~ubuntu-branches/debian/squeeze/maxima/squeeze

<code>["with lines 3", "with lines 1", "with lines 2", "with lines 5", "with lines 4", "with lines 6", "with lines 7"]</code>, which cycles through different colors. See the

675

gnuplot documentation for <code>plot</code> for more information.

676

677

<p>Example:

678

</p>

679

<table><tr><td> </td><td><pre class="example">[gnuplot_curve_styles, ["with lines 7", "with lines 2"]]

680

</pre></td></tr></table>

681

</li><li>

682

Option: <code>gnuplot_default_term_command</code> The gnuplot command to set the

683

terminal type for the default terminal. The default value is the empty string <code>""</code>,

684

i.e., use gnuplot's default.

685

686

<p>Example:

687

</p>

688

<table><tr><td> </td><td><pre class="example">[gnuplot_default_term_command, "set term x11"]

689

</pre></td></tr></table>

690

</li><li>

691

Option: <code>gnuplot_dumb_term_command</code> The gnuplot command to set the

692

terminal type for the dumb terminal. The default value is <code>"set term dumb 79 22"</code>,

693

which makes the text output 79 characters by 22

694

characters.

695

696

<p>Example:

697

</p>

698

<table><tr><td> </td><td><pre class="example">[gnuplot_dumb_term_command, "set term dumb 132 50"]

699

</pre></td></tr></table>

700

</li><li>

701

Option: <code>gnuplot_ps_term_command</code> The gnuplot command to set the terminal

702

type for the PostScript terminal. The default value is

703

<code>"set size 1.5, 1.5;set term postscript eps enhanced color solid 24"</code>,

704

which sets the

705

size to 1.5 times gnuplot's default, and the font size to 24, among

706

other things. See the gnuplot documentation for <code>set term postscript</code> for more information.

707

708

<p>Example:

709

</p>

710

<table><tr><td> </td><td><pre class="example">[gnuplot_ps_term_command,

711

"set term postscript eps enhanced color solid 18"]

712

</pre></td></tr></table>

713

</li></ul>

714

715

<p><b>Examples:</b>

716

</p>

717

<ul>

718

<li>

719

Saves a plot of <code>sin(x)</code> to the file <code>sin.eps</code>.

720

</li></ul>

721

<table><tr><td> </td><td><pre class="example">(%i1) plot2d (sin(x), [x, 0, 2*%pi], [gnuplot_term, ps],

722

[gnuplot_out_file, "sin.eps"])$

723

</pre></td></tr></table>

724

<ul>

725

<li>

726

Uses the y option to chop off singularities and the gnuplot_preamble

727

option to put the key at the bottom of the plot instead of the top.

728

</li></ul>

729

<table><tr><td> </td><td><pre class="example">(%i2) plot2d ([gamma(x), 1/gamma(x)], [x, -4.5, 5], [y, -10, 10],

730

[gnuplot_preamble, "set key bottom"])$

731

</pre></td></tr></table>

732

733

</p>

734

<ul>

735

<li>

736

Uses a very complicated <code>gnuplot_preamble</code> to produce fancy x-axis labels.

737

(Note that the <code>gnuplot_preamble</code> string must be entered without any line breaks.)

738

</li></ul>

739

<table><tr><td> </td><td><pre class="example">(%i3) my_preamble: "set xzeroaxis; set xtics ('-2pi' -6.283, \

740

'-3pi/2' -4.712, '-pi' -3.1415, '-pi/2' -1.5708, '0' 0, \

741

'pi/2' 1.5708, 'pi' 3.1415,'3pi/2' 4.712, '2pi' 6.283)"$

742

743

(%i4) plot2d([cos(x), sin(x), tan(x), cot(x)],

744

[x, -2*%pi, 2.1*%pi], [y, -2, 2],

745

[gnuplot_preamble, my_preamble]);

746

</pre></td></tr></table>

747

748

</p>

749

<ul>

750

<li>

751

Uses a very complicated <code>gnuplot_preamble</code> to produce fancy x-axis labels,

752

and produces PostScript

753

output that takes advantage of the advanced text formatting available

754

in gnuplot.

