Ops.mvp: Arithmetic Ops Group Methods for 'mvp' objects

In mvp: Fast Symbolic Multivariate Polynomials

Arithmetic Ops Group Methods for mvp objects

Description

Allows arithmetic operators to be used for multivariate polynomials such as addition, multiplication, integer powers, etc.

Usage

## S3 method for class 'mvp'
Ops(e1, e2)
mvp_negative(S)
mvp_times_mvp(S1,S2)
mvp_times_scalar(S,x)
mvp_plus_mvp(S1,S2)
mvp_plus_numeric(S,x)
mvp_eq_mvp(S1,S2)
mvp_modulo(S1,S2)

Arguments

e1, e2, S, S1, S2	Objects of class mvp
x	Scalar, length one numeric vector

Details

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

The most interesting operator is “*”, which is passed to mvp_times_mvp(). I guess “+” is quite interesting too.

The caret “^” denotes arithmetic exponentiation, as in x^3==x*x*x. As an experimental feature, this is (sort of) vectorised: if n is a vector, then a^n returns the sum of a raised to the power of each element of n. For example, a^c(n1,n2,n3) is a^n1 + a^n2 + a^n3. Internally, n is tabulated in the interests of efficiency, so a^c(0,2,5,5,5) = 1 + a^2 + 3a^5 is evaluated with only a single fifth power. Similar functionality is implemented in the freealg package.

Value

The high-level functions documented here return an object of mvp, the low-level functions documented at lowlevel.Rd return lists. But don't use the low-level functions.

Note

Function mvp_modulo() is distinctly sub-optimal and inst/mvp_modulo.Rmd details ideas for better implementation.

Author(s)

Robin K. S. Hankin

See Also

lowlevel

Examples

(p1 <- rmvp(3))
(p2 <- rmvp(3))

p1*p2

p1+p2

p1^3


p1*(p1+p2) == p1^2+p1*p2  # should be TRUE

mvp documentation built on April 4, 2025, 3:48 a.m.