan                  Cartan map between clifford algebras
clifford                Create, coerce, and test for 'clifford' objects
clifford-package        Arbitrary Dimensional Clifford Algebras
const                   The constant term of a Clifford object
drop                    Drop redundant information
even                    Even and odd clifford objects
grade                   The grade of a clifford object
homog                   Homogenous Clifford objects
horner                  Horner's method
involution              Clifford involutions
lowlevel                Low-level helper functions for 'clifford'
                        objects
magnitude               Magnitude of a clifford object
minus                   Take the negative of a vector
numeric_to_clifford     Coercion from numeric to Clifford form
print.clifford          Print clifford objects
quaternion              Quaternions using Clifford algebras
rcliff                  Random clifford objects
signature               The signature of the Clifford algebra
summary.clifford        Summary methods for clifford objects
term                    Deal with terms
zap                     Zap small values in a clifford object
zero                    The zero Clifford object

Author(s)

NA

Maintainer: Robin K. S. Hankin <[e-mail]>

References

• J. Snygg (2012). A new approach to differential geometry using Clifford's geometric Algebra, Birkhauser. ISBN 978-0-8176-8282-8

• D. Hestenes (1987). Clifford algebra to geometric calculus, Kluwer. ISBN 90-277-1673-0

• C. Perwass (2009). Geometric algebra with applications in engineering, Springer. ISBN 978-3-540-89068-3

• D. Hildenbrand (2013). Foundations of geometric algebra computing. Springer, ISBN 978-3-642-31794-1

See Also

clifford

Examples

as.1vector(1:4)

as.1vector(1:4) * rcliff()

# Following from Ablamowicz and Fauser (see vignette):
x <- clifford(list(1:3,c(1,5,7,8,10)),c(4,-10)) + 2
y <- clifford(list(c(1,2,3,7),c(1,5,6,8),c(1,4,6,7)),c(4,1,-3)) - 1
x*y # signature irrelevant