README.Rmd

---
title: "The 'giacR' package"
output: github_document
---

*R interface to 'Giac'*

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___

Giac is a general purpose symbolic algebra software. It powers the graphical 
interface Xcas. This package allows to execute Giac commands in R. You can 
find the [documentation of Giac here](https://www-fourier.ujf-grenoble.fr/~parisse/giac/doc/en/cascmd_en/cascmd_en.html).


## Installation

```r
remotes::install_github("rstudio/chromote")
remotes::install_github("stla/giacR")
```

```{r setup, include=FALSE}
knitr::opts_chunk$set(collapse = TRUE)
```


## Initialisation of a Giac session

The 'chromote' package is used to create a Giac session. If the `find_chrome()` 
function of 'chromote' returns `NULL`, you can set the path to the Chrome 
executable (or Chromium, Brave, etc) to the environment variable 
`CHROMOTE_CHROME`. Or you can pass it to the the `Giac$new` function. 
Since the Chrome executable is in my system path, I can use 
`Sys.which("chrome")`.

```{r giacNew}
library(giacR)
giac <- Giac$new(Sys.which("chrome"))
```


## Examples 

### Elementary calculus

```{r}
giac$execute("2 + 3/7")
```


### Gröbner basis

```{r}
giac$execute("gbasis([x^3 - 2*x*y, x^2*y - 2*y^2 + x], [x, y])")
```


### Antiderivative

```{r}
giac$execute("integrate(ln(x))")
```


### Infinite sum

```{r}
giac$execute("sum(1/(n^2), n, 1, +(infinity))")
```


### Exact rational roots of a polynomial

```{r}
giac$execute("crationalroot(2*x^3 - 3*x^2 + 8*x - 12)")
```


### Solve a system of equations (and simplify the solutions)

```{r}
giac$execute(
  "apply(simplify, solve([x^2+y+z=1, x+y^2+z=1, x+y+z^2=1], [x, y, z]))"
)
```


### Determinant of a matrix with symbolic entries

```{r}
giac$execute("det([[1, 2, 3], [3/4, a, b], [c, 4, 5]])")
```


### Check whether a variable occurs in an expression

```{r}
giac$execute("has(x*y + u^2*z, u)")
```

```{r}
giac$execute("has(x*y + u^2*z, w)")
```


## Close session

```{r}
giac$close()
```


## Blog posts

- [Gröbner implicitization and the 'giacR' package](https://laustep.github.io/stlahblog/posts/giacR01.html)

- [Using implicitization to split a ball](https://laustep.github.io/stlahblog/posts/giacR02.html)