It is with great pleasure that I can announce that `Ryacas`

version 1.0.0 is
now released to CRAN (https://cran.r-project.org/package=Ryacas).
I wish to thank all co-authors:
Rob Goedman, Gabor Grothendieck, Søren Højsgaard, Grzegorz Mazur, Ayal Pinkus.

It means that you can install the package by (possible after binaries have been built):

`install.packages("Ryacas")`

Followed by:

`library(Ryacas)`

(The source code is available at https://github.com/mikldk/ryacas/.)

Now you have the `yacas`

computer algebra system fully available!
See documentation at https://yacas.readthedocs.io/en/latest/.
`Ryacas`

allows one to send unprocessed yacas strings and certain other R objects to yacas process from R and get back the result. It also has facilities for manipulating yacas strings and R expressions destined for yacas processing.

It can be used for arbitrary-precision arithmetic, symbolic math, ASCII pretty printing and translating R to TeX.

Below I will demonstrate a few ways to use `Ryacas`

, but I also refer to a number of blog posts that I have made already:

- Major update of
`Ryacas`

(R Interface to the Yacas Computer Algebra System) - How much pizza and how much frozen yogurt?
- How much pizza and how much frozen yogurt? …with Gröbner bases
- Correlation is not transitive, in general at least

## Examples of usage

I will just give a few examples and then refer to the package webpage especially the vignettes:

- Getting started
- The low-level interface
- The high-level (symbol) interface
- (Note there are more vignettes than these.)

There are two main functions in the low-level interface:

`yac_str(x)`

: Evaluate`yacas`

command`x`

(a string) and get result as**string/character**.`yac_expr(x)`

: Evaluate`yacas`

command`x`

(a string) and get result as an.`R`

expression

And one main function in the high-level interface:

`yac_symbol(x)`

: Takes a`yacas`

command (e.g.`x`

,`2*a`

), or an`R`

vector or matrix and creates a`yac_symbol`

Simple examples of the low-level interface:

```
yac_str("x+x+x+x")
## [1] "4*x"
yac_str("Factor(x^2+x-6)")
## [1] "(x-2)*(x+3)"
yac_str("D(x) x^2 + 4*x")
## [1] "2*x+4"
ex <- yac_expr("D(x) x^2 + 4*x")
ex
## expression(2 * x + 4)
eval(ex, list(x = 2))
## [1] 8
yac_str("Limit(x, 1) (x^2 - 1)/(x - 1)")
## [1] "2"
yac_str("Sum(n, 1, Infinity, (1/2)^n)")
## [1] "1"
yac_str("Fibonacci(10)")
## [1] "55"
yac_str("Sum(n, 1, 10, Fibonacci(n))")
## [1] "143"
yac_str("TeXForm(x^2 - 1)")
## [1] "x ^{2} - 1"
yac_str("Solve(a*x^2 + b*x + c == 0, x)")
## [1] "{x==(Sqrt(b^2-4*a*c)-b)/(2*a),x==(-(b+Sqrt(b^2-4*a*c)))/(2*a)}"
```

Simple examples of the high-level interface:

```
x <- yac_symbol("x")
2*x^2 - 5
## [1] 2*x^2-5
c(-2, 5)*x
## [1] {(-2)*x,5*x}
as_r(c(-2, 5)*x)
## expression(c(-2 * x, 5 * x))
A <- outer(0:3, 1:4, "-") + diag(2:5)
a <- 1:4
B <- yac_symbol(A)
B
## {{ 1, -2, -3, -4},
## { 0, 2, -2, -3},
## { 1, 0, 3, -2},
## { 2, 1, 0, 4}}
b <- yac_symbol(a)
b
## [1] {1,2,3,4}
B %*% b
## [1] {-28,-14,2,20}
t(B)
## {{ 1, 0, 1, 2},
## {-2, 2, 0, 1},
## {-3, -2, 3, 0},
## {-4, -3, -2, 4}}
exp(B)
## {{ Exp(1), Exp(-2), Exp(-3), Exp(-4)},
## { 1, Exp(2), Exp(-2), Exp(-3)},
## { Exp(1), 1, Exp(3), Exp(-2)},
## { Exp(2), Exp(1), 1, Exp(4)}}
as_r(exp(B))
## [,1] [,2] [,3] [,4]
## [1,] 2.718282 0.1353353 0.04978707 0.01831564
## [2,] 1.000000 7.3890561 0.13533528 0.04978707
## [3,] 2.718282 1.0000000 20.08553692 0.13533528
## [4,] 7.389056 2.7182818 1.00000000 54.59815003
B[, 2:3]
## {{-2, -3},
## { 2, -2},
## { 0, 3},
## { 1, 0}}
B[upper.tri(B)] <- 1
B
## {{1, 1, 1, 1},
## {0, 2, 1, 1},
## {1, 0, 3, 1},
## {2, 1, 0, 4}}
2*B - B
## {{1, 1, 1, 1},
## {0, 2, 1, 1},
## {1, 0, 3, 1},
## {2, 1, 0, 4}}
B %*% solve(B)
## {{1, 0, 0, 0},
## {0, 1, 0, 0},
## {0, 0, 1, 0},
## {0, 0, 0, 1}}
solve(B %*% t(B))
## {{ 363/98, (-123)/98, (-87)/98, (-61)/98},
## {(-123)/98, 34/49, 23/98, 15/98},
## { (-87)/98, 23/98, 33/98, 13/98},
## { (-61)/98, 15/98, 13/98, 17/98}}
```

And it even works with variables:

```
D <- B
D[2, 3] <- "x"
D
## {{1, 1, 1, 1},
## {0, 2, x, 1},
## {1, 0, 3, 1},
## {2, 1, 0, 4}}
d <- b
d[2] <- "x"
d
## [1] {1,x,3,4}
D %*% d
## [1] {x+8,5*x+4,14,x+18}
ex <- as_r(D %*% d)
ex
## expression(c(x + 8, 5 * x + 4, 14, x + 18))
eval(ex, list(x = 2))
## [1] 10 14 14 20
```