Various functions to create simple spray objects

Various functions to create simple spray objects such as single-term, homogeneous, and constant multivariate polynomials.

Usage

product(power)
homog(d,power=1)
linear(x,power=1)
lone(n,d=n)
one(d)
as.id(S)
xyz(d)

Arguments

d

An integer; generally, the dimension or arity of the resulting spray object

power

Integer vector of powers

x

Numeric vector of coefficients

S

A spray object

n

In function lone(), the term to raise to power 1

Value

All functions documented here return a spray object

Author

Robin K. S. Hankin

Note

The functions here are related to their equivalents in the multipol package, but are not exactly the same.

Function zero() is documented at zero.Rd, but is listed below for convenience.

See also

constant, zero

Examples

product(1:3)                   #      x * y^2 * z^3
#>            val
#>  1 2 3  =    1
homog(3)                       #      x + y + z
#>            val
#>  0 0 1  =    1
#>  0 1 0  =    1
#>  1 0 0  =    1
homog(3,2)                     #      x^2  + xy + xz + y^2 + yz + z^2
#>            val
#>  0 0 2  =    1
#>  0 1 1  =    1
#>  1 0 1  =    1
#>  0 2 0  =    1
#>  1 1 0  =    1
#>  2 0 0  =    1
linear(1:3)                    #      1*x + 2*y + 3*z
#>            val
#>  0 0 1  =    3
#>  0 1 0  =    2
#>  1 0 0  =    1
linear(1:3,2)                  #      1*x^2 + 2*y^2 + 3*z^2
#>            val
#>  0 0 2  =    3
#>  0 2 0  =    2
#>  2 0 0  =    1
lone(3)                        #      z
#>            val
#>  0 0 1  =    1
lone(2,3)                      #      y
#>            val
#>  0 1 0  =    1
one(3)                         #      1
#>            val
#>  0 0 0  =    1
zero(3)                        #      0
#> empty sparse array with 3 columns
xyz(3)                         #      xyz
#>            val
#>  1 1 1  =    1