CODEWITHSUNDEEP
revalsubstitutionyacas
CivilEngineerUK
CivilEngineerUK

Reputation: 63

Ryacas substitute but don't simplify or evaluate

I am using the Ryacas package in R and am trying to substitute variables for values but not simplify or solve the equation to show the working out. I have searched Stackoverflow, read the Ryacas documentation and have attempted to find this in the Yacas manual but have so far come up short. I think I am looking to turn simplification off to get the substituted equation and then on again to provide the final result.

Here is an example which provides only the result rather than the working:

library(Ryacas)
# a <- 2
# b <- 3
# c <- 4
eq <- ysym(('(a * b) / c'))

solution <- with_value(with_value(with_value(eq, 'a', 2), 'b', 3), 'c', 4)
tex(solution)
# "\\frac{3}{2}"

What I am trying to get as an output is:

# working out
# "\\frac{2 \times 3}{4}

as well as the actual solution:

# solution
# "\\frac{3}{2}"

Does anyone know whether there is a solution to this problem such as passing a command to yacas through yac_str or similar. I have tried translating to latex using the tex() command and then substituting after though the multiplication operators are removed and this means I need to find and replace them which becomes nasty when dealing with symbolics:

tex(eq)
# "\\frac{a b}{c}"

# substituting string values using stringi requires additional  
# work to deal with the missing `*` between `a` and `b`
# "\\frac{2 3}{4}"

Whilst this can be done for simple expressions, there are numerous exceptions such as the variables a and c being present in \\frac etc.

I have also tried the TexForm command and substitute in various guises but am still not able to capture the unsimplified and unevaluated equation:

y_fn(substitute(with_value(eq, 'a', 2)), "TeXForm")
# "\\frac{2 b}{c}"

eval(substitute(with_value(eval(substitute(with_value(eq, 'a', 2))), 'b', 3)))
# y: 6/c

Any help appreciated.

Upvotes: 1

Views: 302

Answers (1)

G. Grothendieck
G. Grothendieck

Reputation: 269905

You might need to customize this some more but this general approach can work if you are willing to do that.

We translate words to their values using gsubfn and handle the \times part at the end with gsub. Note that frac is not modified because we are matching words and frac it is not a word in the list given in the second arg to gsubfn.

library(magrittr)
library(gsubfn)
library(Ryacas)

eq <- ysym(('(a * b) / c'))

eq %>%
  tex %>%
  gsubfn("(\\w+)", list(a = 2, b = 3, c = 4), .) %>%
  gsub("(\\d) (\\d)", "\\1 \\\\times \\2", .)
## [1] "\\frac{2 \\times 3}{4}"

Added

Take the first three code examples when searching for [r] Ryacas in stackoverflow and it worked on all of them. Note that these used the original version of Ryacas which is currently called Ryacas0 so I used that.

library(Ryacas0)
library(gsubfn)
library(magrittr)

tex_sub <- function(.x, ...) {
  .x %>%
    gsubfn("(\\w+)", list(...), .) %>%
    gsub("(\\d) (\\d)", "\\1 \\\\times \\2", .)
}

# https://stackoverflow.com/questions/21858668/symbolic-matrix-multiplication-by-ryacas
x <- Sym("x")
mat1 <- List(
  List(x, 2),
  List(x^3, x))

mat2 <- List(
  List(x, x),
  List(3, 6 * x))

tt <- TeXForm(mat1 * mat2)
tex_sub(tt, x = 1)

###

# https://stackoverflow.com/questions/22739173/matrix-transpose-in-ryacas
u=Sym("u")
v=Sym("v")
w=Sym("w")
DG=List(List(w-v), List(u-w), List(v-u))
tt2 <- TeXForm(DG)
tex_sub(tt2, u = 2, v = 3, w = 4)

###

# https://stackoverflow.com/questions/49572184/how-to-derivate-using-ryacas

x <- Sym("x")
P <- Sym(1)
for (k in 1:3) {
  P <- Simplify((1+k*x)*P + x*(1-x)*deriv(P, x))
  print(P)
}
tt3 <- TeXForm(P)
tex_sub(tt3, x = 10)

Upvotes: 1

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