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output: github_document

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, the dependencies will be downloaded at build time, and you can install directly with devtools.

Please report any problem installing the package on your system.

library(symengine)
#> SymEngine Version: 0.6.0
#>  _____           _____         _         
#> |   __|_ _ _____|   __|___ ___|_|___ ___ 
#> |__   | | |     |   __|   | . | |   | -_|
#> |_____|_  |_|_|_|_____|_|_|_  |_|_|_|___|
#>       |___|               |___|

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.