755

(Note that the <code>gnuplot_preamble</code> string must be entered without any line breaks.)

756

</li></ul>

757

<table><tr><td> </td><td><pre class="example">(%i5) my_preamble: "set xzeroaxis; set xtics ('-2{/Symbol p}' \

758

-6.283, '-3{/Symbol p}/2' -4.712, '-{/Symbol p}' -3.1415, \

759

'-{/Symbol p}/2' -1.5708, '0' 0,'{/Symbol p}/2' 1.5708, \

760

'{/Symbol p}' 3.1415,'3{/Symbol p}/2' 4.712, '2{/Symbol p}' \

761

6.283)"$

762

763

(%i6) plot2d ([cos(x), sin(x), tan(x)], [x, -2*%pi, 2*%pi],

764

[y, -2, 2], [gnuplot_preamble, my_preamble],

765

[gnuplot_term, ps], [gnuplot_out_file, "trig.eps"]);

766

</pre></td></tr></table>

767

<ul>

768

<li>

769

A three-dimensional plot using the gnuplot pm3d terminal.

770

</li></ul>

771

<table><tr><td> </td><td><pre class="example">(%i7) plot3d (atan (-x^2 + y^3/4), [x, -4, 4], [y, -4, 4],

772

[grid, 50, 50], [gnuplot_pm3d, true])$

773

</pre></td></tr></table>

774

775

</p>

776

<ul>

777

<li>

778

A three-dimensional plot without a mesh and with contours

779

projected on the bottom plane.

780

</li></ul>

781

<table><tr><td> </td><td><pre class="example">(%i8) my_preamble: "set pm3d at s;unset surface;set contour;\

782

set cntrparam levels 20;unset key"$

783

(%i9) plot3d(atan(-x^2 + y^3/4), [x, -4, 4], [y, -4, 4],

784

[grid, 50, 50], [gnuplot_pm3d, true],

785

[gnuplot_preamble, my_preamble])$

786

</pre></td></tr></table>

787

788

</p>

789

<ul>

790

<li>

791

A plot where the z-axis is represented by color only.

792

(Note that the <code>gnuplot_preamble</code> string must be entered without any line breaks.)

793

</li></ul>

794

<table><tr><td> </td><td><pre class="example">(%i10) plot3d (cos (-x^2 + y^3/4), [x, -4, 4], [y, -4, 4],

795

[gnuplot_preamble, "set view map; unset surface"],

796

[gnuplot_pm3d, true], [grid, 150, 150])$

797

</pre></td></tr></table>

798

799

</p>

800

</dd></dl>

801

802

<dl>

803

<dt><u>Function:</u> <b>plot3d</b><i> (<var>expr</var>, <var>x_range</var>, <var>y_range</var>, ..., <var>options</var>, ...)</i>

804

805

</dt>

806

<dt><u>Function:</u> <b>plot3d</b><i> (<var>name</var>, <var>x_range</var>, <var>y_range</var>, ..., <var>options</var>, ...)</i>

807

808

</dt>

809

<dt><u>Function:</u> <b>plot3d</b><i> ([<var>expr_1</var>, <var>expr_2</var>, <var>expr_3</var>], <var>x_rge</var>, <var>y_rge</var>)</i>

810

811

</dt>

812

<dt><u>Function:</u> <b>plot3d</b><i> ([<var>name_1</var>, <var>name_2</var>, <var>name_3</var>], <var>x_range</var>, <var>y_range</var>, ..., <var>options</var>, ...)</i>

813

814

</dt>

815

<dd><p>Displays a plot of one or three expressions as functions of two variables.

816

</p>

817

<table><tr><td> </td><td><pre class="example">(%i1) plot3d (2^(-u^2 + v^2), [u, -3, 3], [v, -2, 2]);

818

</pre></td></tr></table>

819

820

</p>

821

<p>plots <code>z = 2^(-u^2+v^2)</code> with <code>u</code> and <code>v</code> varying in [-3,3] and

822

[-2,2] respectively, and with <var>u</var> on the x axis, and <code>v</code> on the y

823

axis.

