[genius] Fri Oct 10 17:16:38 2014 Jiri (George) Lebl <jirka 5z com>
- From: George Lebl <jirka src gnome org>
- To: commits-list gnome org
- Cc:
- Subject: [genius] Fri Oct 10 17:16:38 2014 Jiri (George) Lebl <jirka 5z com>
- Date: Fri, 10 Oct 2014 22:17:19 +0000 (UTC)
commit 59cd88f4285fa2afc64175d86a57b840abe485fc
Author: Jiri (George) Lebl <jiri lebl gmail com>
Date: Fri Oct 10 17:17:05 2014 -0500
Fri Oct 10 17:16:38 2014 Jiri (George) Lebl <jirka 5z com>
* src/funclib.c: min/max now check their arguments better, especially
if argument is a single element.
* src/geniustests.txt: Add a bunch of tests to the suite
* help/C/genius.xml: A bunch of updates to the manual
ChangeLog | 9 +
NEWS | 11 +
help/C/genius.xml | 116 +++++---
help/genius.txt | 787 +++++++++++++++++++++++++++------------------------
src/funclib.c | 19 ++
src/geniustests.txt | 28 ++
6 files changed, 554 insertions(+), 416 deletions(-)
---
diff --git a/ChangeLog b/ChangeLog
index ec15a8a..e1844bb 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,12 @@
+Fri Oct 10 17:16:38 2014 Jiri (George) Lebl <jirka 5z com>
+
+ * src/funclib.c: min/max now check their arguments better, especially
+ if argument is a single element.
+
+ * src/geniustests.txt: Add a bunch of tests to the suite
+
+ * help/C/genius.xml: A bunch of updates to the manual
+
Fri Oct 10 16:05:24 2014 Jiri (George) Lebl <jirka 5z com>
* lib/calculus/fourier.gel: Fix PeriodicExtension
diff --git a/NEWS b/NEWS
index 5a32fd7..80cd06e 100644
--- a/NEWS
+++ b/NEWS
@@ -1,3 +1,14 @@
+Changes to 1.0.20
+
+* Add more sizes of icons including SVG, and add Keywords to the .desktop file
+* Documentation updates
+* Fix PeriodicExtension function
+* A couple of minor fixes in the plotting code including one possible crasher
+* Translation updates (FIXME)
+
+* During making of these changes the author (Jiri) was partially supported by
+ NSF grant DMS 1362337 and the Oklahoma State University
+
Changes to 1.0.19
* New menu: Examples. These are annotated programs that show some
diff --git a/help/C/genius.xml b/help/C/genius.xml
index 8a2bfe3..da48807 100644
--- a/help/C/genius.xml
+++ b/help/C/genius.xml
@@ -192,7 +192,7 @@
</para>
<para>
- This manual describes mostly the graphical version of the calculator,
+ Parts of this manual describe the graphical version of the calculator,
but the language is of course the same. The command line only version
lacks the graphing capabilities and all other capabilities that require
the graphical user interface.
@@ -347,7 +347,9 @@ while a long calculation is running, or to debug a certain program.
</para>
<para>
Alternatively you can write longer programs and those can
- appear in separate tabs and can be stored in files for later
+ appear in separate tabs. The programs are a set of commands or
+ functions that can be run all at once rather than entering them
+ at the command line. The programs can be saved in files for later
retrieval.
</para>
</listitem>
@@ -417,12 +419,18 @@ do <userinput>cd directory</userinput> as in the UNIX command shell.
<sect1 id="genius-usage-create-program">
<title>To Create a New Program </title>
<para>
+ If you wish to enter several more complicated commands, or perhaps write a complicated
+ function using the <link linkend="genius-gel">GEL</link> language. You can create a new
+ program.
+ </para>
+ <para>
To start writing a new program, choose
<menuchoice><guimenu>File</guimenu><guimenuitem>New
Program</guimenuitem></menuchoice>. A new tab will appear in the work area. You
can write a <link linkend="genius-gel">GEL</link> program in this work area.
Once you have written your program you can run it by
-<menuchoice><guimenu>Calculator</guimenu><guimenuitem>Run</guimenuitem></menuchoice>.
+<menuchoice><guimenu>Calculator</guimenu><guimenuitem>Run</guimenuitem></menuchoice> (or
+the <guilabel>Run</guilabel> toolbar button).
This will execute your program and will display any output on the <guilabel>Console</guilabel> tab.
Executing a program is equivalent of taking the text of the program and
typing it into the console. The only difference is that this input is done
@@ -433,7 +441,16 @@ tab. The currently selected program has its tab in bold type. To select a
program, just click on its tab.
</para>
<para>
-To save the program you've just written, choose <menuchoice><guimenu>File</guimenu><guimenuitem>Save
As...</guimenuitem></menuchoice>
+To save the program you've just written, choose <menuchoice><guimenu>File</guimenu><guimenuitem>Save
As...</guimenuitem></menuchoice>.
+Similarly as in other programs you can choose
+<menuchoice><guimenu>File</guimenu><guimenuitem>Save</guimenuitem></menuchoice> to save a program that
already has
+a filename attached to it. If you have many opened programs you have edited and wish to save you can also
choose
+<menuchoice><guimenu>File</guimenu><guimenuitem>Save All Unsaved</guimenuitem></menuchoice>.
+ </para>
+ <para>
+ Programs that have unsaved changes will have a "[+]" next to their filename. This way you can
see if the file
+ on disk and the currently opened tab differ in content. Programs which have not yet had a
filename associated
+ with them are always considered unsaved and no "[+]" is printed.
</para>
</sect1>
@@ -451,6 +468,12 @@ To run a program from a file, choose
Run...</guimenuitem></menuchoice>. This will run the program without opening it
in a separate tab. This is equivalent to the <command>load</command> command.
</para>
+ <para>
+ If you have made edits to a file you wish to throw away and want to reload to the version
that's on disk,
+ you can choose the
+ <menuchoice><guimenu>File</guimenu><guimenuitem>Reload from Disk</guimenuitem></menuchoice>
menuitem. This is useful for experimenting
+ with a program and making temporary edits, to run a program, but that you do not intend to keep.
+ </para>
</sect1>
</chapter>
@@ -1118,28 +1141,16 @@ Not all functions can be used in this way. For example, when you use a binary o
</sect1>
- <sect1 id="genius-gel-absolute-value-modulus">
- <title>Absolute Value / Modulus</title>
- <para>
-You can make an absolute value of something by putting the
-<literal>|</literal>'s around it. For example:
-<programlisting>|a-b|</programlisting>
-</para>
-<para>
-In case the expression is a complex number the result will be the modulus
-(distance from the origin). For example:
-<userinput>|3 * e^(1i*pi)|</userinput>
-returns 3.
- </para>
- </sect1>
-
<sect1 id="genius-gel-separator">
<title>Separator</title>
<para>
-In GEL if you want to type more than one command you have to use
-the <literal>;</literal> operator, which is a way to separate expressions,
-such a combined expression will return whatever is the result of the last
-one, so suppose you type the following:
+ GEL is somewhat different from other languages in how it deals with multiple commands and
functions.
+ In GEL you must chain commands together with a separator operator.
+That is, if you want to type more than one expression you have to use
+the <literal>;</literal> operator in between the expressions. This is
+a way in which both expressions are evaluated and the result of the second one (or the last one
+if there is more than two expressions) is returned.
+Suppose you type the following:
<programlisting>3 ; 5
</programlisting>
This expression will yield 5.
@@ -1150,13 +1161,18 @@ especially if the <literal>;</literal> is not the top most primitive. This sligh
other programming languages where the <literal>;</literal> is a terminator of statements, whereas
in GEL it’s actually a binary operator. If you are familiar with pascal
this should be second nature. However genius can let you pretend it is a
-terminator somewhat, if a <literal>;</literal> is found at the end of a parenthesis or a block,
-genius will itself append a null node to it as if you would have written
+terminator to some degree. If a <literal>;</literal> is found at the end of a parenthesis or a block,
+genius will append a null to it as if you would have written
<userinput>;null</userinput>.
This is useful in case you do not want to return a value from say a loop,
or if you handle the return differently. Note that it will slightly slow down
the code if it is executed too often as there is one more operator involved.
</para>
+ <para>
+ If you are typing expressions in a program you do not have to add a semicolon. In this case
+ genius will simply print the return value whenever it executes the expression. However, do
note that if you are defining a
+ function, the body of the function is a single expression.
+ </para>
</sect1>
<sect1 id="genius-gel-comments">
@@ -1179,7 +1195,7 @@ x=123;
&appname; implements modular arithmetic.
