# Edugraphe: User's manual

## Contents

- 1. Overview
- 2. Objects' creation

- Points

- Normal point
- Point on a curve or a line
- Intersection point
- Mark

- Lines

- Line
- Tangent line to a curve

- Curves

- Function's curve
- Differential equation's solution

- Sequences

- Recurring sequence
- Sequence defined with a function

- Equation f(x) = k
- Domain under a curve
- Text
- Object's name and color

- 3. Changes

- Changing objects' properties
- Moving objects
- New settings

- 4. Saving the graph

- tsm format
- png and eps graphics formats
- html format

- 5. Menus

Edugraphe © Joël Amblard - Distributed under the terms of the GNU General Public License
Project home site : http://perso.wanadoo.fr/joel.amblard/edugraphe/

# 1. Overview

Basics.
Look at this first snapshot :

You can see :

- a menu bar with 5 menus
- a tools bar with 20 buttons
- a canvas with a few graphics objects

Under the mac OSX system , the screen menu bar contains the application's menus . Under other systems, the application's window contains the whole menu bar.
When you click on an object :

- a dialog bar is visible at the bottom of the window.

For example, clicking on the curve C , you can see :

The dialog bar displays some of the selected object's properties. It is then easy to modify them. Sometimes, you can display additional informations.

Working with edugraphe.
The application is running under three main modes : create , select and delete . Usually :

- You initiate the creation of an objet with a tools bar's button, e.g. , or selecting the appropriate option in the Create menu : the application runs now in the create mode , make the dialog bar visible and wait for your instructions.
- The object is created : the application turns in the select mode and shows the object's properties in the dialog bar.
  There is only one exception : after choosing , you create a normal point when clicking in the window. Then the application stays in the create mode and you can create other points with new clicks.
- You ask for suppressing objects with : the application turns then in the delete mode . When clicking on an object you delete it and all the depending ones.
  The application stays in the delete mode : you turn to the select mode with the button .

There are twelve objects you can create.They belong to one of these six groups :

- points
- lines
- curves
- sequences
- domains
- texts

When you ask for creating an object, the dialog bar is visible. If a message is displayed in the bar, the application is waiting for one or more clicks. If one or more fieds are displayed, you must generally type informations for creating the desired object.
There are three other objects you can use :

- the labels which are a small text beside an existing object : you can create and modify them in the Appearance dialog
- the axes and the grids : you can't delete them but you can modify them in the Settings dialog.

Summary of the possibilities. You can with edugraphe :

- create objets , add names , change colors
- delete or modify the existing objects
- move objects , move the whole graph
- change the color and the scales of the axes and the grids
- choose another font
- save your job under the eps et png graphics formats
- save a part only of the window
- create an applet

contents

# 2. Objects' creation

### 2.1 Points

#### Normal point

Click on the Point button in the tools bar. The dialog bar shows the message Point ... ? : you have to click at any empty place in the window. Then the dialog bar looks like :

Modify the coordinates in the first textfield. You validate the datas

- with a line's end in the textfield : the point moves to a new place and the bar stays visible
- with a click on the Ok button : datas are registered and the bar is no more visible

You create other points with new clicks in the window.

#### Point on a curve or a line

Click on the Point on a curve button in the tools bar. The dialog bar shows the message Point on ... ? : you have to click on any curve or line.

- When you click on a curve, the dialog bar looks like :
  Modify the X-coordinate of the point : a new Y-value will be computed for the point on the curve.
- When you click on a line, the dialog bar looks like :
  Modify the coordinates of the point : the point will move to the nearest place on the line.

See normal point for datas' validation.

#### Intersection point

Click on the Intersection point button in the tools bar. The dialog bar shows the message Intersection with ... ? : you have to click on two objets which are lines or curves. The dialog bar looks like :

When the two objects intersect, the result is the intersection point which is nearest with the last click. The Ok button hide the bar.

#### Mark on the axis

Click on the Mark button in the tools bar. The dialog bar shows the message Mark ... ? : you have to click on one of the axis. The dialog bar looks like :

You can see a segment perpendicular to the choosen axis. The default name of the point is the X-coordinate or the Y-coordinate, according with the choosen axis.
See point on a line or a curve for datas' validation and modifications.
Points samples :
contents

### 2.2 Lines

#### Line

Click on the Line button in the tools bar. The dialog bar looks like :

A line is defined several ways.

- with an equation
  Type a mathematical expression which defines a line in the textfield.
  This expression should look like y = m*x + p or a*x + b*y = c or a*x + b*y + c (in the latest case = 0 is supplied). You validate the datas with a line's end in the textfield or a click on the Ok button. In the first case the dialog bar looks like :
  If you click on the Ok button , the bar is hidden. You will be able to modify the datas when you select the line.
- with two clicks
  You first click on a point or at an empty place in the window (in this case a new point is created). The dialog bar looks like :
  It is no more possible to choose any equation. Then you have to click :
  - at an empty place : the line is defined with a point and a direction
  - on an existing point : the line is defined with two points
  The dialog bar looks like :
  No modification is allowed : the bar is read-only.

#### Tangent line to a curve

Click on the Tangent button in the tools bar. The dialog bar shows the message Tangent to ... ? . You have to click on :

- a curve : the tangent is created according with the X-coordinate of the click and the dialog bar looks like
  You will be able to modify the X-coordinate when you select the tangent line.
- or a point on a curve : the tangent is created at this point and the dialog bar looks like
  No modification is allowed : the bar is read-only.

