Output Tools for Handling Symbolic Math

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

library(iomath)

Output

Conversion to `tex`

e <- Ryacas::ysym("((2*Sin(2+x))^2 + (a+b)^2)^3")
e
o <- Ryacas::tex(e)
o

$$ r o $$

All as hard brackets:

o2 <- hbtex(e)
o2

$$ r o2 $$

Customised bracketing:

o3 <- btex(e)
o3

$$ r o3 $$

An argument specifying brackets can be given (recycled):

o4 <- btex(e, 
           brackets = list(
             c("\\langle", "\\rangle"),
             c("\\{", "\\}")))
o4

$$ r o4 $$

Input

Assumptions

Variables are single letters: a-z, A-Z (e.g. $x$, $y$, $a$, $b$)
This has been done to better interpret user-input such as 2x to mean 2*x

Implicit product

make_products_explicit("2x")
make_products_explicit("2(1+2)")
make_products_explicit("x(y)")
make_products_explicit("(1+2)3") # Not allowed by definition
make_products_explicit("(1+2)x") # Is allowed
make_products_explicit("x(2+1) + sin(y)")
make_products_explicit("sin(2+1) + x(y+1)")
make_products_explicit("(2x)(y+1)")

By default, the allowed functions are those of getGroupMembers("Math"):

getGroupMembers("Math")

This can be changed:

make_products_explicit("sin(1) + cos(1)", allowed_functions = c('cos'))

Safe evaluation

By default, safe evaluation inserts inner products.

safe_eval("2.2", vars = NULL)
safe_eval("2.2x^2", vars = list(x = 0.2))
safe_eval("2.2*x^2", vars = list(x = 0.2))
safe_eval("2,2*x^2", vars = list(x = 0.2))

Efterything after first ; is ignored:

safe_eval("1; 2; 3")

Disallowed inputs

safe_eval("print(2)")

Comparing

grd <- expand.grid(x = seq(-10, 10, length.out = 10))
answer <- Ryacas::ysym("2*x^2")
compare_reply_answer(reply = "2x^2", 
                     answer = answer, 
                     compare_grid = grd)
compare_reply_answer(reply = "2.3x^2", 
                     answer = answer, 
                     compare_grid = grd)

m <- matrix(c("2+z^3", "2*sin(x)", "3*y^2", "1.1*x^2"), 2, 2)
m
ans <- Ryacas::ysym(m)
ans
grd <- expand.grid(x = seq(-10, 10, length.out = 5),
                   y = seq(-10, 10, length.out = 5),
                   z = seq(-10, 10, length.out = 5))
compare_reply_answer(reply = m, 
                     answer = ans, 
                     compare_grid = grd)
compare_reply_answer(reply = m[1, 1], 
                     answer = ans, 
                     compare_grid = grd)
m2 <- apply(m, 2, paste0, '+0.1')
m2
compare_reply_answer(reply = m2, 
                     answer = ans, 
                     compare_grid = grd)