Ops.mvp: Arithmetic Ops Group Methods for 'mvp' objects
| Ops.mvp | R Documentation |
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 |
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
