Package: clifford 1.2-0

clifford: Arbitrary Dimensional Clifford Algebras

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 Grassmann algebra, are discussed. Vignettes presenting conformal geometric algebra, quaternions and split quaternions, dual numbers, and Lorentz transforms are included. The package follows 'disordR' discipline.

Authors:Robin K. S. Hankin [aut, cre]

clifford_1.2-0.tar.gz
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clifford_1.2-0.tgz(r-4.6-emscripten)
manual.pdf |manual.html✨
DESCRIPTION |NEWS
card.svg |card.png
clifford/json (API)

# Install 'clifford' in R:
install.packages('clifford', repos = c('https://robinhankin.r-universe.dev', 'https://cloud.r-project.org'))

Bug tracker:https://github.com/robinhankin/clifford/issues

Pkgdown/docs site:https://robinhankin.github.io

Uses libs:
  • c++– GNU Standard C++ Library v3
Datasets:
  • . - Class "dot"

On CRAN:

Conda:

cpp

6.64 score 6 stars 2 scripts 414 downloads 125 exports 14 dependencies

Last updated from:85532ffb64. Checks:13 OK. Indexed: yes.

TargetResultTimeFilesSyslog
linux-devel-arm64OK216
linux-devel-x86_64OK204
source / vignettesOK231
linux-release-arm64OK198
linux-release-x86_64OK213
macos-release-arm64OK164
macos-release-x86_64OK306
macos-oldrel-arm64OK142
macos-oldrel-x86_64OK232
windows-develOK192
windows-releaseOK178
windows-oldrelOK159
wasm-releaseOK160

Exports:% %%_|%%.%%^%%|_%%dot%%euc%%o%%star%%X%allcliffantivectoras.1vectoras.antivectoras.character.cliffordas.cliffordas.scalaras.vector.cliffordbasisc_addc_cartanc_cartan_inversec_equalc_fatdotprodc_getcoeffsc_gradec_identityc_innerprodc_lefttickprodc_multiplyc_outerprodc_overwritec_powerc_righttickprodcartancartan_inversecattermcliffconjcliffdotprodcliffordclifford_eq_cliffordclifford_inverseclifford_negativeclifford_plus_cliffordclifford_power_scalarclifford_times_scalarcoeffscoeffs<-coeffs<-.cliffordConj.cliffordconstconst<-const<-.cliffordcrossdim.clifforddropdrop_clifforddualeeucprodevenpartfatdotfirst_n_lastgeoprodgetcoeffsgradegrade<-gradeinvgradesgradesminusgradesplusgradeszerohornerIm.cliffordis_ok_cliffordis_ok_sigis.1vectoris.antivectoris.basisbladeis.bladeis.cliffordis.evenis.homogis.oddis.pseudoscalaris.realis.scalaris.zerois.zero.cliffordlapplyleftticklist_modifiermaxytermminusMod.cliffordmymaxnbitsnegntermsnumeric_to_cliffordoddpartOps.cliffordprint_clifford_defaultprint_clifford_quaternionprint_specialprint.cliffordprint.sigobjprint.summary.cliffordpseudoscalarrbladercliffrclifffRe.cliffordrev.cliffordrighttickscalarscalprodshowsigsignaturesortstarsummary.cliffordtermswedgezap

Dependencies:BHdigestdisordRfreealggmplatticemagrittrMatrixpartitionspolynomrbibutilsRcppRdpacksets

Complex arithmetic using Clifford algebra
First method | Second method | Note | Default | References
Rendered fromcomplex_clifford.Rmdusingknitr::rmarkdown

Last update: 2025-10-21
Started: 2023-09-20

Function getcoeffs() in the clifford package
References
Rendered fromgetcoeffs.Rmdusingknitr::rmarkdown

Last update: 2025-10-21
Started: 2024-04-04

Lorentz transforms via Clifford algebra
Lorentz transforms in terms of rapidity | $$\begin | Lorentz transforms in Clifford algebra | Numerical methods: Lorentz transforms using the Clifford package | Multiple boosts | Algebra of Clifford representations | References
Rendered fromlorentz_clifford.Rmdusingknitr::rmarkdown

Last update: 2025-10-21
Started: 2023-09-14

Pauli matrices via Clifford algebra
Implementation | R implementation | Closure | References
Rendered frompauli_clifford.Rmdusingknitr::rmarkdown

Last update: 2025-10-21
Started: 2023-09-21

Quaternionic arithmetic with Clifford algebra
Alternative mapping | References
Rendered fromquaternion_clifford.Rmdusingknitr::rmarkdown

Last update: 2025-10-21
Started: 2023-09-21

Function signature() in the clifford package
References
Rendered fromsignature.Rmdusingknitr::rmarkdown

Last update: 2025-10-21
Started: 2023-10-10

Function pseudoscalar() in the clifford package
References
Rendered frompseudoscalar.Rmdusingknitr::rmarkdown

Last update: 2025-10-21
Started: 2023-10-10

Conformal geometry with Clifford algebra
Points | Sphere, IPNS | Sphere, OPNS | Planes | Circle | Lines and point pairs | References
Rendered fromconformal_algebra_clifford.Rmdusingknitr::rmarkdown

