multipol (version 1.0-9)

multipol-package: Multivariate polynomials

Description

Various tools to manipulate and combine multivariate polynomials

Author

tools:::Rd_package_author("multipol")

Maintainer: tools:::Rd_package_maintainer("multipol")

Details

Multidimensional arrays are interpreted in a natural way as multivariate polynomials.

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The package is almost completely superceded by the spray and mvp packages, which use a sparse array system for efficiency.

Examples

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))