In ggrothendieck/ryacas: R Interface to the 'Yacas' Computer Algebra System

# - \usepackage[fontsize=11pt]{scrextend}
knitr::opts_chunk$set(echo = TRUE)

library(Ryacas)
packageVersion("Ryacas")

\btwocol

Sums

k <- ysym("k")
s <- sum(1/k^2, "k", 1, Inf)
s
as_r(s)
tex(s)

Also:

Integrals (integrate())
Limits (lim())

\vfill\null

\columnbreak

Solving systems of non-linear equations

x <- ysym("x"); y <- ysym("y")
lhs <- c(3*x*y - y, x)
rhs <- c(-5*x, y + 4)

\vspace{-1em}

[ r tex(lhs[[1]]) = r tex(rhs[[1]]) \quad \text{and} \quad r tex(lhs[[2]]) = r tex(rhs[[2]]) ]

sol <- solve(lhs, rhs, c("x", "y")) 
sol
y_rmvars(sol)

\etwocol

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