Last update: 2025-10-20
Started: 2023-09-20

Cramer's rule in civilised form with Clifford algebra
Using Clifford algebra | Higher dimensional space | References
Rendered fromcramer_clifford.Rmdusingknitr::rmarkdown

Last update: 2025-10-20
Started: 2023-09-21

Determinants using Clifford algebra
References
Rendered fromdeterminants_clifford.Rmdusingknitr::rmarkdown

Last update: 2025-10-20
Started: 2023-09-21

Dual quaternions via Clifford algebra
References
Rendered fromdual_quaternion_clifford.Rmdusingknitr::rmarkdown

Last update: 2025-10-20
Started: 2023-09-22

The clifford package
Introduction | The package in use | Pseudo-Euclidean spaces | Grassmann algebra | Positive-definite inner product | Left and right contractions | Higher dimensional spaces | Conclusions and further work
Rendered fromclifford.Rnwusingutils::Sweave

Last update: 2025-10-20
Started: 2019-11-27

Readme and manuals

Help Manual

Help pageTopics
Arbitrary Dimensional Clifford Algebrasclifford-package
Clifford object containing all possible termsallcliff
Antivectors or pseudovectorsantivector as.antivector is.antivector
Coerce a clifford vector to a numeric vectoras.vector as.vector.clifford
Cartan map between clifford algebrascartan cartan_inverse
Create, coerce, and test for 'clifford' objectsas.clifford clifford clifford-class dim dim.clifford dimension is.clifford is_ok_clifford nbits nterms
The constant term of a Clifford objectconst const<- const<-.clifford constant constant<- constant<-.clifford is.real
Class "dot". commutator dot dot-class dot_error jacobi [,dot,ANY,ANY-method [,dot,ANY,missing-method [,dot,clifford,ANY,ANY-method [,dot,clifford,ANY-method [,dot,matrix,matrix-method [,dot,missing,ANY-method [,dot,missing,missing-method [,dot-method [.dot
Drop redundant informationdrop drop,clifford-method drop_clifford
Even and odd clifford objectseven evenpart is.even is.odd oddpart
Extract or Replace Parts of a cliffordcoeffs coeffs<- coeffs<-.clifford extract extract.clifford getcoeffs Im Im.clifford list_modifier Re Re.clifford replace replace.clifford warn_on_repeats [.clifford [<-.clifford
The grade of a clifford objectgrade grade<- grademinus gradeplus grades gradesminus gradesplus gradeszero gradezero
Homogenous Clifford objectshomog homogenous is.homog is.homogenous
Horner's methodhorner
Clifford involutionscliffconj Conj conj Conj.clifford conjugate dagger dual gradeinv involution involutions neg rev rev.clifford reverse tilde
Low-level helper functions for 'clifford' objectsc_add c_cartan c_cartan_inverse c_equal c_fatdotprod c_getcoeffs c_grade c_identity c_innerprod c_lefttickprod c_multiply c_outerprod c_overwrite c_power c_righttickprod lowlevel
Magnitude of a clifford objectmagnitude Mod mod Mod.clifford
Take the negative of a vectoris.minus minus
Coercion from numeric to Clifford formas.1vector as.cliffvector as.scalar basis e is.1vector is.scalar numeric_to_clifford scalar
Arithmetic Ops Group Methods for 'clifford' objects% % % %.clifford %.% %.%.clifford %dot% %euc% %euc%.clifford %o% %o%.clifford %star% %star%.clifford %X% %X%.clifford %^% %^%.clifford %_|% %_|%.clifford %|_% %|_%.clifford cliffdotprod clifford_cross_clifford clifford_dot_clifford clifford_eq_clifford clifford_fatdot_clifford clifford_inverse clifford_lefttick_clifford clifford_negative clifford_plus_clifford clifford_plus_numeric clifford_plus_scalar clifford_power_scalar clifford_righttick_clifford clifford_star_clifford clifford_times_clifford clifford_times_scalar clifford_wedge_clifford cross euclidean_product euclid_product eucprod fatdot geometric_prod geometric_product geoprod lefttick left_contraction maxyterm Ops Ops.clifford right contraction righttick scalar_product scalprod star wedge
Print clifford objectsas.character as.character.clifford basissep catterm print.cliff print.clifford print_clifford print_clifford_default print_clifford_pauli print_clifford_quaternion print_special
Coercion from numeric to Clifford formas.pseudoscalar is.pseudoscalar pseudoscalar
Quaternions using Clifford algebrasclifford_to_quaternion quaternion quaternion_to_clifford
Random clifford objectsrblade rcliff rclifff
The signature of the Clifford algebrais_ok_sig maxdim mymax print.sigobj showsig sig signature
Summary methods for clifford objectsfirst_n_last print.summary.clifford summary.clifford
Deal with termsblade is.basisblade is.blade term terms
Zap small values in a clifford objectzap zap.clifford zapsmall zaptiny
The zero Clifford objectis.zero is.zero,ANY-method is.zero,clifford-method is.zero.clifford zero zero.cliff zero.clifford