# Arbitrary Dimensional Clifford Algebras

## Documentation for package ‘clifford’ version 1.2-0-2

- DESCRIPTION file.
- User guides, package vignettes and other documentation.
- Package NEWS.

## Help Pages

A B C D E F G H I J L M N O P Q R S T W Z misc

clifford-package | Arbitrary Dimensional Clifford Algebras

## -- A --

allcliff | Clifford object containing all possible terms
antivector | Antivectors or pseudovectors
as.1vector | Coercion from numeric to Clifford form
as.antivector | Antivectors or pseudovectors
as.character | Print clifford objects
as.character.clifford | Print clifford objects
as.clifford | Create, coerce, and test for 'clifford' objects
as.cliffvector | Coercion from numeric to Clifford form
as.pseudoscalar | Coercion from numeric to Clifford form
as.scalar | Coercion from numeric to Clifford form
as.vector | Coerce a clifford vector to a numeric vector
as.vector.clifford | Coerce a clifford vector to a numeric vector

## -- B --

basis | Coercion from numeric to Clifford form
basissep | Print clifford objects
blade | Deal with terms

## -- C --

cartan | Cartan map between clifford algebras
cartan_inverse | Cartan map between clifford algebras
catterm | Print clifford objects
cliffconj | Clifford involutions
cliffdotprod | Arithmetic Ops Group Methods for 'clifford' objects
clifford | Create, coerce, and test for 'clifford' objects
clifford-class | Create, coerce, and test for 'clifford' objects
clifford_cross_clifford | Arithmetic Ops Group Methods for 'clifford' objects
clifford_dot_clifford | Arithmetic Ops Group Methods for 'clifford' objects
clifford_eq_clifford | Arithmetic Ops Group Methods for 'clifford' objects
clifford_fatdot_clifford | Arithmetic Ops Group Methods for 'clifford' objects
clifford_inverse | Arithmetic Ops Group Methods for 'clifford' objects
clifford_lefttick_clifford | Arithmetic Ops Group Methods for 'clifford' objects
clifford_negative | Arithmetic Ops Group Methods for 'clifford' objects
clifford_plus_clifford | Arithmetic Ops Group Methods for 'clifford' objects
clifford_plus_numeric | Arithmetic Ops Group Methods for 'clifford' objects
clifford_plus_scalar | Arithmetic Ops Group Methods for 'clifford' objects
clifford_power_scalar | Arithmetic Ops Group Methods for 'clifford' objects
clifford_righttick_clifford | Arithmetic Ops Group Methods for 'clifford' objects
clifford_star_clifford | Arithmetic Ops Group Methods for 'clifford' objects
clifford_times_clifford | Arithmetic Ops Group Methods for 'clifford' objects
clifford_times_scalar | Arithmetic Ops Group Methods for 'clifford' objects
clifford_to_quaternion | Quaternions using Clifford algebras
clifford_wedge_clifford | Arithmetic Ops Group Methods for 'clifford' objects
coeffs | Extract or Replace Parts of a clifford
coeffs<- | Extract or Replace Parts of a clifford
coeffs<-.clifford | Extract or Replace Parts of a clifford
commutator | Class "dot"
Conj | Clifford involutions
conj | Clifford involutions
Conj.clifford | Clifford involutions
conjugate | Clifford involutions
const | The constant term of a Clifford object
const<- | The constant term of a Clifford object
const<-.clifford | The constant term of a Clifford object
constant | The constant term of a Clifford object
constant<- | The constant term of a Clifford object
constant<-.clifford | The constant term of a Clifford object
cross | Arithmetic Ops Group Methods for 'clifford' objects
c_add | Low-level helper functions for 'clifford' objects
c_cartan | Low-level helper functions for 'clifford' objects
c_cartan_inverse | Low-level helper functions for 'clifford' objects
c_equal | Low-level helper functions for 'clifford' objects
c_fatdotprod | Low-level helper functions for 'clifford' objects
c_getcoeffs | Low-level helper functions for 'clifford' objects
c_grade | Low-level helper functions for 'clifford' objects
c_identity | Low-level helper functions for 'clifford' objects
c_innerprod | Low-level helper functions for 'clifford' objects
c_lefttickprod | Low-level helper functions for 'clifford' objects
c_multiply | Low-level helper functions for 'clifford' objects
c_outerprod | Low-level helper functions for 'clifford' objects
c_overwrite | Low-level helper functions for 'clifford' objects
c_power | Low-level helper functions for 'clifford' objects
c_righttickprod | Low-level helper functions for 'clifford' objects

