Skip to contents

Multivariate polynomials, mvp objects

mvp.Rd

Create, test for, and coerce to, mvp objects

Usage

mvp(vars, powers, coeffs)
is_ok_mvp(vars,powers,coeffs)
is.mvp(x)
as.mvp(x)
# S3 method for class 'character'
as.mvp(x)
# S3 method for class 'list'
as.mvp(x)
# S3 method for class 'mpoly'
as.mvp(x)
# S3 method for class 'mvp'
as.mvp(x)
# S3 method for class 'numeric'
as.mvp(x)

Arguments

vars

List of variables comprising each term of an mvp object

powers

List of powers corresponding to the variables of the vars argument

coeffs

Numeric vector corresponding to the coefficients to each element of the var and powers lists

x

Object to be coerced to or tested for being class mvp

Details

Function mvp() is the formal creation mechanism for mvp objects. However, it is not very user-friendly; it is better to use as.mvp() in day-to-day use.

Function is_ok_mvp() checks for consistency of its arguments.

Author

Robin K. S. Hankin

Examples


mvp(list("x", c("x","y"), "a", c("y","x")), list(1,1:2,3,c(-1,4)), 1:4)
#> mvp object algebraically equal to
#> 3 a^3 + x + 2 x y^2 + 4 x^4 y^-1

## Note how the terms appear in an arbitrary order, as do
## the symbols within a term.

kahle  <- mvp(
    vars   = split(cbind(letters,letters[c(26,1:25)]),rep(seq_len(26),each=2)),
    powers = rep(list(1:2),26),
    coeffs = 1:26
)
kahle
#> mvp object algebraically equal to
#> a b^2 + 14 a^2 z + 15 b c^2 + 2 c d^2 + 16 d e^2 + 3 e f^2 + 17 f g^2 + 4 g h^2
#> + 18 h i^2 + 5 i j^2 + 19 j k^2 + 6 k l^2 + 20 l m^2 + 7 m n^2 + 21 n o^2 + 8 o
#> p^2 + 22 p q^2 + 9 q r^2 + 23 r s^2 + 10 s t^2 + 24 t u^2 + 11 u v^2 + 25 v w^2
#> + 12 w x^2 + 26 x y^2 + 13 y z^2
## again note arbitrary order of terms and symbols within a term

## Standard arithmetic rules apply:

a <- as.mvp("1 + 4*x*y + 7*z")
b <- as.mvp("-7*z + 3*x^34 - 2*z*x")

a+b
#> mvp object algebraically equal to
#> 1 + 4 x y - 2 x z + 3 x^34
a*b^2
#> mvp object algebraically equal to
#> 196 x y z^2 + 28 x z^2 + 196 x z^3 + 112 x^2 y z^2 + 4 x^2 z^2 + 28 x^2 z^3 +
#> 16 x^3 y z^2 - 42 x^34 z - 294 x^34 z^2 - 168 x^35 y z - 12 x^35 z - 84 x^35
#> z^2 - 48 x^36 y z + 9 x^68 + 63 x^68 z + 36 x^69 y + 49 z^2 + 343 z^3

(a+b)*(a-b) == a^2-b^2 # should be TRUE
#> [1] TRUE


## variable "xy" is distinct from "x*y":

as.mvp("x + y + xy")^2
#> mvp object algebraically equal to
#> 2 x xy + 2 x y + x^2 + 2 xy y + xy^2 + y^2
as.mvp(paste(state.name[1:5],collapse="+"))^2
#> mvp object algebraically equal to
#> 2 Alabama Alaska + 2 Alabama Arizona + 2 Alabama Arkansas + 2 Alabama
#> California + Alabama^2 + 2 Alaska Arizona + 2 Alaska Arkansas + 2 Alaska
#> California + Alaska^2 + 2 Arizona Arkansas + 2 Arizona California + Arizona^2 +
#> 2 Arkansas California + Arkansas^2 + California^2