To use it you just add "mod <integer>" after
the expression. Example:
-<programlisting>2^(5!) * 3^(6!) mod 5</programlisting>
+<userinput>2^(5!) * 3^(6!) mod 5</userinput>
It could be possible to do modular arithmetic by computing with integers and then modding in the end with
the <literal>%</literal> operator, which simply gives the remainder, but
that may be time consuming if not impossible when working with larger numbers.
@@ -1285,9 +1301,12 @@ different from <literal>=</literal> because it never gets translated to a
<term><userinput>|a|</userinput></term>
<listitem>
<para>
- Absolute value or modulus (if <varname>a</varname>
- is a complex number).
- </para>
+ Absolute value.
+ In case the expression is a complex number the result will be the modulus
+(distance from the origin). For example:
+<userinput>|3 * e^(1i*pi)|</userinput>
+returns 3.
+ </para>
<para>
See
<ulink url="http://mathworld.wolfram.com/AbsoluteValue.html";>Mathworld</ulink> for more
information.
@@ -3017,7 +3036,7 @@ and this builtin function makes it possible to make GEL functions aware of modul
<term><anchor id="gel-function-Identity"/>Identity</term>
<listitem>
<synopsis>Identity (x)</synopsis>
- <para>Identity function, returns its argument.</para>
+ <para>Identity function, returns its argument. It is equivalent to <userinput>function
Identity(x)=x</userinput>.</para>
</listitem>
</varlistentry>
@@ -3796,6 +3815,7 @@ vectorfield plot. (See <link linkend="gel-function-VectorfieldPlot"><function>V
</para>
<para>
See
+ <ulink url="http://en.wikipedia.org/wiki/Catalan%27s_constant";>Wikipedia</ulink>, or
<ulink url="http://mathworld.wolfram.com/CatalansConstant.html";>Mathworld</ulink> for more
information.
</para>
</listitem>
@@ -3807,7 +3827,7 @@ vectorfield plot. (See <link linkend="gel-function-VectorfieldPlot"><function>V
<synopsis>EulerConstant</synopsis>
<para>Aliases: <function>gamma</function></para>
<para>
- Euler's Constant gamma. Sometimes called the
+ Euler's constant gamma. Sometimes called the
Euler-Mascheroni constant.
</para>
<para>
@@ -3837,7 +3857,9 @@ vectorfield plot. (See <link linkend="gel-function-VectorfieldPlot"><function>V
<term><anchor id="gel-function-Gravity"/>Gravity</term>
<listitem>
<synopsis>Gravity</synopsis>
- <para>Free fall acceleration at sea level.</para>
+ <para>Free fall acceleration at sea level in meters per second squared. This is the standard
gravity constant 9.80665. The gravity
+ in your particular neck of the woods might be different due to different altitude and the
fact that the earth is not perfectly
+ round and uniform.</para>
<para>
See
<ulink url="http://en.wikipedia.org/wiki/Standard_gravity";>Wikipedia</ulink> for more information.
@@ -3852,8 +3874,9 @@ vectorfield plot. (See <link linkend="gel-function-VectorfieldPlot"><function>V
<para>
The base of the natural logarithm. <userinput>e^x</userinput>
is the exponential function
- <link linkend="gel-function-exp"><function>exp</function></link>. This is the
- number approximately 2.71828182846...
+ <link linkend="gel-function-exp"><function>exp</function></link>. It is approximately
+ 2.71828182846... This number is sometimes called Euler's number, although there are
+ several numbers that are also called Euler's. An example is the gamma constant: <link
linkend="gel-function-EulerConstant"><function>EulerConstant</function></link>.
</para>
<para>
See
@@ -3895,7 +3918,8 @@ vectorfield plot. (See <link linkend="gel-function-VectorfieldPlot"><function>V
<para>
Absolute value of a number and if <varname>x</varname> is
a complex value the modulus of <varname>x</varname>. I.e. this
- the distance of <varname>x</varname> to the origin.
+ the distance of <varname>x</varname> to the origin. This is equivalent
+ to <userinput>|x|</userinput>.
</para>
<para>
See
@@ -3960,7 +3984,7 @@ all its elements are conjugated.</para>
<listitem>
<synopsis>Im (z)</synopsis>
<para>Aliases: <function>ImaginaryPart</function></para>
- <para>Get the imaginary part of a complex number.</para>
+ <para>Get the imaginary part of a complex number. For example <userinput>Re(3+4i)</userinput>
yields 4.</para>
<para>
See
<ulink url="http://en.wikipedia.org/wiki/Imaginary_part";>Wikipedia</ulink> for more information.
@@ -3980,7 +4004,9 @@ all its elements are conjugated.</para>
<term><anchor id="gel-function-IsComplex"/>IsComplex</term>
<listitem>
<synopsis>IsComplex (num)</synopsis>
- <para>Check if argument is a complex (non-real) number.</para>
+ <para>Check if argument is a complex (non-real) number. Do note that we really mean nonreal
number. That is,
+ <userinput>IsComplex(3)</userinput> yields false, while
+ <userinput>IsComplex(3-1i)</userinput> yields true.</para>
</listitem>
</varlistentry>
@@ -3997,7 +4023,7 @@ all its elements are conjugated.</para>
<term><anchor id="gel-function-IsFloat"/>IsFloat</term>
<listitem>
<synopsis>IsFloat (num)</synopsis>
- <para>Check if argument is a floating point number (non-complex).</para>
+ <para>Check if argument is a real floating point number (non-complex).</para>
</listitem>
</varlistentry>
@@ -4006,7 +4032,9 @@ all its elements are conjugated.</para>
<listitem>
<synopsis>IsGaussInteger (num)</synopsis>
<para>Aliases: <function>IsComplexInteger</function></para>
- <para>Check if argument is a possibly complex integer.</para>
+ <para>Check if argument is a possibly complex integer. That is a complex integer is a number of
+ the form <userinput>n+1i*m</userinput> where <varname>n</varname> and <varname>m</varname>
+ are integers.</para>
</listitem>
</varlistentry>
@@ -4022,7 +4050,7 @@ all its elements are conjugated.</para>
<term><anchor id="gel-function-IsNonNegativeInteger"/>IsNonNegativeInteger</term>
<listitem>
<synopsis>IsNonNegativeInteger (num)</synopsis>
- <para>Check if argument is a non-negative real integer.</para>
+ <para>Check if argument is a non-negative real integer. That is, either a positive integer or
zero.</para>
</listitem>
</varlistentry>
@@ -4069,7 +4097,7 @@ we accept the convention that 0 is not a natural number.</para>
<listitem>
<synopsis>Re (z)</synopsis>
<para>Aliases: <function>RealPart</function></para>
- <para>Get the real part of a complex number.</para>
+ <para>Get the real part of a complex number. For example <userinput>Re(3+4i)</userinput> yields
3.</para>
<para>
See
<ulink url="http://en.wikipedia.org/wiki/Real_part";>Wikipedia</ulink> for more information.
@@ -4155,6 +4183,12 @@ value then <function>Sign</function> returns the direction or 0.
<listitem>
<synopsis>ln (x)</synopsis>
<para>The natural logarithm, the logarithm to base <varname>e</varname>.</para>
+ <para>
+ See
+ <ulink url="http://en.wikipedia.org/wiki/Natural_logarithm";>Wikipedia</ulink> or
+ <ulink url="http://planetmath.org/encyclopedia/LogarithmFunction.html";>Planetmath</ulink> or
+ <ulink url="http://mathworld.wolfram.com/NaturalLogarithm.html";>Mathworld</ulink> for more
information.
+ </para>
</listitem>
</varlistentry>
diff --git a/help/genius.txt b/help/genius.txt
index d96974e..261a1d8 100644
--- a/help/genius.txt
+++ b/help/genius.txt
@@ -1,6 +1,6 @@
Genius Manual
-Jiří Lebl
+Jiř Lebl
Oklahoma State University
@@ -12,10 +12,12 @@ Kai Willadsen
<kaiw itee uq edu au>
- Copyright © 1997-2014 Jiří (George) Lebl
+ Copyright © 1997-2014 Jiř (George) Lebl
Copyright © 2004 Kai Willadsen
+ Manual for the Genius Math Tool.
+
Permission is granted to copy, distribute and/or modify this
document under the terms of the GNU Free Documentation License
(GFDL), Version 1.1 or any later version published by the Free
@@ -75,134 +77,140 @@ Kai Willadsen
To report a bug or make a suggestion regarding the Genius
Mathematics Tool application or this manual, please visit the
Genius Web page or email me at <jirka 5z com>.
- This manual describes version 1.0.20 of Genius.
