mirror of
https://github.com/LCTT/TranslateProject.git
synced 2024-12-26 21:30:55 +08:00
306 lines
10 KiB
Markdown
306 lines
10 KiB
Markdown
|
[#]: subject: (Getting started with Maxima in Fedora Linux)
|
|||
|
|
[#]: via: (https://fedoramagazine.org/getting-started-with-maxima-in-fedora-linux/)
|
|||
|
|
[#]: author: (Jagat Kafle https://fedoramagazine.org/author/jkafle/)
|
|||
|
|
[#]: collector: (lujun9972)
|
|||
|
|
[#]: translator: ( )
|
|||
|
|
[#]: reviewer: ( )
|
|||
|
|
[#]: publisher: ( )
|
|||
|
|
[#]: url: ( )
|
|||
|
|
|
|||
|
|
Getting started with Maxima in Fedora Linux
|
|||
|
|
======
|
|||
|
|
|
|||
|
|
![][1]
|
|||
|
|
|
|||
|
|
Photo by [Roman Mager][2] on [Unsplash][3]
|
|||
|
|
|
|||
|
|
[Maxima][4] is an open source computer algebra system (CAS) with powerful symbolic, numerical, and graphical capabilities. You can perform matrix operations, differentiation, integration, solve ordinary differential equations as well as plot functions and data in two and three dimensions. As such, it is helpful for anyone interested in science and math. This article goes through installing and using Maxima in Fedora Linux.
|
|||
|
|
|
|||
|
|
### Installing Maxima
|
|||
|
|
|
|||
|
|
Maxima is a command line system. You can install Maxima from the official Fedora repository using the following command:
|
|||
|
|
|
|||
|
|
```
|
|||
|
|
sudo dnf install maxima
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
You can then use Maxima from the terminal by invoking the command _maxima_.
|
|||
|
|
|
|||
|
|
![Maxima session in gnome terminal in Fedora Linux 34][5]
|
|||
|
|
|
|||
|
|
### Installing wxMaxima
|
|||
|
|
|
|||
|
|
[wxMaxima][6] is a document based interface for Maxima. To install it in Fedora Linux, use the following command:
|
|||
|
|
|
|||
|
|
```
|
|||
|
|
sudo dnf install wxmaxima
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
You can launch wxMaxima either by invoking the command _wxmaxima_ in the terminal or clicking its application icon from the app grid or menu.
|
|||
|
|
|
|||
|
|
![wxMaxima session in Fedora Linux 34][7]
|
|||
|
|
|
|||
|
|
### Basic Commands
|
|||
|
|
|
|||
|
|
After calling _maxima_, you should see terminal output as in the [figure above][8].
|
|||
|
|
|
|||
|
|
The _(%i1)_ is the input label where you enter the commands. Command in Maxima is an expression that can span over many lines and is closed with a semicolon (;). The _o_ labels denote the outputs. Comments are enclosed between _/*_ and _*/_. You can use the special symbol percent _(%)_ to refer to the immediately preceding result computed by Maxima. If you don’t want to print a result, you can finish your command with _$_ instead of _;_. Here are basic arithmetic commands in Maxima:
|
|||
|
|
|
|||
|
|
```
|
|||
|
|
(%i1) (19 + 7)/(52 - 2 * 13);
|
|||
|
|
(%o1) 1
|
|||
|
|
(%i2) 127 / 5;
|
|||
|
|
127
|
|||
|
|
(%o2) ---
|
|||
|
|
5
|
|||
|
|
(%i3) float (127 / 5);
