Simple interface between Common Lisp and Maxima

eb6bf75 `Add MINF to represent minus infinity.`

~jmbr pushed to ~jmbr/maxima-interface git

- Introduction
- Installation
- LaTeX rendering
- High level interface
- Low level interface
- Contact and support

Maxima is a featureful and versatile symbolic computation package. While it runs on most (possibly all) Common Lisp (CL) implementations, using it as an external CL library is not entirely straight-forward despite the fact that the functionality exists. The purpose of this package is to provide a simple interface between Common Lisp and Maxima and facilitate its use.

The simplest way to install this package is to compile and install Maxima
from source and add the directory `/path/to/maxima/src`

to the ASDF registry.
Next, add `maxima-interface`

's directory to the ASDF registry (see ASDF
documentation
for details).

The expressions returned by Maxima can be rendered in LaTeX using either
Emacs, Jupyter notebooks, or printing the LaTeX strings to a stream. The
precise output is governed by the special variable `*latex-output*`

which can
be `:emacs`

, `:jupyter`

, or `:console`

.

The function that accomplishes this is named `latex`

. The way a symbol is
represented in LaTeX can be controlled by the `maxima::texword`

property of
the symbol's property list (see examples below).

LaTeX can be rendered in a resizable fashion within Emacs using `tex2svg`

in
order to convert LaTeX strings to SVG files. This requires the custom patch
to SLIME included in the file slime.patch as well as the
`tex2svg`

utility
from MathJax.

Using
`common-lisp-jupyter`

it
is easy to interface with a Jupyter notebook. Just run the Common Lisp kernel
and start using `maxima-interface`

.

This is the default setting. It outputs the LaTeX string corresponding to the given expression.

The aim of this interface is to translate and evaluate expressions back and forth from Common Lisp to Maxima's internal representation as seamlessly as possible.

`diff`

Takes the (partial) derivative of an s-expression with regard to a variable, possibly more than once.

```
MAXIMA-INTERFACE-USER> (diff '(sin x) 'x)
(COS X)
```

```
MAXIMA-INTERFACE-USER> (diff '(* (expt x 2) (expt y 3)) 'x 2)
(* 2 (EXPT Y 3))
```

`integrate`

Evaluates the definite or indefinite integral of an s-expression with respect to a symbol.

```
MAXIMA-INTERFACE-USER> (integrate '(* (exp x) (sin (exp x))) 'x)
(* -1 (COS (EXPT (EXP 1) X)))
```

```
MAXIMA-INTERFACE-USER> (integrate '(/ x) 'x 1 '(exp 1))
1
```

`expand`

Expands products.

```
MAXIMA-INTERFACE-USER> (expand '(expt (+ x y) 2))
(+ (EXPT X 2) (* 2 X Y) (EXPT Y 2))
```

`simplify`

Applies trigonometric and rational simplifications.

```
MAXIMA-INTERFACE-USER> (simplify '(/ (1- (1+ x)) 1))
X
```

```
MAXIMA-INTERFACE-USER> (simplify '(+ (expt (cos x) 2) (expt (sin x) 2)))
1
```

`limit`

Takes the limit of an s-expression with regard to a symbol.

```
MAXIMA-INTERFACE-USER> (limit '(/ (+ (expt x 3) x) (* 2 (expt x 5))) 'x 'inf)
0
```

```
MAXIMA-INTERFACE-USER> (limit '(/ (sin x) x) 'x 0 'plus)
1
```

`factor`

Factorize an expression.

```
MAXIMA-INTERFACE-USER> (factor '(+ (expt x 2) (* 2 x y) (expt y 2)))
(EXPT (+ X Y) 2)
```

```
MAXIMA-INTERFACE-USER> (factor '(- (expt x 2) (expt y 2)))
(* -1 (+ (* -1 X) Y) (+ X Y))
```

`maxima-init`

This function is called when the module is loaded. It instructs Maxima to set the path names for the packages that will be loaded on-demand when carrying out different types of operations (e.g., simplification, eigendecompositions, etc.).

`maxima-run`

Evaluates a Maxima expression passed as a string and prints the result.

```
MAXIMA-INTERFACE-USER> (maxima-run "assume(sigma > 0)$" :display2d t)
[sigma > 0]
```

```
MAXIMA-INTERFACE-USER> (maxima-run "integrate(exp(-x^2/(2*sigma^2)), x, -inf, inf);" :display2d t)
sqrt(2) sqrt(%pi) sigma
```

```
MAXIMA-INTERFACE-USER> (maxima-run "exp(-x^2/(2*sigma^2));" :display2d nil :return-expression t)
%e^-(x^2/(2*sigma^2))
((MAXIMA::MEXPT MAXIMA::SIMP) MAXIMA::$%E
((MAXIMA::MTIMES MAXIMA::SIMP) ((MAXIMA::RAT MAXIMA::SIMP) -1 2)
((MAXIMA::MEXPT MAXIMA::SIMP) MAXIMA::$SIGMA -2)
((MAXIMA::MEXPT MAXIMA::SIMP) MAXIMA::$X 2)))
```

```
MAXIMA-INTERFACE-USER> (maxima-run "trigsimp(cos(x)^2 + sin(x)^2);")
1
```

`maxima-read`

Takes a Maxima expression (represented as a string) as input and returns its internal representation in (Maxima) Lisp.

```
MAXIMA-INTERFACE-USER> (maxima-read "x^2$")
((MAXIMA::MEXPT) MAXIMA::$X 2)
```

`maxima-eval`

Evaluates the internal Lisp representation of a Maxima expression and returns the internal Lisp representation of its result.

```
MAXIMA-INTERFACE-USER> (maxima-eval '((maxima::$expand)
((maxima::mexpt) ((maxima::mplus) maxima::$x maxima::$y) 2)))
((MAXIMA::MPLUS MAXIMA::SIMP) ((MAXIMA::MEXPT MAXIMA::SIMP) MAXIMA::$X 2)
((MAXIMA::MTIMES MAXIMA::SIMP) 2 MAXIMA::$X MAXIMA::$Y)
((MAXIMA::MEXPT MAXIMA::SIMP) MAXIMA::$Y 2))
```

`maxima-print`

Prints the internal Lisp representation of a Maxima expression in
human-readable form to `output-stream`

(which is `*standard-output*`

by
default).

The keyword argument `display2d`

is a boolean indicating whether the
representation should be done in 2D or not. The keyword argument
`return-expression`

is another boolean that determines whether the original
expression should be returned by `maxima-print`

.

```
MAXIMA-INTERFACE-USER> (maxima-print '((maxima::%integrate maxima::simp)
((maxima::mexpt) maxima::$%e
((maxima::mtimes) -1 ((maxima::mexpt) maxima::$x 2)))
maxima::$x 0 maxima::$inf)
:display2d t)
inf
/ 2
[ (- 1) x
I %e dx
]
/
0
```

The document Macsymaâ€™s General Simplifier: Philosophy and Operation by R. Fateman is a useful guide to better understand the inner workings of Maxima.

It is sometimes useful to execute `:lisp (trace meval)`

inside a regular
Maxima session (i.e., the REPL you get when invoking `maxima`

from the
command line) to see how commands are processed.

Subscribe to the
`maxima-interface-devel`

mailing list for development discussion and to send patches related to the
project. For help sending patches to this list, please consult
git-send-email.io.