multipol (version 1.0-7)

# multipol-package: Multivariate polynomials

## Description

Various tools to manipulate and combine multivariate polynomials

## Details

 Package: multipol Type: Package Version: 1.0 Date: 2008-01-24 License: GPL

Basically, coerce an array to a multivariate polynomial (a “multipol”) using `as.multipol()`.

Taking a matrix `a` as an example, because this has two dimensions it may be viewed as a bivariate polynomial with `a[i,j]` being the coefficient of \(x^iy^j\). Note the off-by-one issue; see `?Extract`.

Multivariate polynomials of arbitrary arity are a straightforward generalization using appropriately dimensioned arrays.

Arithmetic operations “`+`”,“`-`”, “`*`”, “`^`” operate as though their arguments are multivariate polynomials.

Even quite small multipols are computationally intense; many coefficients have to be calculated and each is the sum of many terms.

The package would benefit enormously by being able to use a sparse array class.

none really

## Examples

```# NOT RUN {
ones(2)*linear(c(1,-1))                             # x^2-y^2
ones(2)*(ones(2,2)-uni(2))                          # x^3+y^3

a <- as.multipol(matrix(1:12,3,4))
a

a[1,1] <- 11

f <- as.function(a*a)

f(c(1,pi))

# }
```