__________________________________________________________
Table of Contents
- Introduction
- Getting Started
-
- To Start Genius Mathematics Tool
- When You Start Genius
-
- Basic Usage
-
- Using the Work Area
- To Create a New Program
- To Open and Run a Program
-
- Plotting
-
- Line Plots
- Parametric Plots
- Slopefield Plots
- Vectorfield Plots
- Surface Plots
-
- GEL Basics
-
- Values
-
- Numbers
- Booleans
- Strings
- Null
-
- Using Variables
-
- Setting Variables
- Built-in Variables
- Previous Result Variable
-
- Using Functions
+ 1. Introduction
+ 2. Getting Started
- Defining Functions
- Variable Argument Lists
- Passing Functions to Functions
- Operations on Functions
+ 2.1. To Start Genius Mathematics Tool
+ 2.2. When You Start Genius
- Absolute Value / Modulus
- Separator
- Comments
- Modular Evaluation
- List of GEL Operators
+ 3. Basic Usage
- Programming with GEL
+ 3.1. Using the Work Area
+ 3.2. To Create a New Program
+ 3.3. To Open and Run a Program
- Conditionals
- Loops
+ 4. Plotting
- While Loops
- For Loops
- Foreach Loops
- Break and Continue
+ 4.1. Line Plots
+ 4.2. Parametric Plots
+ 4.3. Slopefield Plots
+ 4.4. Vectorfield Plots
+ 4.5. Surface Plots
- Sums and Products
- Comparison Operators
- Global Variables and Scope of Variables
- Parameter variables
- Returning
- References
- Lvalues
+ 5. GEL Basics
- Advanced Programming with GEL
+ 5.1. Values
- Error Handling
- Toplevel Syntax
- Returning Functions
- True Local Variables
- GEL Startup Procedure
- Loading Programs
-
- Matrices in GEL
-
- Entering Matrices
- Conjugate Transpose and Transpose Operator
- Linear Algebra
-
- Polynomials in GEL
-
- Using Polynomials
-
- Set Theory in GEL
-
- Using Sets
-
- List of GEL functions
-
- Commands
- Basic
- Parameters
- Constants
- Numeric
- Trigonometry
- Number Theory
- Matrix Manipulation
- Linear Algebra
- Combinatorics
- Calculus
- Functions
- Equation Solving
- Statistics
- Polynomials
- Set Theory
- Commutative Algebra
- Miscellaneous
- Symbolic Operations
- Plotting
-
- Example Programs in GEL
- Settings
-
- Output
- Precision
- Terminal
- Memory
-
- About Genius Mathematics Tool
+ 5.1.1. Numbers
+ 5.1.2. Booleans
+ 5.1.3. Strings
+ 5.1.4. Null
+
+ 5.2. Using Variables
+
+ 5.2.1. Setting Variables
+ 5.2.2. Built-in Variables
+ 5.2.3. Previous Result Variable
+
+ 5.3. Using Functions
+
+ 5.3.1. Defining Functions
+ 5.3.2. Variable Argument Lists
+ 5.3.3. Passing Functions to Functions
+ 5.3.4. Operations on Functions
+
+ 5.4. Separator
+ 5.5. Comments
+ 5.6. Modular Evaluation
+ 5.7. List of GEL Operators
+
+ 6. Programming with GEL
+
+ 6.1. Conditionals
+ 6.2. Loops
+
+ 6.2.1. While Loops
+ 6.2.2. For Loops
+ 6.2.3. Foreach Loops
+ 6.2.4. Break and Continue
+
+ 6.3. Sums and Products
+ 6.4. Comparison Operators
+ 6.5. Global Variables and Scope of Variables
+ 6.6. Parameter variables
+ 6.7. Returning
+ 6.8. References
+ 6.9. Lvalues
+
+ 7. Advanced Programming with GEL
+
+ 7.1. Error Handling
+ 7.2. Toplevel Syntax
+ 7.3. Returning Functions
+ 7.4. True Local Variables
+ 7.5. GEL Startup Procedure
+ 7.6. Loading Programs
+
+ 8. Matrices in GEL
+
+ 8.1. Entering Matrices
+ 8.2. Conjugate Transpose and Transpose Operator
+ 8.3. Linear Algebra
+
+ 9. Polynomials in GEL
+
+ 9.1. Using Polynomials
+
+ 10. Set Theory in GEL
+
+ 10.1. Using Sets
+
+ 11. List of GEL functions
+
+ 11.1. Commands
+ 11.2. Basic
+ 11.3. Parameters
+ 11.4. Constants
+ 11.5. Numeric
+ 11.6. Trigonometry
+ 11.7. Number Theory
+ 11.8. Matrix Manipulation
+ 11.9. Linear Algebra
+ 11.10. Combinatorics
+ 11.11. Calculus
+ 11.12. Functions
+ 11.13. Equation Solving
+ 11.14. Statistics
+ 11.15. Polynomials
+ 11.16. Set Theory
+ 11.17. Commutative Algebra
+ 11.18. Miscellaneous
+ 11.19. Symbolic Operations
+ 11.20. Plotting
+
+ 12. Example Programs in GEL
+ 13. Settings
+
+ 13.1. Output
+ 13.2. Precision
+ 13.3. Terminal
+ 13.4. Memory
+
+ 14. About Genius Mathematics Tool
+
+ List of Figures
+ 2-1. Genius Mathematics Tool Window
+ 4-1. Create Plot Window
+ 4-2. Plot Window
+ 4-3. Parametric Plot Tab
+ 4-4. Parametric Plot
+ 4-5. Surface Plot
__________________________________________________________
-Introduction
+Chapter 1. Introduction
The Genius Mathematics Tool application is a general calculator
for use as a desktop calculator, an educational tool in
@@ -224,7 +232,7 @@ Introduction
of course does not implement any feature that requires the
graphical interface.
- This manual describes mostly the graphical version of the
+ Parts of this manual describe the graphical version of the
calculator, but the language is of course the same. The command
line only version lacks the graphing capabilities and all other
capabilities that require the graphical user interface.
@@ -235,9 +243,9 @@ Introduction
file.
__________________________________________________________
-Getting Started
+Chapter 2. Getting Started
-To Start Genius Mathematics Tool
+2.1. To Start Genius Mathematics Tool
You can start Genius Mathematics Tool in the following ways:
@@ -266,14 +274,14 @@ To Start Genius Mathematics Tool
plotting will not be available.
__________________________________________________________
-When You Start Genius
+2.2. When You Start Genius
When you start the GNOME edition of Genius Mathematics Tool,
- the window pictured in Figure 1 is displayed.
+ the window pictured in Figure 2-1 is displayed.
- [genius_window.png]
+ Figure 2-1. Genius Mathematics Tool Window
- Figure 1. Genius Mathematics Tool Window
+ [genius_window.png]
The Genius Mathematics Tool window contains the following
elements:
@@ -326,13 +334,15 @@ When You Start Genius
are immediately returned after you hit the Enter key.
Alternatively you can write longer programs and those
- can appear in separate tabs and can be stored in files
- for later retrieval.
+ can appear in separate tabs. The programs are a set of
+ commands or functions that can be run all at once rather
+ than entering them at the command line. The programs can
+ be saved in files for later retrieval.
__________________________________________________________
-Basic Usage
+Chapter 3. Basic Usage
-Using the Work Area
+3.1. Using the Work Area
Normally you interact with the calculator in the Console tab of
the work area. If you are running the text only version then
@@ -377,26 +387,40 @@ genius> load path/to/program.gel
directory do cd directory as in the UNIX command shell.
__________________________________________________________
-To Create a New Program
+3.2. To Create a New Program
+
+ If you wish to enter several more complicated commands, or
+ perhaps write a complicated function using the GEL language.
+ You can create a new program.
To start writing a new program, choose File->New Program. A new
tab will appear in the work area. You can write a GEL program
in this work area. Once you have written your program you can
- run it by Calculator->Run. This will execute your program and
- will display any output on the Console tab. Executing a program
- is equivalent of taking the text of the program and typing it
- into the console. The only difference is that this input is
- done independent of the console and just the output goes onto
- the console. Calculator->Run will always run the currently
- selected program even if you are on the Console tab. The
- currently selected program has its tab in bold type. To select
- a program, just click on its tab.
+ run it by Calculator->Run (or the Run toolbar button). This
+ will execute your program and will display any output on the
+ Console tab. Executing a program is equivalent of taking the
+ text of the program and typing it into the console. The only
+ difference is that this input is done independent of the
+ console and just the output goes onto the console.
+ Calculator->Run will always run the currently selected program
+ even if you are on the Console tab. The currently selected
+ program has its tab in bold type. To select a program, just
+ click on its tab.
To save the program you've just written, choose File->Save
- As...
+ As.... Similarly as in other programs you can choose File->Save
+ to save a program that already has a filename attached to it.