## -- D --

dagger | Clifford involutions
dim | Create, coerce, and test for 'clifford' objects
dim.clifford | Create, coerce, and test for 'clifford' objects
dimension | Create, coerce, and test for 'clifford' objects
dot | Class "dot"
dot-class | Class "dot"
dot_error | Class "dot"
drop | Drop redundant information
drop-method | Drop redundant information
drop_clifford | Drop redundant information
dual | Clifford involutions

## -- E --

e | Coercion from numeric to Clifford form
euclidean_product | Arithmetic Ops Group Methods for 'clifford' objects
euclid_product | Arithmetic Ops Group Methods for 'clifford' objects
eucprod | Arithmetic Ops Group Methods for 'clifford' objects
even | Even and odd clifford objects
evenpart | Even and odd clifford objects
extract | Extract or Replace Parts of a clifford
extract.clifford | Extract or Replace Parts of a clifford

## -- F --

fatdot | Arithmetic Ops Group Methods for 'clifford' objects
first_n_last | Summary methods for clifford objects

## -- G --

geometric_prod | Arithmetic Ops Group Methods for 'clifford' objects
geometric_product | Arithmetic Ops Group Methods for 'clifford' objects
geoprod | Arithmetic Ops Group Methods for 'clifford' objects
getcoeffs | Extract or Replace Parts of a clifford
grade | The grade of a clifford object
grade<- | The grade of a clifford object
gradeinv | Clifford involutions
grademinus | The grade of a clifford object
gradeplus | The grade of a clifford object
grades | The grade of a clifford object
gradesminus | The grade of a clifford object
gradesplus | The grade of a clifford object
gradeszero | The grade of a clifford object
gradezero | The grade of a clifford object

## -- H --

homog | Homogenous Clifford objects
homogenous | Homogenous Clifford objects
horner | Horner's method

## -- I --

Im | Extract or Replace Parts of a clifford
Im.clifford | Extract or Replace Parts of a clifford
involution | Clifford involutions
involutions | Clifford involutions
is.1vector | Coercion from numeric to Clifford form
is.antivector | Antivectors or pseudovectors
is.basisblade | Deal with terms
is.blade | Deal with terms
is.clifford | Create, coerce, and test for 'clifford' objects
is.even | Even and odd clifford objects
is.homog | Homogenous Clifford objects
is.homogenous | Homogenous Clifford objects
is.minus | Take the negative of a vector
is.odd | Even and odd clifford objects
is.pseudoscalar | Coercion from numeric to Clifford form
is.real | The constant term of a Clifford object
is.scalar | Coercion from numeric to Clifford form
is.zero | The zero Clifford object
is.zero-method | The zero Clifford object
is.zero.clifford | The zero Clifford object
is_ok_clifford | Create, coerce, and test for 'clifford' objects
is_ok_sig | The signature of the Clifford algebra

## -- J --

jacobi | Class "dot"

## -- L --

lefttick | Arithmetic Ops Group Methods for 'clifford' objects
left_contraction | Arithmetic Ops Group Methods for 'clifford' objects
list_modifier | Extract or Replace Parts of a clifford
lowlevel | Low-level helper functions for 'clifford' objects

## -- M --

magnitude | Magnitude of a clifford object
maxdim | The signature of the Clifford algebra
maxyterm | Arithmetic Ops Group Methods for 'clifford' objects
minus | Take the negative of a vector
Mod | Magnitude of a clifford object
mod | Magnitude of a clifford object
Mod.clifford | Magnitude of a clifford object
mymax | The signature of the Clifford algebra

