symengine is an R interface to the SymEngine C++
library for symbolic
computation.
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#> _____ _____ _ #> | __|_ _ _____| __|___ ___|_|___ ___ #> |__ | | | | __| | . | | | -_|#> |_____|_ |_|_|_|_____|_|_|_ |_|_|_|___|#> |___| |___|Also check the documentation site with built vignettes and help pages at http://symengine.marlin.pub.
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^2Substitue 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)^2Second 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^2Solve 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)) )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 5.134714The next prime number greater than 2^400.
n<- nextprime(S(~2^400))
n#> (Integer) 2582249878086908589655919172003011874329705792829223512830659356540647622016841194629645353280137831435903171972747493557The greatest common divisor between the prime number and 42.
GCD(n, 42)
#> (Integer) 1The binomial coefficient (2^30 ¦ 5).
choose(S(~2^30), 5L)
#> (Integer) 11893730661780666387808571314613824587300864Pi “computed” to 400-bit precision number.
if (symengine_have_component("mpfr"))
evalf(Constant("pi"), bits=400)
#> (RealMPFR,prec400) 3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066x+y== S("x + y")
#> [1] TRUEx+y!= S("x + y")
#> [1] FALSEsin(x)/cos(x)
#> (Mul) sin(x)/cos(x)
tan(x) == sin(x)/cos(x) # Different internal representation#> [1] FALSEThis 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.