+ If you have many opened programs you have edited and wish to
+ save you can also choose File->Save All Unsaved.
+
+ Programs that have unsaved changes will have a "[+]" next to
+ their filename. This way you can see if the file on disk and
+ the currently opened tab differ in content. Programs which have
+ not yet had a filename associated with them are always
+ considered unsaved and no "[+]" is printed.
__________________________________________________________
-To Open and Run a Program
+3.3. To Open and Run a Program
To open a file, choose File->Open. A new tab containing the
file will appear in the work area. You can use this to edit the
@@ -405,9 +429,15 @@ To Open and Run a Program
To run a program from a file, choose File->Load and Run....
This will run the program without opening it in a separate tab.
This is equivalent to the load command.
+
+ If you have made edits to a file you wish to throw away and
+ want to reload to the version that's on disk, you can choose
+ the File->Reload from Disk menuitem. This is useful for
+ experimenting with a program and making temporary edits, to run
+ a program, but that you do not intend to keep.
__________________________________________________________
-Plotting
+Chapter 4. Plotting
Plotting support is only available in the graphical GNOME
version. All plotting accessible from the graphical interface
@@ -415,11 +445,11 @@ Plotting
window by either clicking on the Plot button on the toolbar or
selecting Plot from the Calculator menu. You can also access
the plotting functionality by using the plotting functions of
- the GEL language. See the Chapter called GEL Basics to find out
- how to enter expressions that Genius understands.
+ the GEL language. See Chapter 5 to find out how to enter
+ expressions that Genius understands.
__________________________________________________________
-Line Plots
+4.1. Line Plots
To graph real valued functions of one variable open the Create
Plot window. You can also use the LinePlot function on the
@@ -428,11 +458,11 @@ Line Plots
Once you click the Plot button, a window opens up with some
notebooks in it. You want to be in the Function line plot
notebook tab, and inside you want to be on the Functions /
- Expressions notebook tab. See Figure 1.
+ Expressions notebook tab. See Figure 4-1.
- [line_plot.png]
+ Figure 4-1. Create Plot Window
- Figure 1. Create Plot Window
+ [line_plot.png]
Type expressions with x as the independent variable into the
textboxes. Alternatively you can give names of functions such
@@ -445,7 +475,7 @@ Line Plots
dialog. The y (dependent) range can be set automatically by
turning on the Fit dependent axis checkbox. The names of the
variables can also be changed. Pressing the Plot button
- produces the graph shown in Figure 2.
+ produces the graph shown in Figure 4-2.
The variables can be renamed by clicking the Change variable
names... button, which is useful if you wish to print or save
@@ -454,9 +484,9 @@ Line Plots
completely, which is also useful if printing or saving, when
the legend might simply be clutter.
- [line_plot_graph.png]
+ Figure 4-2. Plot Window
- Figure 2. Plot Window
+ [line_plot_graph.png]
From here you can print out the plot, create encapsulated
postscript or a PNG version of the plot or change the zoom. If
@@ -467,7 +497,7 @@ Line Plots
the LinePlot function.
__________________________________________________________
-Parametric Plots
+4.2. Parametric Plots
In the create plot window, you can also choose the Parametric
notebook tab to create two dimensional parametric plots. This
@@ -477,24 +507,24 @@ Parametric Plots
variable t is given explicitly, and the function is sampled
according to the given increment. The x and y range can be set
automatically by turning on the Fit dependent axis checkbox, or
- it can be specified explicitly. See Figure 3.
+ it can be specified explicitly. See Figure 4-3.
- [parametric.png]
+ Figure 4-3. Parametric Plot Tab
- Figure 3. Parametric Plot Tab
+ [parametric.png]
- An example of a parametric plot is given in Figure 4. Similar
+ An example of a parametric plot is given in Figure 4-4. Similar
operations can be done on such graphs as can be done on the
other line plots. For plotting using the command line see the
documentation of the LinePlotParametric or LinePlotCParametric
function.
- [parametric_graph.png]
+ Figure 4-4. Parametric Plot
- Figure 4. Parametric Plot
+ [parametric_graph.png]
__________________________________________________________
-Slopefield Plots
+4.3. Slopefield Plots
In the create plot window, you can also choose the Slope field
notebook tab to create a two dimensional slope field plot.
@@ -520,7 +550,7 @@ Slopefield Plots
from the command line or programs.
__________________________________________________________
-Vectorfield Plots
+4.4. Vectorfield Plots
In the create plot window, you can also choose the Vector field
notebook tab to create a two dimensional vector field plot.
@@ -549,7 +579,7 @@ Vectorfield Plots
command line or programs.
__________________________________________________________
-Surface Plots
+4.5. Surface Plots
Genius can also plot surfaces. Select the Surface plot tab in
the main notebook of the Create Plot window. Here you can
@@ -558,8 +588,8 @@ Surface Plots
is the real part of z and y is the imaginary part). For example
to plot the modulus of the cosine function for complex
parameters, you could enter |cos(z)|. This would be equivalent
- to |cos(x+1i*y)|. See Figure 5. For plotting using the command
- line see the documentation of the SurfacePlot function.
+ to |cos(x+1i*y)|. See Figure 4-5. For plotting using the
+ command line see the documentation of the SurfacePlot function.
The z range can be set automatically by turning on the Fit
dependent axis checkbox. The variables can be renamed by
@@ -569,9 +599,9 @@ Surface Plots
legend, which is also useful if printing or saving, when the
legend might simply be clutter.
- [surface_graph.png]
+ Figure 4-5. Surface Plot
- Figure 5. Surface Plot
+ [surface_graph.png]
In surface mode, left and right arrow keys on your keyboard
will rotate the view along the z axis. Alternatively you can
@@ -586,7 +616,7 @@ Surface Plots
an audience.
__________________________________________________________
-GEL Basics
+Chapter 5. GEL Basics
GEL stands for Genius Extension Language. It is the language
you use to write programs in Genius. A program in GEL is simply
@@ -597,7 +627,7 @@ GEL Basics
possible, especially for use as a calculator.
__________________________________________________________
-Values
+5.1. Values
Values in GEL can be numbers, Booleans, or strings. GEL also
treats matrices as values. Values can be used in calculations,
@@ -605,7 +635,7 @@ Values
uses.
__________________________________________________________
-Numbers
+5.1.1. Numbers
Integers are the first type of number in GEL. Integers are
written in the normal way.
@@ -658,19 +688,19 @@ Numbers
8.01i
77*e^(1.3i)
- Important
+Important
- When entering imaginary numbers, a number must be in front of
- the i. If you use i by itself, Genius will interpret this as
- referring to the variable i. If you need to refer to i by
- itself, use 1i instead.
+ When entering imaginary numbers, a number must be in front of
+ the i. If you use i by itself, Genius will interpret this as
+ referring to the variable i. If you need to refer to i by
+ itself, use 1i instead.
- In order to use mixed fraction notation with imaginary numbers
- you must have the mixed fraction in parentheses. (i.e., (1
- 2/5)i)
+ In order to use mixed fraction notation with imaginary numbers
+ you must have the mixed fraction in parentheses. (i.e., (1
+ 2/5)i)
__________________________________________________________
-Booleans
+5.1.2. Booleans
Genius also supports native Boolean values. The two Boolean
constants are defined as true and false; these identifiers can
@@ -701,7 +731,7 @@ Booleans
before being compared to true.
__________________________________________________________
-Strings
+5.1.3. Strings
Like numbers and Booleans, strings in GEL can be stored as
values inside variables and passed to functions. You can also
@@ -736,7 +766,7 @@ string(22)
and <=> (comparison) operators
__________________________________________________________
-Null
+5.1.4. Null
There is a special value called null. No operations can be
performed on it, and nothing is printed when it is returned.
@@ -755,7 +785,7 @@ x=5;
or an empty reference.
__________________________________________________________
-Using Variables
+5.2. Using Variables
Syntax:
VariableName
@@ -768,25 +798,24 @@ genius> e
variable. This will return the value of the variable. You can
use a variable anywhere you would normally use a number or
string. In addition, variables are necessary when defining
- functions that take arguments (see the Section called Defining
- Functions).
+ functions that take arguments (see Section 5.3.1).
Tip Using Tab completion
- You can use Tab completion to get Genius to complete variable
- names for you. Try typing the first few letters of the name and
- pressing Tab.
+ You can use Tab completion to get Genius to complete variable
+ names for you. Try typing the first few letters of the name and
+ pressing Tab.
Important Variable names are case sensitive
- The names of variables are case sensitive. That means that
- variables named hello, HELLO and Hello are all different
- variables.