824

</p>

825

<p>The same graph can be plotted using openmath:

826

</p>

827

<table><tr><td> </td><td><pre class="example">(%i2) plot3d (2^(-u^2 + v^2), [u, -3, 3], [v, -2, 2],

828

[plot_format, openmath]);

829

</pre></td></tr></table>

830

831

</p>

832

833

<p>in this case the mouse can be used to rotate the plot to look at the surface

834

from different sides.

835

</p>

836

<p>An example of the third pattern of arguments is

837

</p>

838

<table><tr><td> </td><td><pre class="example">(%i3) plot3d ([cos(x)*(3 + y*cos(x/2)), sin(x)*(3 + y*cos(x/2)),

839

y*sin(x/2)], [x, -%pi, %pi], [y, -1, 1], ['grid, 50, 15]);

840

</pre></td></tr></table>

841

842

</p>

843

<p>which plots a Moebius band, parametrized by the three expressions given

844

as the first argument to <code>plot3d</code>. An additional optional argument

845

<code>['grid, 50, 15]</code> gives the grid number of rectangles in the x direction and

846

y direction.

847

</p>

848

<p>The function to be plotted

849

may be specified as the name of a Maxima or Lisp function or operator,

850

a Maxima lambda expression, or a general Maxima expression.

851

In the form <code>plot3d (<var>f</var>, ...)</code> where <var>f</var> is the

852

name of a function or a lambda expression,

853

the function must be a function of two arguments.

854

In the form <code>plot3d ([<var>f_1</var>, <var>f_2</var>, <var>f_3</var>], ...)</code>

855

where <var>f_1</var>, <var>f_2</var>, and <var>f_3</var> are names of functions or lambda expressions,

856

each function must be a function of three arguments.

857

</p>

858

<p>This example shows a plot of the real part of <code>z^1/3</code>.

859

</p>

860

<table><tr><td> </td><td><pre class="example">(%i4) plot3d (r^.33*cos(th/3), [r, 0, 1], [th, 0, 6*%pi],

861

['grid, 12, 80], ['transform_xy, polar_to_xy],

862

['view_direction, 1, 1, 1.4], ['colour_z, true]);

863

</pre></td></tr></table>

864

865

</p>

866

867

<p>Here the <code>view_direction</code> option indicates the direction from which we

868

take a projection. We actually do this from infinitely far away,

869

but parallel to the line from <code>view_direction</code> to the origin. This

870

is currently only used in <code>ps</code> plot_format, since the other viewers

871

allow interactive rotating of the object.

872

</p>

873

<p>Other examples are the Klein bottle:

874

</p>

875

<table><tr><td> </td><td><pre class="example">(%i5) expr_1: 5*cos(x)*(cos(x/2)*cos(y) + sin(x/2)*sin(2*y)

876

+ 3.0) - 10.0$

877

(%i6) expr_2: -5*sin(x)*(cos(x/2)*cos(y) + sin(x/2)*sin(2*y)

878

+ 3.0)$

879

(%i7) expr_3: 5*(-sin(x/2)*cos(y) + cos(x/2)*sin(2*y))$

880

881

(%i8) plot3d ([expr_1, expr_2, expr_3], [x, -%pi, %pi],

882

[y, -%pi, %pi], ['grid, 40, 40]);

883

</pre></td></tr></table>

884

885

</p>

886

<p>and a torus:

887

</p>

888

<table><tr><td> </td><td><pre class="example">(%i9) expr_1: cos(y)*(10.0+6*cos(x))$

889

(%i10) expr_2: sin(y)*(10.0+6*cos(x))$

890

(%i11) expr_3: -6*sin(x)$

891

(%i12) plot3d ([expr_1, expr_2, expr_3], [x, 0, 2*%pi],

892

[y, 0, 2*%pi], ['grid, 40, 40]);

893

</pre></td></tr></table>

894

895

</p>

896

<p>Sometimes it is necessary to define a function to plot the expression. All

897

the arguments to plot3d are evaluated before being passed to plot3d, and

898

so trying to make an expression which does just what is needed may be

899

difficult, and it is just easier to make a function.

