Ops.spray: Arithmetic Ops Group Methods for sprays

Description

Allows arithmetic operators to be used for spray calculations, such as addition, multiplication, division, integer powers, etc. Objects of class spray are interpreted as sparse multivariate polynomials.

Usage

# S3 method for spray
Ops(e1, e2 = NULL)
spray_negative(S)
spray_times_spray(S1,S2)
spray_times_scalar(S,x)
spray_plus_spray(S1,S2)
spray_plus_scalar(S,x)
spray_power_scalar(S,n)
spray_eq_spray(S1,S2)

Arguments

e1,e2,S,S1,S2

Objects of class spray, here interpreted as sparse multivariate polynomials

Real valued scalar

Non-negative integer

Value

The functions all return spray objects except “==”, which returns a logical.

Details

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

The most interesting operators are “*” and “+” which execute multivariate polynomial multiplication and addition respectively.

Testing for equality uses spray_eq_spray(). Note that spray_eq_spray(S1,S2) is algebraically equivalent to is.zero(S1-S2), but faster (FALSE is returned as soon as a mismatch is found).

Examples

Run this code

# NOT RUN {

M <- matrix(sample(0:3,21,replace=TRUE),ncol=3)
a <- spray(M,sample(7))
b <- homog(3,4)


# arithmetic operators mostly work as expected:
a + 2*b
a - a*b^2/4
a+b

S1 <- spray(partitions::compositions(4,3))
S2 <- spray(diag(3))  # S2 = x+y+z


stopifnot( (S1+S2)^3 == S1^3 + 3*S1^2*S2 + 3*S1*S2^2 + S2^3 )






# }