+ The names of variables are case sensitive. That means that
+ variables named hello, HELLO and Hello are all different
+ variables.
__________________________________________________________
-Setting Variables
+5.2.1. Setting Variables
Syntax:
<identifier> = <value>
@@ -810,25 +839,22 @@ a = b = 5
where a Boolean expression is expected.
For more information about the scope of variables, that is when
- are what variables visible, see the Section called Global
- Variables and Scope of Variables in the Chapter called
- Programming with GEL.
+ are what variables visible, see Section 6.5.
__________________________________________________________
-Built-in Variables
+5.2.2. Built-in Variables
GEL has a number of built-in ‘variables’, such as e, pi or
GoldenRatio. These are widely used constants with a preset
value, and they cannot be assigned new values. There are a
- number of other built-in variables. See the Section called
- Constants in the Chapter called List of GEL functions for a
- full list. Note that i is not by default the square root of
- negative one (the imaginary number), and is undefined to allow
- its use as a counter. If you wish to write the imaginary number
- you need to use 1i.
+ number of other built-in variables. See Section 11.4 for a full
+ list. Note that i is not by default the square root of negative
+ one (the imaginary number), and is undefined to allow its use
+ as a counter. If you wish to write the imaginary number you
+ need to use 1i.
__________________________________________________________
-Previous Result Variable
+5.2.3. Previous Result Variable
The Ans and ans variables can be used to get the result of the
last expression. For example, if you had performed some
@@ -836,7 +862,7 @@ Previous Result Variable
Ans+389
__________________________________________________________
-Using Functions
+5.3. Using Functions
Syntax:
FunctionName(argument1, argument2, ...)
@@ -854,25 +880,24 @@ gcd(921,317)
There are many built-in functions, such as sin, cos and tan.
You can use the help built-in command to get a list of
- available functions, or see the Chapter called List of GEL
- functions for a full listing.
+ available functions, or see Chapter 11 for a full listing.
Tip Using Tab completion
- You can use Tab completion to get Genius to complete function
- names for you. Try typing the first few letters of the name and
- pressing Tab.
+ You can use Tab completion to get Genius to complete function
+ names for you. Try typing the first few letters of the name and
+ pressing Tab.
- Important Function names are case sensitive
+ Important Function names are case sensitive
- The names of functions are case sensitive. That means that
- functions named dosomething, DOSOMETHING and DoSomething are
- all different functions.
+ The names of functions are case sensitive. That means that
+ functions named dosomething, DOSOMETHING and DoSomething are
+ all different functions.
__________________________________________________________
-Defining Functions
+5.3.1. Defining Functions
Syntax:
function <identifier>(<comma separated arguments>) = <function body>
@@ -892,7 +917,7 @@ function addup(a,b,c) = a+b+c
then addup(1,4,9) yields 14
__________________________________________________________
-Variable Argument Lists
+5.3.2. Variable Argument Lists
If you include ... after the last argument name in the function
declaration, then Genius will allow any number of arguments to
@@ -905,7 +930,7 @@ function f(a,b...) = b
Then f(1,2,3) yields [2,3], while f(1) yields a null.
__________________________________________________________
-Passing Functions to Functions
+5.3.3. Passing Functions to Functions
In Genius, it is possible to pass a function as an argument to
another function. This can be done using either ‘function
@@ -920,9 +945,8 @@ function b(x) = x*x;
f(b,2)
To pass functions that are not defined, you can use an
- anonymous function (see the Section called Defining Functions).
- That is, you want to pass a function without giving it a name.
- Syntax:
+ anonymous function (see Section 5.3.1). That is, you want to
+ pass a function without giving it a name. Syntax:
function(<comma separated arguments>) = <function body>
`(<comma separated arguments>) = <function body>
@@ -933,7 +957,7 @@ f(`(x) = x*x,2)
This will return 5.
__________________________________________________________
-Operations on Functions
+5.3.4. Operations on Functions
Some functions allow arithmetic operations, and some single
argument functions such as exp or ln, to operate on the
@@ -955,28 +979,21 @@ LinePlot(sin^2)
Warning
- Not all functions can be used in this way. For example, when
- you use a binary operation the functions must take the same
- number of arguments.
+ Not all functions can be used in this way. For example, when
+ you use a binary operation the functions must take the same
+ number of arguments.
__________________________________________________________
-Absolute Value / Modulus
-
- You can make an absolute value of something by putting the |'s
- around it. For example:
- |a-b|
-
- In case the expression is a complex number the result will be
- the modulus (distance from the origin). For example: |3 *
- e^(1i*pi)| returns 3.
- __________________________________________________________
+5.4. Separator
-Separator
-
- In GEL if you want to type more than one command you have to
- use the ; operator, which is a way to separate expressions,
- such a combined expression will return whatever is the result
- of the last one, so suppose you type the following:
+ GEL is somewhat different from other languages in how it deals
+ with multiple commands and functions. In GEL you must chain
+ commands together with a separator operator. That is, if you
+ want to type more than one expression you have to use the ;
+ operator in between the expressions. This is a way in which
+ both expressions are evaluated and the result of the second one
+ (or the last one if there is more than two expressions) is
+ returned. Suppose you type the following:
3 ; 5
This expression will yield 5.
@@ -987,16 +1004,22 @@ Separator
the ; is a terminator of statements, whereas in GEL it’s
actually a binary operator. If you are familiar with pascal
this should be second nature. However genius can let you
- pretend it is a terminator somewhat, if a ; is found at the end
- of a parenthesis or a block, genius will itself append a null
- node to it as if you would have written ;null. This is useful
- in case you do not want to return a value from say a loop, or
- if you handle the return differently. Note that it will
- slightly slow down the code if it is executed too often as
- there is one more operator involved.
+ pretend it is a terminator to some degree. If a ; is found at
+ the end of a parenthesis or a block, genius will append a null
+ to it as if you would have written ;null. This is useful in
+ case you do not want to return a value from say a loop, or if
+ you handle the return differently. Note that it will slightly
+ slow down the code if it is executed too often as there is one
+ more operator involved.
+
+ If you are typing expressions in a program you do not have to
+ add a semicolon. In this case genius will simply print the
+ return value whenever it executes the expression. However, do
+ note that if you are defining a function, the body of the
+ function is a single expression.
__________________________________________________________
-Comments
+5.5. Comments
GEL is similar to other scripting languages in that # denotes a
comments, that is text that is not meant to be evaluated.
@@ -1008,21 +1031,20 @@ Comments
x=123;
__________________________________________________________
-Modular Evaluation
+5.6. Modular Evaluation
Genius implements modular arithmetic. To use it you just add
- "mod <integer>" after the expression. Example:
- 2^(5!) * 3^(6!) mod 5
-
- It could be possible to do modular arithmetic by computing with
- integers and then modding in the end with the % operator, which
- simply gives the remainder, but that may be time consuming if
- not impossible when working with larger numbers. For example,
- 10^(10^10) % 6 will simply not work (the exponent will be too
- large), while 10^(10^10) mod 6 is instantaneous. The first
- expression first tries to compute the integer 10^(10^10) and
- then find remainder after division by 6, while the second
- expression evaluates everything modulo 6 to begin with.
+ "mod <integer>" after the expression. Example: 2^(5!) * 3^(6!)
+ mod 5 It could be possible to do modular arithmetic by
+ computing with integers and then modding in the end with the %
+ operator, which simply gives the remainder, but that may be
+ time consuming if not impossible when working with larger
+ numbers. For example, 10^(10^10) % 6 will simply not work (the
+ exponent will be too large), while 10^(10^10) mod 6 is
+ instantaneous. The first expression first tries to compute the
+ integer 10^(10^10) and then find remainder after division by 6,
+ while the second expression evaluates everything modulo 6 to
+ begin with.
You can calculate the inverses of numbers mod some integer by
just using rational numbers (of course the inverse has to
@@ -1063,7 +1085,7 @@ genius> 2*2 mod 7
mod.
__________________________________________________________
-List of GEL Operators
+5.7. List of GEL Operators
Everything in gel is really just an expression. Expressions are
stringed together with different operators. As we have seen,
@@ -1086,7 +1108,9 @@ List of GEL Operators
gets translated to a ==.
|a|
- Absolute value or modulus (if a is a complex number).
+ Absolute value. In case the expression is a complex
+ number the result will be the modulus (distance from the
+ origin). For example: |3 * e^(1i*pi)| returns 3.
See Mathworld for more information.
@@ -1145,9 +1169,8 @@ List of GEL Operators
a mod b
Modular evaluation operator. The expression a is
- evaluated modulo b. See the Section called Modular
- Evaluation. Some functions and operators behave
- differently modulo an integer.