|
|||
|
|
(%o3) 25.4
|
|||
|
|
(%i4) 127.0 / 5;
|
|||
|
|
(%o4) 25.4
|
|||
|
|
(%i5) sqrt(2.0);
|
|||
|
|
(%o5) 1.414213562373095
|
|||
|
|
(%i6) sin(%pi/2);
|
|||
|
|
(%o6) 1
|
|||
|
|
(%i7) abs(-12);
|
|||
|
|
(%o7) 12
|
|||
|
|
(%i8) 2+3%i + 5 - 4%i; /*complex arithmetic*/
|
|||
|
|
(%o8) 7 - %i
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
To end the Maxima session, type the command:
|
|||
|
|
|
|||
|
|
```
|
|||
|
|
quit();
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
### Algebra
|
|||
|
|
|
|||
|
|
Maxima can expand and factor polynomials:
|
|||
|
|
|
|||
|
|
```
|
|||
|
|
(%i1) (x+y)^3 + (x+y)^2 + (x+y);
|
|||
|
|
3 2
|
|||
|
|
(%o1) (y + x) + (y + x) + y + x
|
|||
|
|
(%i2) expand(%);
|
|||
|
|
3 2 2 2 3 2
|
|||
|
|
(%o2) y + 3 x y + y + 3 x y + 2 x y + y + x + x + x
|
|||
|
|
(%i3) factor(%);
|
|||
|
|
2 2
|
|||
|
|
(%o3) (y + x) (y + 2 x y + y + x + x + 1)
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
To substitute _y_ with _z_ and _x_ with _5,_ refer the output label above and use the following command:
|
|||
|
|
|
|||
|
|
```
|
|||
|
|
(%i4) %o3, y=z, x=5;
|
|||
|
|
2
|
|||
|
|
(%o4) (z + 5) (z + 11 z + 31)
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
You can easily manipulate trigonometric identities:
|
|||
|
|
|
|||
|
|
```
|
|||
|
|
(%i1) sin(x) * cos(x+y)^2;
|
|||
|
|
2
|
|||
|
|
(%o1) sin(x) cos (y + x)
|
|||
|
|
(%i2) trigexpand(%);
|
|||
|
|
2
|
|||
|
|
(%o2) sin(x) (cos(x) cos(y) - sin(x) sin(y))
|
|||
|
|
(%i3) trigreduce(%o1);
|
|||
|
|
sin(2 y + 3 x) - sin(2 y + x) sin(x)
|
|||
|
|
(%o3) ----------------------------- + ------
|
|||
|
|
4 2
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
You can also solve algebraic equations in one or more variables:
|
|||
|
|
|
|||
|
|
```
|
|||
|
|
(%i1) solve(x^2+5*x+6);
|
|||
|
|
(%o1) [x = - 3, x = - 2]
|
|||
|
|
(%i2) solve(x^3 + 1);
|
|||
|
|
sqrt(3) %i - 1 sqrt(3) %i + 1
|
|||
|
|
(%o2) [x = - --------------, x = --------------, x = - 1]
|
|||
|
|
2 2
|
|||
|
|
(%i3) eqns: [x^2 + y^2 = 9, x + y = 3];
|
|||
|
|
2 2
|
|||
|
|
(%o3) [y + x = 9, y + x = 3]
|
|||
|
|
(%i4) solve(eqns, [x,y]);
|
|||
|
|
(%o4) [[x = 3, y = 0], [x = 0, y = 3]]
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
### Calculus
|
|||
|
|
|
|||
|
|
Define _f_ to be a function of _x._ You can then find the limit, derivative and integral of the function:
|
|||
|
|
|
|||
|
|
```
|
|||
|
|
(%i1) f: x^2;
|
|||
|
|
2
|
|||
|
|
(%o1) x
|
|||
|
|
(%i2) limit(f,x,0);
|
|||
|
|
(%o2) 0
|
|||
|
|
(%i3) limit(1/f,x,0);
|
|||
|
|
(%o3) inf
|
|||
|
|
(%i4) diff(f, x);
|
|||
|
|
(%o4) 2 x
|
|||
|
|
(%i5) integrate(f, x);
|
|||
|
|
3
|
|||
|
|
x
|
|||
|
|
(%o5) --
|
|||
|
|
3
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
To find definite integrals, slightly modify the syntax above.
|
|||
|
|
|
|||
|
|
```
|
|||
|
|
(%i6) integrate(f, x, 1, inf);
|
|||
|
|
defint: integral is divergent.