900

</p>

901

<table><tr><td> </td><td><pre class="example">(%i13) M: matrix([1, 2, 3, 4], [1, 2, 3, 2], [1, 2, 3, 4],

902

[1, 2, 3, 3])$

903

(%i14) f(x, y) := float (M [?round(x), ?round(y)])$

904

(%i15) plot3d (f, [x, 1, 4], [y, 1, 4], ['grid, 4, 4])$

905

</pre></td></tr></table>

906

907

</p>

908

<p>See <code>plot_options</code> for more examples.

909

</p>

910

</dd></dl>

911

912

913

<dl>

914

<dt><u>Function:</u> <b>make_transform</b><i> (<var>vars</var>, <var>fx</var>, <var>fy</var>, <var>fz</var>)</i>

915

916

</dt>

917

<dd><p>Returns a function suitable for the transform function in plot3d. Use

918

with the plot option <code>transform_xy</code>.

919

</p><table><tr><td> </td><td><pre class="example">make_transform ([r, th, z], r*cos(th), r*sin(th), z)$

920

</pre></td></tr></table><p>is a transformation to polar coordinates.

921

</p></dd></dl>

922

923

<dl>

924

<dt><u>Function:</u> <b>plot2d_ps</b><i> (<var>expr</var>, <var>range</var>)</i>

925

926

</dt>

927

<dd><p>Writes to pstream a sequence of PostScript commands which

928

plot <var>expr</var> over <var>range</var>.

929

</p>

930

<p><var>expr</var> is an expression.

931

<var>range</var> is a list of the form <code>[<var>x</var>, <var>min</var>, <var>max</var>]</code>

932

in which <var>x</var> is a variable which appears in <var>expr</var>.

933

</p>

934

<p>See also <code>closeps</code>.

935

</p>

936

</dd></dl>

937

938

939

<dl>

940

<dt><u>Function:</u> <b>closeps</b><i> ()</i>

941

942

</dt>

943

<dd><p>This should usually becalled at the end of a sequence of plotting

944

commands. It closes the current output stream <var>pstream</var>, and sets

945

it to nil. It also may be called at the start of a plot, to ensure

946

pstream is closed if it was open. All commands which write to

947

pstream, open it if necessary. <code>closeps</code> is separate from the other

948

plotting commands, since we may want to plot 2 ranges or superimpose

949

several plots, and so must keep the stream open.

950

</p></dd></dl>

951

952

<dl>

953

<dt><u>Function:</u> <b>set_plot_option</b><i> (<var>option</var>)</i>

954

955

</dt>

956

<dd><p>Assigns one of the global variables for plotting.

957

<var>option</var> is specified as a list of two or more elements,

958

in which the first element is one of the keywords

959

on the <code>plot_options</code> list.

960

</p>

961

<p><code>set_plot_option</code> evaluates its argument.

962

<code>set_plot_option</code> returns <code>plot_options</code>

963

(after modifying one of its elements).

964

</p>

965

<p>See also <code>plot_options</code>, <code>plot2d</code>, and <code>plot3d</code>.

966

</p>

967

<p>Examples:

968

</p>

969

<p>Modify the <code>grid</code> and <code>x</code> values.

970

When a <code>plot_options</code> keyword has an assigned value,

971

quote it to prevent evaluation.