+ evaluated modulo b. See Section 5.6. Some functions and
+ operators behave differently modulo an integer.
a!
Factorial operator. This is like 1*...*(n-2)*(n-1)*n.
@@ -1221,13 +1244,11 @@ List of GEL Operators
&a
Variable referencing (to pass a reference to a
- variable). See the Section called References in the
- Chapter called Programming with GEL.
+ variable). See Section 6.8.
*a
Variable dereferencing (to access a referenced
- variable). See the Section called References in the
- Chapter called Programming with GEL.
+ variable). See Section 6.8.
a'
Matrix conjugate transpose. That is, rows and columns
@@ -1327,34 +1348,34 @@ genius> 1:2:9
Note
- The @() operator makes the : operator most useful. With this
- you can specify regions of a matrix. So that a@(2:4,6) is the
- rows 2,3,4 of the column 6. Or a@(,1:2) will get you the first
- two columns of a matrix. You can also assign to the @()
- operator, as long as the right value is a matrix that matches
- the region in size, or if it is any other type of value.
+ The @() operator makes the : operator most useful. With this
+ you can specify regions of a matrix. So that a@(2:4,6) is the
+ rows 2,3,4 of the column 6. Or a@(,1:2) will get you the first
+ two columns of a matrix. You can also assign to the @()
+ operator, as long as the right value is a matrix that matches
+ the region in size, or if it is any other type of value.
Note
- The comparison operators (except for the <=> operator, which
- behaves normally), are not strictly binary operators, they can
- in fact be grouped in the normal mathematical way, e.g.:
- (1<x<=y<5) is a legal boolean expression and means just what it
- should, that is (1<x and x≤y and y<5)
+ The comparison operators (except for the <=> operator, which
+ behaves normally), are not strictly binary operators, they can
+ in fact be grouped in the normal mathematical way, e.g.:
+ (1<x<=y<5) is a legal boolean expression and means just what it
+ should, that is (1<x and x≤y and y<5)
Note
- The unitary minus operates in a different fashion depending on
- where it appears. If it appears before a number it binds very
- closely, if it appears in front of an expression it binds less
- than the power and factorial operators. So for example -1^k is
- really (-1)^k, but -foo(1)^k is really -(foo(1)^k). So be
- careful how you use it and if in doubt, add parentheses.
+ The unitary minus operates in a different fashion depending on
+ where it appears. If it appears before a number it binds very
+ closely, if it appears in front of an expression it binds less
+ than the power and factorial operators. So for example -1^k is
+ really (-1)^k, but -foo(1)^k is really -(foo(1)^k). So be
+ careful how you use it and if in doubt, add parentheses.
__________________________________________________________
-Programming with GEL
+Chapter 6. Programming with GEL
-Conditionals
+6.1. Conditionals
Syntax:
if <expression1> then <expression2> [else <expression3>]
@@ -1376,9 +1397,9 @@ if a=5 then a=a-1
if a==5 then a:=a-1
__________________________________________________________
-Loops
+6.2. Loops
-While Loops
+6.2.1. While Loops
Syntax:
while <expression1> do <expression2>
@@ -1393,7 +1414,7 @@ do <expression2> until <expression1>
is translated into == just as for the if statement.
__________________________________________________________
-For Loops
+6.2.2. For Loops
Syntax:
for <identifier> = <from> to <to> do <body>
@@ -1430,10 +1451,10 @@ for x = 0 to 1 by 1/10 do print(x)
execution of your code may differ on older versions.
__________________________________________________________
-Foreach Loops
+6.2.3. Foreach Loops
Syntax:
- for <identifier> in <matrix> do <body>
+for <identifier> in <matrix> do <body>
For each element in the matrix, going row by row from left to
right we execute the body with the identifier set to the
@@ -1449,7 +1470,7 @@ for n in RowsOf ([1,2:3,4]) do print(n)
will print out [1,2] and then [3,4].
__________________________________________________________
-Break and Continue
+6.2.4. Break and Continue
You can also use the break and continue commands in loops. The
continue continue command will restart the current loop at its
@@ -1461,7 +1482,7 @@ while(<expression1>) do (
)
__________________________________________________________
-Sums and Products
+6.3. Sums and Products
Syntax:
sum <identifier> = <from> to <to> do <body>
@@ -1480,10 +1501,10 @@ prod <identifier> in <matrix> do <body>
sum returns 0 and prod returns 1 as is the standard convention.
For floating point numbers the same roundoff error protection
- is done as in the for loop. See the Section called For Loops.
+ is done as in the for loop. See Section 6.2.2.
__________________________________________________________
-Comparison Operators
+6.4. Comparison Operators
The following standard comparison operators are supported in
GEL and have the obvious meaning: ==, >=, <=, !=, <>, <, >.
@@ -1515,7 +1536,7 @@ if a==b then c
a=1 will not set a=1 since the first argument was true.
__________________________________________________________
-Global Variables and Scope of Variables
+6.5. Global Variables and Scope of Variables
GEL is a dynamically scoped language. We will explain what this
means below. That is, normal variables and functions are
@@ -1608,7 +1629,7 @@ set("a",3)
Variables and Returning Functions.
__________________________________________________________
-Parameter variables
+6.6. Parameter variables
As we said before, there exist special variables called
parameters that exist in all scopes. To declare a parameter
@@ -1625,7 +1646,7 @@ parameter foo = 1
Some parameters are built-in and modify the behavior of genius.
__________________________________________________________
-Returning
+6.7. Returning
Normally a function is one or several expressions separated by
a semicolon, and the value of the last expression is returned.
@@ -1646,7 +1667,7 @@ function f(x) = (
)
__________________________________________________________
-References
+6.8. References
It may be necessary for some functions to return more than one
value. This may be accomplished by returning a vector of
@@ -1681,7 +1702,7 @@ t=&f;
gives us 4.
__________________________________________________________
-Lvalues
+6.9. Lvalues
An lvalue is the left hand side of an assignment. In other
words, an lvalue is what you assign something to. Valid lvalues
@@ -1712,9 +1733,9 @@ a@(4:8,3) := [1,2,3,4,5]'
comparison.
__________________________________________________________
-Advanced Programming with GEL
+Chapter 7. Advanced Programming with GEL
-Error Handling
+7.1. Error Handling
If you detect an error in your function, you can bail out of
it. For normal errors, such as wrong types of arguments, you
@@ -1733,7 +1754,7 @@ function f(M) = (
)
__________________________________________________________
-Toplevel Syntax
+7.2. Toplevel Syntax
The syntax is slightly different if you enter statements on the
top level versus when they are inside parentheses or inside
@@ -1766,7 +1787,7 @@ if Something() then (
)
__________________________________________________________
-Returning Functions
+7.3. Returning Functions
It is possible to return functions as value. This way you can
build functions that construct special purpose functions
@@ -1860,7 +1881,7 @@ g(10)
of 5 was added to the private dictionary.
__________________________________________________________
-True Local Variables
+7.4. True Local Variables
When passing functions into other functions, the normal scoping
of variables might be undesired. For example:
@@ -1912,7 +1933,7 @@ function f(g,x) = (
function does not see implementation details and get confused.
__________________________________________________________
-GEL Startup Procedure
+7.5. GEL Startup Procedure
First the program looks for the installed library file (the
compiled version lib.cgel) in the installed directory, then it
@@ -1924,7 +1945,7 @@ GEL Startup Procedure
lib.cgel
__________________________________________________________
-Loading Programs
+7.6. Loading Programs
Sometimes you have a larger program you wrote into a file and
want to read that file into Genius Mathematics Tool. In these
@@ -1950,14 +1971,14 @@ cd directory_with_gel_programs
ls *.gel
__________________________________________________________
-Matrices in GEL
+Chapter 8. Matrices in GEL
Genius has support for vectors and matrices and possesses a
sizable library of matrix manipulation and linear algebra
functions.
__________________________________________________________
-Entering Matrices
+8.1. Entering Matrices
To enter matrices, you can use one of the following two
syntaxes. You can either enter the matrix on one line,
@@ -2008,12 +2029,12 @@ b = [ a, 10
Note
- Be careful about using returns for expressions inside the [ ]
- brackets, as they have a slightly different meaning there. You
- will start a new row.
+ Be careful about using returns for expressions inside the [ ]
+ brackets, as they have a slightly different meaning there. You
+ will start a new row.
__________________________________________________________
-Conjugate Transpose and Transpose Operator
+8.2. Conjugate Transpose and Transpose Operator
You can conjugate transpose a matrix by using the ' operator.
That is the entry in the ith column and the jth row will be the
@@ -2033,7 +2054,7 @@ Conjugate Transpose and Transpose Operator
with real matrices and vectors.