|
|||
|
|
-- an error. To debug this try: debugmode(true);
|
|||
|
|
(%i7) integrate(1/f, x, 1, inf);
|
|||
|
|
(%o7) 1
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
Maxima can perform Taylor expansion. Here’s the Taylor expansion of sin(x) up to order 5 terms.
|
|||
|
|
|
|||
|
|
```
|
|||
|
|
(%i1) taylor(sin(x), x, 0, 5);
|
|||
|
|
3 5
|
|||
|
|
x x
|
|||
|
|
(%o1)/T/ x - -- + --- + . . .
|
|||
|
|
6 120
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
To represent derivatives in unevaluated form, use the following syntax.
|
|||
|
|
|
|||
|
|
```
|
|||
|
|
(%i2) 'diff(y,x);
|
|||
|
|
dy
|
|||
|
|
(%o2) --
|
|||
|
|
dx
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
The ode2 function can solve first and second order ordinary differential equations (ODEs).
|
|||
|
|
|
|||
|
|
```
|
|||
|
|
(%i1) 'diff(y,x,2) + y = 0;
|
|||
|
|
2
|
|||
|
|
d y
|
|||
|
|
(%o1) --- + y = 0
|
|||
|
|
2
|
|||
|
|
dx
|
|||
|
|
(%i2) ode2(%o1,y,x);
|
|||
|
|
(%o2) y = %k1 sin(x) + %k2 cos(x)
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
### Matrix Operations
|
|||
|
|
|
|||
|
|
To enter a matrix, use the entermatrix function. Here’s an example of a general 2×2 matrix.
|
|||
|
|
|
|||
|
|
```
|
|||
|
|
(%i1) A: entermatrix(2,2);
|
|||
|
|
Is the matrix 1. Diagonal 2. Symmetric 3. Antisymmetric 4. General
|
|||
|
|
Answer 1, 2, 3 or 4 :
|
|||
|
|
4;
|
|||
|
|
Row 1 Column 1:
|
|||
|
|
1;
|
|||
|
|
Row 1 Column 2:
|
|||
|
|
2;
|
|||
|
|
Row 2 Column 1:
|
|||
|
|
3;
|
|||
|
|
Row 2 Column 2:
|
|||
|
|
4;
|
|||
|
|
Matrix entered.
|
|||
|
|
[ 1 2 ]
|
|||
|
|
(%o1) [ ]
|
|||
|
|
[ 3 4 ]
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
You can then find the determinant, transpose, inverse, eigenvalues and eigenvectors of the matrix.
|
|||
|
|
|
|||
|
|
```
|
|||
|
|
(%i2) determinant(A);
|
|||
|
|
(%o2) - 2
|
|||
|
|
(%i3) transpose(A);
|
|||
|
|
[ 1 3 ]
|
|||
|
|
(%o3) [ ]
|
|||
|
|
[ 2 4 ]
|
|||
|
|
(%i4) invert(A);
|
|||
|
|
[ - 2 1 ]
|
|||
|
|
[ ]
|
|||
|
|
(%o4) [ 3 1 ]
|
|||
|
|
[ - - - ]
|
|||
|
|
[ 2 2 ]
|
|||
|
|
(%i5) eigenvectors(A);
|
|||
|
|
sqrt(33) - 5 sqrt(33) + 5
|
|||
|
|
(%o5) [[[- ------------, ------------], [1, 1]],
|
|||
|
|
2 2
|
|||
|
|
sqrt(33) - 3 sqrt(33) + 3
|
|||
|
|
[[[1, - ------------]], [[1, ------------]]]]
|
|||
|
|
4 4
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
In the output label _(%o5)_ the first array gives the eigenvalues, the second array gives the multiplicity of the respective eigenvalues, and the next two arrays give the corresponding eigenvectors of the matrix A.
