Interface to the 'SymEngine' Library.
symengine
symengine is an R interface to the SymEngine C++ library for symbolic computation.
Installation
There are some dependencies needed on Unix systems. You may install them with
zypper install cmake gmp-devel mpfr-devel mpc-devel ## openSUSE
dnf install cmake gmp-devel mpfr-devel libmpc-devel ## Fedora
apt install cmake libgmp-dev libmpfr-dev libmpc-dev ## Debian
brew install cmake gmp mpfr libmpc ## Mac OS
Then you can install the R package with
devtools::install_github("symengine/symengine.R")
On Windows, you will need to install Rtools42 for building the package from source.
Please report any problem installing the package on your system.
library(symengine)
#> SymEngine Version: 0.9.0
#> _____ _____ _
#> | __|_ _ _____| __|___ ___|_|___ ___
#> |__ | | | | __| | . | | | -_|
#> |_____|_ |_|_|_|_____|_|_|_ |_|_|_|___|
#> |___| |___|
Usage
Also check the documentation site with built vignettes and help pages at http://symengine.marlin.pub.
Manipulating Symbolic Expressions
use_vars(x, y, z)
#> Initializing 'x', 'y', 'z'
expr <- (x + y + z) ^ 2L - 42L
expand(expr)
#> (Add) -42 + 2*x*y + 2*x*z + 2*y*z + x^2 + y^2 + z^2
Substitue z as a and y as x^2.
a <- S("a")
expr <- subs(expr, z, a)
expr <- subs(expr, y, x^2L)
expr
#> (Add) -42 + (a + x + x^2)^2
Second derivative of expr with regards to x:
d1_expr <- D(expr, "x")
d2_expr <- D(d1_expr, "x")
expand(d2_expr)
#> (Add) 2 + 4*a + 12*x + 12*x^2
Solve the equation of d2_expr == 0 with regards to x.
solutions <- solve(d2_expr, "x")
solutions
#> VecBasic of length 2
#> V( -1/2 + (-1/2)*sqrt(1 + (-1/3)*(2 + 4*a)), -1/2 + (1/2)*sqrt(1 + (-1/3)*(2 + 4*a)) )
Numerically Evaluate Symbolic Expressions
For the two solutions above, we can convert them into a function that gives numeric output with regards to given input.
func <- as.function(solutions)
ans <- func(a = -100:-95)
colnames(ans) <- c("Solution1", "Solution2")
ans
#> Solution1 Solution2
#> [1,] -6.280715 5.280715
#> [2,] -6.251811 5.251811
#> [3,] -6.222762 5.222762
#> [4,] -6.193564 5.193564
#> [5,] -6.164215 5.164215
#> [6,] -6.134714 5.134714
Numbers
The next prime number greater than 2^400.
n <- nextprime(S(~ 2 ^ 400))
n
#> (Integer) 2582249878086908589655919172003011874329705792829223512830659356540647622016841194629645353280137831435903171972747493557
The greatest common divisor between the prime number and 42.
GCD(n, 42)
#> (Integer) 1
The binomial coefficient (2^30 ¦ 5).
choose(S(~ 2^30), 5L)
#> (Integer) 11893730661780666387808571314613824587300864
Pi “computed” to 400-bit precision number.
if (symengine_have_component("mpfr"))
evalf(Constant("pi"), bits = 400)
#> (RealMPFR,prec400) 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066
Object Equality
x + y == S("x + y")
#> [1] TRUE
x + y != S("x + y")
#> [1] FALSE
sin(x)/cos(x)
#> (Mul) sin(x)/cos(x)
tan(x) == sin(x)/cos(x) # Different internal representation
#> [1] FALSE
Acknowledgement
This project was a Google Summer of Code project under the organization of The R Project for Statistical Computing in 2018. The student was Xin Chen, mentored by Jialin Ma and Isuru Fernando.