Package: clifford 1.0-9
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:
clifford_1.0-9.tar.gz
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clifford.pdf |clifford.html✨
clifford/json (API)
NEWS
| # 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
- . - Class "dot"
Last updated 2 months agofrom:d4595b3adc. Checks:OK: 9. Indexed: yes.
| Target | Result | Date |
|---|---|---|
| Doc / Vignettes | OK | Oct 23 2024 |
| R-4.5-win-x86_64 | OK | Oct 23 2024 |
| R-4.5-linux-x86_64 | OK | Oct 23 2024 |
| R-4.4-win-x86_64 | OK | Oct 23 2024 |
| R-4.4-mac-x86_64 | OK | Oct 23 2024 |
| R-4.4-mac-aarch64 | OK | Oct 23 2024 |
| R-4.3-win-x86_64 | OK | Oct 23 2024 |
| R-4.3-mac-x86_64 | OK | Oct 23 2024 |
| R-4.3-mac-aarch64 | OK | Oct 23 2024 |
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.cliffordprint.sigobjprint.summary.cliffordpseudoscalarrbladercliffrclifffRe.cliffordrev.cliffordrighttickscalarscalprodshowsigsignaturesortstarsummary.cliffordtermswedgezap
Dependencies:BHdigestdisordRfreealggmplatticemagrittrmathjaxrMatrixpartitionspolynomrbibutilsRcppRdpacksets
Complex arithmetic using Clifford algebra
Rendered fromcomplex_clifford.Rmdusingknitr::rmarkdownon Oct 23 2024.Last update: 2023-10-10
Started: 2023-09-20
Conformal geometry with Clifford algebra
Rendered fromconformal_algebra_clifford.Rmdusingknitr::rmarkdownon Oct 23 2024.Last update: 2024-08-23
Started: 2023-09-20
Cramer's rule in civilised form with Clifford algebra
Rendered fromcramer_clifford.Rmdusingknitr::rmarkdownon Oct 23 2024.Last update: 2024-03-21
Started: 2023-09-21
Determinants using Clifford algebra
Rendered fromdeterminants_clifford.Rmdusingknitr::rmarkdownon Oct 23 2024.Last update: 2023-10-09
Started: 2023-09-21
Dual quaternions via Clifford algebra
Rendered fromdual_quaternion_clifford.Rmdusingknitr::rmarkdownon Oct 23 2024.Last update: 2023-09-22
Started: 2023-09-22
Function getcoeffs() in the clifford package
Rendered fromgetcoeffs.Rmdusingknitr::rmarkdownon Oct 23 2024.Last update: 2024-04-18
Started: 2024-04-04
Lorentz transforms via Clifford algebra
Rendered fromlorentz_clifford.Rmdusingknitr::rmarkdownon Oct 23 2024.Last update: 2024-03-21
Started: 2023-09-14
Pauli matrices via Clifford algebra
Rendered frompauli_clifford.Rmdusingknitr::rmarkdownon Oct 23 2024.Last update: 2024-08-08
Started: 2023-09-21
Quaternionic arithmetic with Clifford algebra
Rendered fromquaternion_clifford.Rmdusingknitr::rmarkdownon Oct 23 2024.Last update: 2024-01-25
Started: 2023-09-21
Function signature() in the clifford package
Rendered fromsignature.Rmdusingknitr::rmarkdownon Oct 23 2024.Last update: 2023-10-10
Started: 2023-10-10
The clifford package
Rendered fromclifford.Rnwusingutils::Sweaveon Oct 23 2024.Last update: 2024-04-18
Started: 2019-11-27
Function pseudoscalar() in the clifford package
Rendered frompseudoscalar.Rmdusingknitr::rmarkdownon Oct 23 2024.Last update: 2024-03-26
Started: 2023-10-10
Readme and manuals
Help Manual
| Help page | Topics |
|---|---|
| Arbitrary Dimensional Clifford Algebras | clifford-package |
| Clifford object containing all possible terms | allcliff |
| Antivectors or pseudovectors | antivector as.antivector is.antivector |
| Coerce a clifford vector to a numeric vector | as.vector as.vector.clifford |
| Cartan map between clifford algebras | cartan cartan_inverse |
| Create, coerce, and test for 'clifford' objects | as.clifford clifford clifford-class dim dim.clifford dimension is.clifford is_ok_clifford nbits nterms |
| The constant term of a Clifford object | const 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 information | drop drop,clifford-method drop_clifford |
| Even and odd clifford objects | even evenpart is.even is.odd oddpart |
| Extract or Replace Parts of a clifford | coeffs 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 object | grade grade<- grademinus gradeplus grades gradesminus gradesplus gradeszero gradezero |
| Homogenous Clifford objects | homog homogenous is.homog is.homogenous |
| Horner's method | horner |
| Clifford involutions | cliffconj Conj conj Conj.clifford conjugate dagger dual gradeinv involution involutions neg rev rev.clifford reverse tilde |
| Low-level helper functions for 'clifford' objects | c_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 object | magnitude Mod mod Mod.clifford |
| Take the negative of a vector | is.minus minus |
| Coercion from numeric to Clifford form | as.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 objects | as.character as.character.clifford basissep catterm print.cliff print.clifford |
| Coercion from numeric to Clifford form | as.pseudoscalar is.pseudoscalar pseudoscalar |
| Quaternions using Clifford algebras | clifford_to_quaternion quaternion quaternion_to_clifford |
| Random clifford objects | rblade rcliff rclifff |
| The signature of the Clifford algebra | is_ok_sig maxdim mymax print.sigobj showsig sig signature |
| Summary methods for clifford objects | first_n_last print.summary.clifford summary.clifford |
| Deal with terms | blade is.basisblade is.blade term terms |
| Zap small values in a clifford object | zap zap.clifford zapsmall zaptiny |
| The zero Clifford object | is.zero is.zero,ANY-method is.zero,clifford-method is.zero.clifford zero zero.cliff zero.clifford |
