mvp (version 1.0-18)

Ops.mvp: 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 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)

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.

Arguments

e1,e2,S,S1,S2

Objects of class mvp

x

Scalar, length one numeric vector

Author

Robin K. S. Hankin

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.

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