A sparse multivariate polynomial

A sparse multivariate polynomial inspired by Kahle (2013)

Usage

kahle(n = 26, r = 1, p = 1, coeffs = 1, symbols = letters)

Arguments

n

Number of different symbols to use

r

Number of symbols in a single term

p

Power of each symbol in each terms

coeffs

Coefficients of the terms

symbols

Alphabet of symbols

References

David Kahle 2013. “mpoly: multivariate polynomials in R”. R Journal, volume 5/1.

Author

Robin K. S. Hankin

See also

special

Examples

kahle()  # a+b+...+z
#> mvp object algebraically equal to
#> a + b + c + d + e + f + g + h + i + j + k + l + m + n + o + p + q + r + s + t +
#> u + v + w + x + y + z
kahle(r=2,p=1:2)  # Kahle's original example
#> mvp object algebraically equal to
#> a z^2 + a^2 b + b^2 c + c^2 d + d^2 e + e^2 f + f^2 g + g^2 h + h^2 i + i^2 j +
#> j^2 k + k^2 l + l^2 m + m^2 n + n^2 o + o^2 p + p^2 q + q^2 r + r^2 s + s^2 t +
#> t^2 u + u^2 v + v^2 w + w^2 x + x^2 y + y^2 z

## example where mvp runs faster than spray (mvp does not need a 200x200 matrix):
k <- kahle(200,r=3,p=1:3,symbols=paste("x",sprintf("%02d",1:200),sep=""))
system.time(ignore <- k^2)
#>    user  system elapsed 
#>   1.250   0.016   1.267 
#system.time(ignore <- mvp_to_spray(k)^2)   # needs spray package loaded