Multivariate polynomials are interesting and useful objects. Here I
present the mvp package which hopefully improves upon previous R
functionality provided by the packages multipol, mpoly, and spray.
The mvp package follows mpoly in using a symbolic, rather than
numeric, representation of a multivariate polynomial; but it offers
speed advantages over mpoly. mvp uses the excellent print and
coercion methods of the mpoly package. mvp includes some pleasing
substitution idiom not found elsewhere; it is theoretically comparable
in speed to the spray package and I present some timings in the
package vignette.
The mvp package uses C++’s STL map class for efficiency, which has
the downside that the order of the terms, and the order of the symbols
within each term, is undefined. This does not matter as the mathematical
value of a multivariate polynomial is unaffected by reordering; and the
print method (taken from mpoly) does a good job in producing
human-readable output.
You can install the released version of mvp from
CRAN with:
# install.packages("mvp") # uncomment this to install the package
library("mvp")Creating a multivariate polynomial is straightforward:
X <- as.mvp("1 + a^2 + a*b*c^3")
X
#> mvp object algebraically equal to
#> 1 + a b c^3 + a^2and arithmetic operations work as expected:
Y <- as.mvp("12*a^2 + b - c^2 + 4*d")
X+Y
#> mvp object algebraically equal to
#> 1 + a b c^3 + 13 a^2 + b - c^2 + 4 d
X-3*Y
#> mvp object algebraically equal to
#> 1 + a b c^3 - 35 a^2 - 3 b + 3 c^2 - 12 d
X^2
#> mvp object algebraically equal to
#> 1 + 2 a b c^3 + 2 a^2 + a^2 b^2 c^6 + 2 a^3 b c^3 + a^4Substitution uses the subs() function:
X
#> mvp object algebraically equal to
#> 1 + a b c^3 + a^2
subs(X,a=1)
#> mvp object algebraically equal to
#> 2 + b c^3
subs(X,a=1,b=2)
#> mvp object algebraically equal to
#> 2 + 2 c^3
subs(X,a=1,b=2,c=3)
#> [1] 56
subs(X+Y,a="1+x^2",b="x+y",c=0)
#> mvp object algebraically equal to
#> 14 + 4 d + x + 26 x^2 + 13 x^4 + yFor more detail, see the package vignette
vignette("mvp")