Arith: Methods for Function Arith in package Jordan

In jordan: A Suite of Routines for Working with Jordan Algebras

Methods for Function Arith in package Jordan

Description

Methods for Arithmetic functions for jordans: +, -, *, /, ^

Usage

jordan_negative(z)
jordan_plus_jordan(e1,e2)
jordan_plus_numeric(e1,e2)
jordan_prod_numeric(e1,e2)
jordan_power_jordan(e1,e2)
albert_arith_albert(e1,e2)
albert_arith_numeric(e1,e2)
albert_inverse(e1)
albert_power_albert(...)
albert_power_numeric(e1,e2)
albert_power_single_n(e1,n)
albert_prod_albert(e1,e2)
chm_arith_chm(e1,e2)
chm_arith_numeric(e1,e2)
chm_inverse(e1)
chm_power_numeric(e1,e2)
chm_prod_chm(e1,e2)
numeric_arith_albert(e1,e2)
numeric_arith_chm(e1,e2)
numeric_arith_qhm(e1,e2)
numeric_arith_rsm(e1,e2)
qhm_arith_numeric(e1,e2)
qhm_arith_qhm(e1,e2)
qhm_inverse(x)
qhm_power_numeric(e1,e2)
qhm_prod_qhm(e1,e2)
rsm_arith_numeric(e1,e2)
rsm_arith_rsm(e1,e2)
rsm_inverse(e1)
rsm_power_numeric(e1,e2)
rsm_prod_rsm(e1,e2)
spin_plus_numeric(e1,e2)
spin_plus_spin(e1,e2)
spin_power_numeric(e1,e2)
spin_power_single_n(e1,n)
spin_power_spin(...)
spin_prod_numeric(e1,e2)
spin_prod_spin(e1,e2)
spin_inverse(...)
spin_negative(e1)
vec_albertprod_vec(x,y)
vec_chmprod_vec(x,y)
vec_qhmprod_vec(x,y)
vec_rsmprod_vec(x,y)

Arguments

z, e1, e2	Jordan objects or numeric vectors
n	Integer for powers
...	Further arguments (ignored)
x, y	Numeric vectors, Jordan objects in independent form

Details

The package implements the Arith group of S4 generics so that idiom like A + B*C works as expected with jordans.

Functions like jordan_inverse() and jordan_plus_jordan() are low-level helper functions. The only really interesting operation is multiplication; functions like jordan_prod_jordan().

Names are implemented and the rules are inherited (via onion::harmonize_oo() and onion::harmonize_on()) from rbind().

Value

generally return jordans

Author(s)

Robin K. S. Hankin

Examples

x <- rspin()
y <- rspin()
z <- rspin()

x*(y*(x*x)) - (x*y)*(x*x) # should be zero

x + y*z

jordan documentation built on July 4, 2024, 5:06 p.m.