__________________________________________________________
-Linear Algebra
+8.3. Linear Algebra
Genius implements many useful linear algebra and matrix
manipulation routines. See the Linear Algebra and Matrix
@@ -2069,14 +2090,14 @@ Linear Algebra
will be very fast.
__________________________________________________________
-Polynomials in GEL
+Chapter 9. Polynomials in GEL
Currently Genius can handle polynomials of one variable written
out as vectors, and do some basic operations with these. It is
planned to expand this support further.
__________________________________________________________
-Using Polynomials
+9.1. Using Polynomials
Currently polynomials in one variable are just horizontal
vectors with value only nodes. The power of the term is the
@@ -2108,19 +2129,18 @@ f(2)
function such as FindRootBisection, FindRootFalsePosition,
FindRootMullersMethod, or FindRootSecant.
- See the Section called Polynomials in the Chapter called List
- of GEL functions in the function list for the rest of functions
- acting on polynomials.
+ See Section 11.15 in the function list for the rest of
+ functions acting on polynomials.
__________________________________________________________
-Set Theory in GEL
+Chapter 10. Set Theory in GEL
Genius has some basic set theoretic functionality built in.
Currently a set is just a vector (or a matrix). Every distinct
object is treated as a different element.
__________________________________________________________
-Using Sets
+10.1. Using Sets
Just like vectors, objects in sets can include numbers,
strings, null, matrices and vectors. It is planned in the
@@ -2154,13 +2174,13 @@ genius> IsIn (1, [0,1,2])
IsSubset(null,X) is always true.
__________________________________________________________
-List of GEL functions
+Chapter 11. List of GEL functions
To get help on a specific function from the console type:
help FunctionName
__________________________________________________________
-Commands
+11.1. Commands
help
@@ -2203,7 +2223,7 @@ plugin plugin_name
the system in the proper directory.
__________________________________________________________
-Basic
+11.2. Basic
AskButtons
@@ -2278,7 +2298,8 @@ GetCurrentModulo
Identity (x)
- Identity function, returns its argument.
+ Identity function, returns its argument. It is
+ equivalent to function Identity(x)=x.
IntegerFromBoolean
@@ -2646,7 +2667,7 @@ warranty
Gives the warranty information.
__________________________________________________________
-Parameters
+11.3. Parameters
ChopTolerance
@@ -2918,7 +2939,7 @@ VectorfieldTicks = [vertical,horizontal]
Version 1.0.10 onwards.
__________________________________________________________
-Constants
+11.4. Constants
CatalanConstant
@@ -2928,7 +2949,7 @@ CatalanConstant
to be the series where terms are (-1^k)/((2*k+1)^2),
where k ranges from 0 to infinity.
- See Mathworld for more information.
+ See Wikipedia, or Mathworld for more information.
EulerConstant
@@ -2936,7 +2957,7 @@ EulerConstant
Aliases: gamma
- Euler's Constant gamma. Sometimes called the
+ Euler's constant gamma. Sometimes called the
Euler-Mascheroni constant.
See Wikipedia or Planetmath or Mathworld for more
@@ -2955,7 +2976,11 @@ GoldenRatio
Gravity
- Free fall acceleration at sea level.
+ Free fall acceleration at sea level in meters per second
+ squared. This is the standard gravity constant 9.80665.
+ The gravity in your particular neck of the woods might
+ be different due to different altitude and the fact that
+ the earth is not perfectly round and uniform.
See Wikipedia for more information.
@@ -2964,8 +2989,11 @@ Gravity
e
The base of the natural logarithm. e^x is the
- exponential function exp. This is the number
- approximately 2.71828182846...
+ exponential function exp. It is approximately
+ 2.71828182846... This number is sometimes called Euler's
+ number, although there are several numbers that are also
+ called Euler's. An example is the gamma constant:
+ EulerConstant.
See Wikipedia or Planetmath or Mathworld for more
information.
@@ -2982,7 +3010,7 @@ pi
information.
__________________________________________________________
-Numeric
+11.5. Numeric
AbsoluteValue
@@ -2992,7 +3020,7 @@ AbsoluteValue (x)
Absolute value of a number and if x is a complex value
the modulus of x. I.e. this the distance of x to the
- origin.
+ origin. This is equivalent to |x|.
See Wikipedia, Planetmath (absolute value), Planetmath
(modulus), Mathworld (absolute value) or Mathworld
@@ -3038,7 +3066,8 @@ Im (z)
Aliases: ImaginaryPart
- Get the imaginary part of a complex number.
+ Get the imaginary part of a complex number. For example
+ Re(3+4i) yields 4.
See Wikipedia for more information.
@@ -3052,7 +3081,10 @@ IntegerQuotient (m,n)
IsComplex (num)
- Check if argument is a complex (non-real) number.
+ Check if argument is a complex (non-real) number. Do
+ note that we really mean nonreal number. That is,
+ IsComplex(3) yields false, while IsComplex(3-1i) yields
+ true.
IsComplexRational
@@ -3067,7 +3099,7 @@ IsComplexRational (num)
IsFloat (num)
- Check if argument is a floating point number
+ Check if argument is a real floating point number
(non-complex).
IsGaussInteger
@@ -3076,7 +3108,9 @@ IsGaussInteger (num)
Aliases: IsComplexInteger
- Check if argument is a possibly complex integer.
+ Check if argument is a possibly complex integer. That is
+ a complex integer is a number of the form n+1i*m where n
+ and m are integers.
IsInteger
@@ -3088,7 +3122,8 @@ IsInteger (num)
IsNonNegativeInteger (num)
- Check if argument is a non-negative real integer.
+ Check if argument is a non-negative real integer. That
+ is, either a positive integer or zero.
IsPositiveInteger
@@ -3127,7 +3162,8 @@ Re (z)
Aliases: RealPart
- Get the real part of a complex number.
+ Get the real part of a complex number. For example
+ Re(3+4i) yields 3.
See Wikipedia for more information.
@@ -3194,6 +3230,9 @@ ln (x)
The natural logarithm, the logarithm to base e.
+ See Wikipedia or Planetmath or Mathworld for more
+ information.
+
log
log (x)
@@ -3300,7 +3339,7 @@ trunc (x)
Truncate number to an integer (return the integer part).
__________________________________________________________
-Trigonometry
+11.6. Trigonometry
acos
@@ -3510,7 +3549,7 @@ tanh (x)
See Planetmath for more information.
__________________________________________________________
-Number Theory
+11.7. Number Theory
AreRelativelyPrime
@@ -4015,7 +4054,7 @@ lcm (a,args...)
See Planetmath or Mathworld for more information.
__________________________________________________________
-Matrix Manipulation
+11.8. Matrix Manipulation
ApplyOverMatrix
@@ -4438,7 +4477,7 @@ zeros (rows,columns...)
columns are zero.
__________________________________________________________
-Linear Algebra
+11.9. Linear Algebra
AuxiliaryUnitMatrix
@@ -5140,7 +5179,7 @@ rref (M)
See Wikipedia or Planetmath for more information.
__________________________________________________________
-Combinatorics
+11.10. Combinatorics
Catalan
@@ -5379,7 +5418,7 @@ nPr (n,r)
See Mathworld or Wikipedia for more information.
__________________________________________________________
-Calculus
+11.11. Calculus
CompositeSimpsonsRule
@@ -5685,7 +5724,7 @@ TwoSidedThreePointFormula (f,x0,h)
Compute two-sided derivative using three-point formula.
__________________________________________________________
-Functions
+11.12. Functions
Argument
@@ -5949,7 +5988,7 @@ sinc (x)
Version 1.0.16 onwards.
__________________________________________________________
-Equation Solving
+11.13. Equation Solving
CubicFormula
@@ -6221,7 +6260,7 @@ d","Second");
Version 1.0.10 onwards.
__________________________________________________________
-Statistics
+11.14. Statistics
Average
@@ -6316,7 +6355,7 @@ StandardDeviation (m)
Calculate the standard deviation of a whole matrix.
__________________________________________________________
-Polynomials
+11.15. Polynomials
AddPoly
@@ -6403,7 +6442,7 @@ TrimPoly (p)
Trim zeros from a polynomial (as vector).
__________________________________________________________
-Set Theory
+11.16. Set Theory
Intersection
@@ -6448,7 +6487,7 @@ Union (X,Y)
vectors pretending to be sets).
__________________________________________________________
-Commutative Algebra
+11.17. Commutative Algebra
MacaulayBound
@@ -6479,7 +6518,7 @@ MacaulayRep (c,d)
Version 1.0.15 onwards.
__________________________________________________________
-Miscellaneous
+11.18. Miscellaneous
ASCIIToString
@@ -6509,7 +6548,7 @@ StringToAlphabet (str,alphabet)
letters.