## -- N --

nbits | Create, coerce, and test for 'clifford' objects
neg | Clifford involutions
nterms | Create, coerce, and test for 'clifford' objects
numeric_to_clifford | Coercion from numeric to Clifford form

## -- O --

oddpart | Even and odd clifford objects
Ops | Arithmetic Ops Group Methods for 'clifford' objects
Ops.clifford | Arithmetic Ops Group Methods for 'clifford' objects

## -- P --

print.cliff | Print clifford objects
print.clifford | Print clifford objects
print.sigobj | The signature of the Clifford algebra
print.summary.clifford | Summary methods for clifford objects
print_clifford | Print clifford objects
print_clifford_default | Print clifford objects
print_clifford_pauli | Print clifford objects
print_clifford_quaternion | Print clifford objects
print_special | Print clifford objects
pseudoscalar | Coercion from numeric to Clifford form

## -- Q --

quaternion | Quaternions using Clifford algebras
quaternion_to_clifford | Quaternions using Clifford algebras

## -- R --

rblade | Random clifford objects
rcliff | Random clifford objects
rclifff | Random clifford objects
Re | Extract or Replace Parts of a clifford
Re.clifford | Extract or Replace Parts of a clifford
replace | Extract or Replace Parts of a clifford
replace.clifford | Extract or Replace Parts of a clifford
rev | Clifford involutions
rev.clifford | Clifford involutions
reverse | Clifford involutions
right contraction | Arithmetic Ops Group Methods for 'clifford' objects
righttick | Arithmetic Ops Group Methods for 'clifford' objects

## -- S --

scalar | Coercion from numeric to Clifford form
scalar_product | Arithmetic Ops Group Methods for 'clifford' objects
scalprod | Arithmetic Ops Group Methods for 'clifford' objects
showsig | The signature of the Clifford algebra
sig | The signature of the Clifford algebra
signature | The signature of the Clifford algebra
star | Arithmetic Ops Group Methods for 'clifford' objects
summary.clifford | Summary methods for clifford objects

## -- T --

term | Deal with terms
terms | Deal with terms
tilde | Clifford involutions

## -- W --

warn_on_repeats | Extract or Replace Parts of a clifford
wedge | Arithmetic Ops Group Methods for 'clifford' objects

## -- Z --

zap | Zap small values in a clifford object
zap.clifford | Zap small values in a clifford object
zapsmall | Zap small values in a clifford object
zaptiny | Zap small values in a clifford object
zero | The zero Clifford object
zero.cliff | The zero Clifford object
zero.clifford | The zero Clifford object

## -- misc --

% % | Arithmetic Ops Group Methods for 'clifford' objects
% %.clifford | Arithmetic Ops Group Methods for 'clifford' objects
%.% | Arithmetic Ops Group Methods for 'clifford' objects
%.%.clifford | Arithmetic Ops Group Methods for 'clifford' objects
%dot% | Arithmetic Ops Group Methods for 'clifford' objects
%euc% | Arithmetic Ops Group Methods for 'clifford' objects
%euc%.clifford | Arithmetic Ops Group Methods for 'clifford' objects
%o% | Arithmetic Ops Group Methods for 'clifford' objects
%o%.clifford | Arithmetic Ops Group Methods for 'clifford' objects
%star% | Arithmetic Ops Group Methods for 'clifford' objects
%star%.clifford | Arithmetic Ops Group Methods for 'clifford' objects
%X% | Arithmetic Ops Group Methods for 'clifford' objects
%X%.clifford | Arithmetic Ops Group Methods for 'clifford' objects
%^% | Arithmetic Ops Group Methods for 'clifford' objects
%^%.clifford | Arithmetic Ops Group Methods for 'clifford' objects
%_|% | Arithmetic Ops Group Methods for 'clifford' objects
%_|%.clifford | Arithmetic Ops Group Methods for 'clifford' objects
%|_% | Arithmetic Ops Group Methods for 'clifford' objects
%|_%.clifford | Arithmetic Ops Group Methods for 'clifford' objects
. | Class "dot"
[-method | Class "dot"
[.clifford | Extract or Replace Parts of a clifford
[<-.clifford | Extract or Replace Parts of a clifford