972

</p>

973

974

<table><tr><td> </td><td><pre class="example">(%i1) set_plot_option ([grid, 30, 40]);

975

(%o1) [[x, - 1.755559702014E+305, 1.755559702014E+305],

976

[y, - 1.755559702014E+305, 1.755559702014E+305], [t, - 3, 3],

977

[grid, 30, 40], [view_direction, 1, 1, 1], [colour_z, false],

978

[transform_xy, false], [run_viewer, true],

979

[plot_format, gnuplot], [gnuplot_term, default],

980

[gnuplot_out_file, false], [nticks, 10], [adapt_depth, 10],

981

[gnuplot_pm3d, false], [gnuplot_preamble, ],

982

[gnuplot_curve_titles, [default]],

983

[gnuplot_curve_styles, [with lines 3, with lines 1,

984

with lines 2, with lines 5, with lines 4, with lines 6,

985

with lines 7]], [gnuplot_default_term_command, ],

986

[gnuplot_dumb_term_command, set term dumb 79 22],

987

[gnuplot_ps_term_command, set size 1.5, 1.5;set term postscript #

988

eps enhanced color solid 24]]

989

(%i2) x: 42;

990

(%o2) 42

991

(%i3) set_plot_option (['x, -100, 100]);

992

(%o3) [[x, - 100.0, 100.0], [y, - 1.755559702014E+305,

993

1.755559702014E+305], [t, - 3, 3], [grid, 30, 40],

994

[view_direction, 1, 1, 1], [colour_z, false],

995

[transform_xy, false], [run_viewer, true],

996

[plot_format, gnuplot], [gnuplot_term, default],

997

[gnuplot_out_file, false], [nticks, 10], [adapt_depth, 10],

998

[gnuplot_pm3d, false], [gnuplot_preamble, ],

999

[gnuplot_curve_titles, [default]],

1000

[gnuplot_curve_styles, [with lines 3, with lines 1,

1001

with lines 2, with lines 5, with lines 4, with lines 6,

1002

with lines 7]], [gnuplot_default_term_command, ],

1003

[gnuplot_dumb_term_command, set term dumb 79 22],

1004

[gnuplot_ps_term_command, set size 1.5, 1.5;set term postscript #

1005

eps enhanced color solid 24]]

1006

</pre></td></tr></table>

1007

</dd></dl>

1008

1009

<dl>

1010

<dt><u>Function:</u> <b>psdraw_curve</b><i> (<var>ptlist</var>)</i>

1011

1012

</dt>

1013

<dd><p>Draws a curve connecting the points in <var>ptlist</var>. The latter

1014

may be of the form <code>[x0, y0, x1, y1, ...]</code> or <code>[[x0, y0], [x1, y1], ...]</code>

1015

</p>

1016

<p>The function <code>join</code> is handy for taking a list of x's and a

1017

list of y's and splicing them together.

1018

</p>

1019

<p><var>psdraw_curve</var> simply invokes the more primitive function

1020

<var>pscurve</var>. Here is the definition:

1021

</p>

1022

<table><tr><td> </td><td><pre class="example">(defun $psdraw_curve (lis)

1023

(p "newpath")

1024

($pscurve lis)

1025

(p "stroke"))

1026

1027

</pre></td></tr></table>

1028

1029

1030

</dd></dl>

1031

1032

<dl>

1033

<dt><u>Function:</u> <b>pscom</b><i> (<var>cmd</var>)</i>

1034

1035

</dt>

1036

<dd><p><var>cmd</var> is inserted in the PostScript file.

1037

Example:

1038

</p><table><tr><td> </td><td><pre class="example">pscom ("4.5 72 mul 5.5 72 mul translate 14 14 scale");

1039

</pre></td></tr></table>

1040

</dd></dl>

1041

1042

1043

1044

1045

1046

1047

1048

1049

1050

1051

1052

1053

1054

1055

<td valign="middle" align="left">[<a href="maxima_toc.html#SEC_Contents" title="Table of contents">Contents</a>]</td>

1056

<td valign="middle" align="left">[<a href="maxima_72.html#SEC264" title="Index">Index</a>]</td>

1057

1058

</tr></table>

1059

<p>

1060

1061

This document was generated by <em>Robert Dodier</em> on <em>September, 20 2006</em> using <a href="http://texi2html.cvshome.org/"><em>texi2html 1.76</em></a>.

1062

</font>

1063

<br>

1064

1065

</p>

1066

</body>

1067

</html>

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