Solve nonlinear equation symbolically in R with `Ryacas` package or an alternative

Out of pure curiosity I'm interested if there is a function/package that allows to solve simple nonlinear equations in R?

Let's say I want to (symbolically) solve 0 = C + 1/x^2. The expected result for the above example is x = sqrt(-1/-C)

I tried the Ryacas package:

library("Ryacas")
Solve(yacas("C+1/x^2"))

That returns an error:

Error in Sym("Solve(", x, ",", y, ")") : argument "y" is missing, with no default

So I did:

Solve(yacas("C+1/x^2"), 0)

which returns nothing useful:

Yacas vector:
character(0)

I followed the instructions on ?yacas to install yacas. It seems as if yacas works, demo(Ryacas) generates output. Here is the first portion:

    demo(Ryacas)
    ---- ~~~~~~

Type  <Return>   to start : 

>   x <- -3 + (0:600)/300

>   exp0 <- expression(x ^ 3)

>   exp1 <- expression(x^2 + 2 * x^2)

>   exp2 <- expression(2 * exp0)

>   exp3 <- expression(6 * pi * x)

>   exp4 <- expression((exp1 * (1 - sin(exp3))) / exp2)

>   res1 <- yacas(exp4); print(res1)
expression(3 * (x^2 * (1 - sin(6 * (x * pi))))/(2 * x^3))

>   exp5 <- expression(Simplify(exp4))

>   res2 <- yacas(exp5); print(res2)
expression(3 * (1 - sin(6 * (x * pi)))/(2 * x))

>   plot(x, eval(res2[[1]]), type="l", col="red")

Any hints?

Solution

We can use package Ryacas (thanks for the hint @Bhas) an interface to the library yacas for symbolic equation solving:

library(Ryacas)

expr <- yacas("C+1/x^2 == 0")  #Generate yacas expression | note the double equals!

solv <- Solve(expr,"x") # Solve the expression for x
[1] x == root(abs(1/C), 2) * complex_cartesian(cos(argument(-1/C)/2), sin(argument(-1/C)/2))                      
[2] x == root(abs(1/C), 2) * complex_cartesian(cos((argument(-1/C) + 2 * pi)/2), sin((argument(-1/C) + 2 * pi)/2))

Yacas obviously generates a complex solution because for positive values of C this equation only has complex roots (square-root of a negative-number). Two solutions is also expected, since we have a quadratic equation. The complex_cartesian part refers to the rotation in the complex plane, that is dependend on the value of C (basically the value of a in a complex number of type z=a*i + b).