# inst/doc/sympy-object.R In caracas: Computer Algebra

```## ---- include = FALSE---------------------------------------------------------
knitr::opts_chunk\$set(
collapse = TRUE,
comment = "#>"
)

## ---- message=FALSE-----------------------------------------------------------
library(caracas)

## ---- include = FALSE---------------------------------------------------------
inline_code <- function(x) {
x
}

if (!has_sympy()) {
# SymPy not available, so the chunks shall not be evaluated
knitr::opts_chunk\$set(eval = FALSE)

inline_code <- function(x) {
deparse(substitute(x))
}
}

## -----------------------------------------------------------------------------
sympy <- get_sympy()

## -----------------------------------------------------------------------------
sympy\$diff("2*a*x", "x")
sympy\$solve("x**2 - 1", "x")

## -----------------------------------------------------------------------------
d <- sympy\$symbols('d')
h <- sympy\$symbols('h')

## -----------------------------------------------------------------------------
lam <- sympy\$symbols('lam')

## -----------------------------------------------------------------------------
area_str <- "Pi/2 * d**2 + Pi * h * d"
vol_str <- "Pi/4 * d**2 * h"
lap_str <- paste0("(", area_str, ") - lam*((", vol_str, ") - 1)")
lap <- sympy\$parsing\$sympy_parser\$parse_expr(
lap_str,
local_dict = list('d' = d, 'h' = h, 'lam' = lam))

## -----------------------------------------------------------------------------
grad <- sympy\$derive_by_array(lap, list(d, h, lam))

## -----------------------------------------------------------------------------
sol <- sympy\$solve(grad, list(d, h, lam), dict = TRUE)
sol

## -----------------------------------------------------------------------------
sol[[1]]

## -----------------------------------------------------------------------------
to_r <- function(x) {
x <- as.character(x)
x <- gsub("Pi", "pi", x, fixed = TRUE)
x <- gsub("**", "^", x, fixed = TRUE)
x <- parse(text = x)
return(x)
}

sol_d <- to_r(sol[[1]]\$d)
sol_d
eval(sol_d)
sol_h <- to_r(sol[[1]]\$h)
sol_h
eval(sol_h)

## -----------------------------------------------------------------------------
x <- sympy\$symbols('x')
x\$assumptions0
x <- sympy\$symbols('x', positive = TRUE)
x\$assumptions0
eq <- sympy\$parsing\$sympy_parser\$parse_expr("x**2 - 1",
local_dict = list('x' = x))
sympy\$solve(eq, x, dict = TRUE)

## -----------------------------------------------------------------------------
x <- sympy\$symbols('x', positive = TRUE)
eq <- sympy\$parsing\$sympy_parser\$parse_expr("x**3/3 - x",
local_dict = list('x' = x))
eq