|
|||
|
|
|
|||
|
|
### Plotting
|
|||
|
|
|
|||
|
|
Maxima can use either [Gnuplot][9], [Xmaxima][10] or [Geomview][11] as graphics program. Maxima package in Fedora Linux comes with _gnuplot_ as a dependency, so Maxima uses _gnuplot_pipes_ as the plotting format. To check the plotting format, use the following command inside Maxima.
|
|||
|
|
|
|||
|
|
```
|
|||
|
|
get_plot_option(plot_format);
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
Below are some plotting examples.
|
|||
|
|
|
|||
|
|
```
|
|||
|
|
(%i1) plot2d([sin(x), cos(x)], [x, -2%pi, 2%pi]);
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
![2d plot using Maxima][12]
|
|||
|
|
|
|||
|
|
```
|
|||
|
|
(%i2) plot3d(sin(sqrt(x^2+y^2)), [x, -7, 7], [y, -7, 7]);
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
![3d plot using Maxima][13]
|
|||
|
|
|
|||
|
|
```
|
|||
|
|
(%i3) mandelbrot ([iterations, 30], [x, -2, 1], [y, -1.2, 1.2],
|
|||
|
|
[grid,400,400]);
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
![The Mandelbrot Set][14]
|
|||
|
|
|
|||
|
|
You can read more about Maxima and its capabilities in its [official website][15] and [documentation][16].
|
|||
|
|
|
|||
|
|
Fedora Linux has plethora of tools for scientific use. You can find the widely used ones in the [Fedora Scientific Guide][17].
|
|||
|
|
|
|||
|
|
--------------------------------------------------------------------------------
|
|||
|
|
|
|||
|
|
via: https://fedoramagazine.org/getting-started-with-maxima-in-fedora-linux/
|
|||
|
|
|
|||
|
|
作者：[Jagat Kafle][a]
|
|||
|
|
选题：[lujun9972][b]
|
|||
|
|
译者：[译者ID](https://github.com/译者ID)
|
|||
|
|
校对：[校对者ID](https://github.com/校对者ID)
|
|||
|
|
|
|||
|
|
本文由 [LCTT](https://github.com/LCTT/TranslateProject) 原创编译，[Linux中国](https://linux.cn/) 荣誉推出
|
|||
|
|
|
|||
|
|
[a]: https://fedoramagazine.org/author/jkafle/
|
|||
|
|
[b]: https://github.com/lujun9972
|
|||
|
|
[1]: https://fedoramagazine.org/wp-content/uploads/2021/07/Getting-started-with-Maxima-in-Fedora-Linux-816x345.png
|
|||
|
|
[2]: https://unsplash.com/@roman_lazygeek
|
|||
|
|
[3]: https://unsplash.com/s/photos/mathematics-tasks
|
|||
|
|
[4]: https://maxima.sourceforge.io/
|
|||
|
|
[5]: https://fedoramagazine.org/wp-content/uploads/2021/07/maxima-terminal.png
|
|||
|
|
[6]: https://wxmaxima-developers.github.io/wxmaxima/index.html
|
|||
|
|
[7]: https://fedoramagazine.org/wp-content/uploads/2021/07/wxmaxima.png
|
|||
|
|
[8]: tmp.LH5pctTy1x#maxima-terminal
|
|||
|
|
[9]: http://www.gnuplot.info/
|
|||
|
|
[10]: https://maxima.sourceforge.io/docs/xmaxima/xmaxima.html
|
|||
|
|
[11]: http://www.geomview.org/
|
|||
|
|
[12]: https://fedoramagazine.org/wp-content/uploads/2021/07/2d-maxima.png
|
|||
|
|
[13]: https://fedoramagazine.org/wp-content/uploads/2021/07/3d-maxima.png
|
|||
|
|
[14]: https://fedoramagazine.org/wp-content/uploads/2021/07/mandelbrot-maxima.png
|
|||
|
|
[15]: https://maxima.sourceforge.io/index.html
|
|||
|
|
[16]: https://maxima.sourceforge.io/docs/manual/maxima_toc.html
|
|||
|
|
[17]: https://fedora-scientific.readthedocs.io/en/latest/index.html
|