Ops.freealg: Arithmetic Ops methods for the the free algebra

Ops.freealgR Documentation

Arithmetic Ops methods for the the free algebra

Description

Arithmetic operators for manipulation of freealg objects such as addition, multiplication, powers, etc

Usage

## S3 method for class 'freealg'
Ops(e1, e2)
free_negative(S)
free_power_scalar(S,n)
free_eq_free(e1,e2)
free_plus_numeric(S,x)
free_plus_free(e1,e2)
lowlevel_simplify(words,coeffs)
lowlevel_free_prod(words1,coeffs1,words2,coeffs2)
lowlevel_free_sum(words1,coeffs1,words2,coeffs2)
lowlevel_free_power(words,coeffs,n)
lowlevel_diffn(words,coeffs,r)
lowlevel_subs(words1, coeffs1, words2, coeffs2, r)
inv(S)

Arguments

S,e1,e2

Objects of class freealg

n

Integer, possibly non-positive

r

Integer vector indicating variables to differentiate with respect to

x

Scalar value

words,words1,words2

A list of words, that is, a list of integer vectors representing the variables in each term

coeffs,coeffs1,coeffs2

Numeric vector representing the coefficients of each word

Details

The function Ops.freealg() passes binary arithmetic operators (“+”, “-”, “*”, “^”, and “==”) to the appropriate specialist function.

The caret, as in a^n, denotes arithmetic exponentiation, as in x^3==x*x*x. The only comparison operators are equality and inequality; x==y is defined as is.zero(x-y).

Functions lowlevel_foo() are low-level functions that interface directly with the C routines in the src/ directory and are not intended for the end-user.

Function inv() is defined only for freealg objects with a single term. If x has a single term we have inv(x)*x=x*inv(x)=1. There is no corresponding division in the package because a/b may be either a*inv(b) or inv(b)*a.

Author(s)

Robin K. S. Hankin

Examples

rfalg()
as.freealg("1+x+xy+yx")  # variables are non-commutative
as.freealg("x") * as.freealg("X") # upper-case letters are lower-case inverses

constant(as.freealg("x+y+X+Y")^6)  # OEIS sequence A035610

inv(as.freealg("2aaabAAAAx"))

freealg documentation built on Aug. 28, 2022, 9:05 a.m.