__________________________________________________________
-Symbolic Operations
+11.19. Symbolic Operations
SymbolicDerivative
@@ -6556,7 +6595,7 @@ SymbolicTaylorApproximationFunction (f,x0,n)
around x0 to the nth degree. (See SymbolicDerivative)
__________________________________________________________
-Plotting
+11.20. Plotting
ExportPlot
@@ -7093,7 +7132,7 @@ VectorfieldPlot (funcx, funcy, x1, x2, y1, y2)
genius> VectorfieldPlot(`(x,y)=x^2-y, `(x,y)=y^2-x, -1, 1, -1, 1)
__________________________________________________________
-Example Programs in GEL
+Chapter 12. Example Programs in GEL
Here is a function that calculates factorials:
function f(x) = if x <= 1 then 1 else (f(x-1)*x)
@@ -7168,30 +7207,28 @@ function MyOwnREF(m) = (
)
__________________________________________________________
-Settings
+Chapter 13. Settings
To configure Genius Mathematics Tool, choose
Settings->Preferences. There are several basic parameters
provided by the calculator in addition to the ones provided by
the standard library. These control how the calculator behaves.
- Note Changing Settings with GEL
+ Note Changing Settings with GEL
- Many of the settings in Genius are simply global variables, and
- can be evaluated and assigned to in the same way as normal
- variables. See the Section called Using Variables in the
- Chapter called GEL Basics about evaluating and assigning to
- variables, and the Section called Parameters in the Chapter
- called List of GEL functions for a list of settings that can be
- modified in this way.
+ Many of the settings in Genius are simply global variables, and
+ can be evaluated and assigned to in the same way as normal
+ variables. See Section 5.2 about evaluating and assigning to
+ variables, and Section 11.3 for a list of settings that can be
+ modified in this way.
- As an example, you can set the maximum number of digits in a
- result to 12 by typing:
-MaxDigits = 12
+ As an example, you can set the maximum number of digits in a
+ result to 12 by typing:
+ MaxDigits = 12
__________________________________________________________
-Output
+13.1. Output
Maximum digits to output
The maximum digits in a result (MaxDigits)
@@ -7254,8 +7291,8 @@ Output
In addition to these preferences, there are some preferences
that can only be changed by setting them in the workspace
- console. For others that may affect the output see the Section
- called Parameters in the Chapter called List of GEL functions.
+ console. For others that may affect the output see Section
+ 11.3.
IntegerOutputBase
The base that will be used to output integers
@@ -7269,7 +7306,7 @@ Output
for typsetting in LaTeX, MathML (XML), or in Troff.
__________________________________________________________
-Precision
+13.2. Precision
Floating point precision
The floating point precision in bits (FloatPrecision).
@@ -7288,7 +7325,7 @@ Precision
box, restart genius and then uncheck it again.
__________________________________________________________
-Terminal
+13.3. Terminal
Terminal refers to the console in the work area.
@@ -7308,7 +7345,7 @@ Terminal
remotely.
__________________________________________________________
-Memory
+13.4. Memory
Maximum number of nodes to allocate
Internally all data is put onto small nodes in memory.
@@ -7331,9 +7368,9 @@ Memory
amount of memory that genius uses.
__________________________________________________________
-About Genius Mathematics Tool
+Chapter 14. About Genius Mathematics Tool
- Genius Mathematics Tool was written by Jiří (George) Lebl
+ Genius Mathematics Tool was written by Jiř (George) Lebl
(<jirka 5z com>). The history of Genius Mathematics Tool goes
back to late 1997. It was the first calculator program for
GNOME, but it then grew beyond being just a desktop calculator.
@@ -7351,7 +7388,7 @@ About Genius Mathematics Tool
in the file COPYING included with the source code of this
program.
- Jiří Lebl was during various parts of the development partially
+ Jiř Lebl was during various parts of the development partially
supported for the work by NSF grants DMS 0900885, DMS 1362337,
the University of Illinois at Urbana-Champaign, the University
of California at San Diego, the University of
diff --git a/src/funclib.c b/src/funclib.c
index 7069719..4132b3f 100644
--- a/src/funclib.c
+++ b/src/funclib.c
@@ -3060,10 +3060,20 @@ max_op (GelCtx *ctx, GelETree * * a, gboolean *exception)
g_assert (max != NULL);
return gel_copynode (max);
} else if (a[0]->type == GEL_VALUE_NODE) {
+ if (mpw_is_complex (a[0]->val.value)) {
+ gel_errorout (_("%s: Cannot compare complex numbers"),
+ "max");
+ return NULL;
+ }
+
/*
* Evil optimization to avoid copying the node from the argument
*/
return gel_stealnode (a[0]);
+ } else {
+ gel_errorout (_("%s: Input not a number of matrix of numbers."),
+ "max");
+ return NULL;
}
}
@@ -3147,10 +3157,19 @@ min_op (GelCtx *ctx, GelETree * * a, gboolean *exception)
g_assert (min != NULL);
return gel_copynode (min);
} else if (a[0]->type == GEL_VALUE_NODE) {
+ if (mpw_is_complex (a[0]->val.value)) {
+ gel_errorout (_("%s: Cannot compare complex numbers"),
+ "min");
+ return NULL;
+ }
/*
* Evil optimization to avoid copying the node from the argument
*/
return gel_stealnode (a[0]);
+ } else {
+ gel_errorout (_("%s: Input not a number of matrix of numbers."),
+ "min");
+ return NULL;
}
}
diff --git a/src/geniustests.txt b/src/geniustests.txt
index 4350cee..66f87eb 100644
--- a/src/geniustests.txt
+++ b/src/geniustests.txt
@@ -175,7 +175,12 @@ max(1.3,5/4) 1.3
max(1.3,1.3) 1.3
min(1.3,1.3) 1.3
min(-1.3,1.3) -1.3
+min(null) min((null))
+max(null) max((null))
+min(3i) min(3i)
+max(3i) max(3i)
min(3i,5) min(3i,5)
+max(3i,5) max(3i,5)
max([1,2,3],2) [2,2,3]
min([1,2,3],2) [1,2,2]
prod k=2 to 4 do k+1 60
@@ -203,6 +208,16 @@ IsRational(3.1) false
IsRational(3) true
IsComplex(3i) true
IsComplex(3) false
+IsComplex(3-1i) true
+IsComplexInteger(3-1i) true
+IsComplexInteger(3) true
+IsComplexInteger(3.0) false
+IsComplexInteger(3+1.1i) false
+IsValue(0.1+8i) true
+IsValue(false) false
+IsValue([0.1]) false
+IsValue(null) false
+IsValue(`(x)=x^2) false
IsFloat(3.1) true
IsFloat(3) false
I(4) [1,0,0,0;0,1,0,0;0,0,1,0;0,0,0,1]
@@ -242,6 +257,8 @@ not &d (not (&d))
not 3i false
if(3=="3")then 1 else 0 1
if(3=="3 ")then 1 else 0 0
+IsNull([1]) false
+IsNull(`(x)=x^2) false
IsNull(1) false
IsNull(.) true
[1,2;3,4]+[5,6;7,8] [6,8;10,12]
@@ -936,6 +953,11 @@ NullSpace([1,1;2,2]) [1;-1]
NullSpace([1,1;2,2;3,3]) [1;-1]
NullSpace([0,0;1,1;2,2;3,3]) [1;-1]
NullSpace([0,0;1,0;2,0;3,0]) [0;-1]
+Parse("3+4") 7
+1+Parse("3+4") 8
+Evaluate("3+4") 7
+1+Evaluate("3+4") 8
+Parse("x+4") (x+4)
Parse("a+b") (a+b)
Parse(null)+1 ((null)+1)
Parse("x=1;x=x+1;x") ((x=1);(x=(x+1));x)
@@ -1184,6 +1206,12 @@ SetElement("r",-1,2,99)
SetElement("r",-1,2,99)
|EvenPeriodicExtension (`(x)=x^3,2) call (-0.7) - (0.7)^3|<10^-20 true
|EvenPeriodicExtension (`(x)=x^3,2) call (-0.7+4) - (0.7)^3|<10^-20 true
|EvenPeriodicExtension (`(x)=x^3,2) call (0.7+2) - (0.7)^3|<10^-20 false
+Re(3+4i) 3
+Im(3+4i) 4
+Im(4i) 4
+Re(4i) 0
+Re(4) 4
+Im(4) 0
load "nullspacetest.gel" true
load "longtest.gel" true
load "testprec.gel" true
[
Date Prev][
Date Next] [
Thread Prev][
Thread Next]
[
Thread Index]
[
Date Index]
[
Author Index]