You cannot create a tangent with a line . You must use a function's curve or a differential equation's solution .
Lines samples :
contents

### 2.3 Curves

#### Function's curve

Click on the Curve button in the tools bar. The dialog bar looks like :

You have to type a mathematical expression in the first textfield. Yon can use

- the usual operators : + , - , * , / , ^
- the usual functions : sqrt (square root) , cos , sin , tan , acos , asin , atan , ln , log , exp and abs

Then you may :

- choose the variable's name (default : x).
- choose the interval where the function is defined.
  If the left value is unknown, it will be -∞ (default) and the application replace it with the minimal X-coordinate in the window for plotting and computing .
  If the right value is unknown, it will be +∞ (default) and the application replace it with the maximal X-coordinate in the window for plotting and computing .

You validate the datas with a line's end in any textfield (the bar stays visible) or a click on the Ok button (the bar is hidden). You will be able to modify the datas when you select the curve.
Curves samples :

#### Differential equation's solution

Click on the Euler button in the tools bar. The dialog bar looks like :

You have to type in the first textfield a mathematical expression with two possible variables : y (the function) and x (the function's variable). The application compute the value of the derivative with this expression. You can refer to Curves for valid mathematical expressions.
Then you may :

- choose the coordinates for the first point : the solution is computed beginning with this point.
  When the first point is not defined, a direction field is drawn using grids' points : every time the grids' point were the first point, the application draws the direction of the tangent line to the solution at this point.
- choose the interval where the expression is defined : you can refer to Function's curve for more information.
- choose the precision which is the number of intervals used for plotting and computing.

Refer to Function's curve for datas' validation. You will be able to modify the datas when you select the solution.
Differential equations samples :
contents

### 2.4 Sequences

#### Recurring sequence

Click on the Recurring sequence button in the tools bar. The dialog bar shows the message Recurring sequence ... ? : you have to click on a curve. The dialog bar looks like :

Then you may :

- choose an initial value
- choose the number of computed values (iteration count)
- show/hide the computed values with the checkbox show

You will be able to modify the datas when you select the sequence : click on the point who lies on the X-axis and whose X-coordinate is the initial value.

#### Sequence defined with a function

Click on the Sequence button in the tools bar. The dialog bar looks like :

A sequence is defined several ways.

- sequence un = f(n)
  You have to type in the first textfield a mathematical expression which defines a function of the variable n. Then choose the first index n0 : the first value of the sequence will be automatically computed in the next textfield.
- sequence un+1 = f(un)
  You have to type in the first textfield a mathematical expression who defines a function of the variable y which represents the previous value of the sequence. Then you must choose the first index n0 and the first value of the sequence.
- sequence un+1 = f(un , n)
  You have to type in the first textfield a mathematical expression who defines a function of the two variables n et y. Then you must choose the first index n0 and the first value of the sequence.

Then you may :

- choose the iteration count
- show/hide the computed values with the checkbox show

The application draw the first points of the sequence. You will be able to modify the datas when you select the sequence : click on one of these points.
Sequences samples :
contents

### 2.5 Equation f(x) = k

Click on the Equation button in the tools bar. The dialog bar shows the message Equation ... ? : you have to click on a curve . The dialog bar looks like :

Then you may :

- chooose the searched-value k
- choose the interval [a , b] where the equation has to be solved. Default : the interval where the function is defined.
- choose a method : dichotomy , scanning or newton
- show/hide the computed values with the checkbox show
- choose the precision

When you choose scanning or dichotomy , computation is stopped when f(a) - k and f(b) - k have the same sign.
When you choose newton , computation is stopped when a value is out of the interval [a , b]. If computation is achieved , the application draw the tangent to the curve for every obtained value.
The application draw a discontinued line from (a , k) to (b , k) : you can click on this line to select the equation and change datas.
contents

### 2.6 Domain under a curve

Click on the Domain button in the tools bar. The dialog bar shows the message Domain ... ? : you have to click on a curve. The dialog bar looks like :

Then you may :

- choose the interval [a , b] where the domain is defined. Default : the interval where the function is itself defined.
- choose the intervals' number used for computation
- show/hide the results with the checkbox show
- choose a method which will be represented : rectangles , trapeziums , median point or simpson

Results are rounded to 10-5.
If an undefined value is computed, a discontinued line on the X-axis is drawn : this line represents the domain.
The domain and the results are visible only if the Y-coordinates of the points lie between the minimal Y-value and the maximal Y-value of the window.
When the results are displayed, note the symbols used for every method :

- L : left rectangles
- R : right rectangles
- T : trapeziums
- M : median point
- S : simpson

You will be able to modify the datas when you select the domain : click inside the domain or click on the discontinued line.
Domains samples :
contents

### 2.7 Text

Choose the Text option in the Objects menu : type a text line in the dialog bar's textfield. You may underline your text or add a frame with the beside combobox.

It's easy to include formulas : the application try to parse the text which lies between two antislash as a mathematical expression.
contents

### 2.8 Object's name and color

Click on the Appearance button in the tools bar which display the Appearance dialog. New properties of the selected object are now available.
Here is a snapshot of this window when a normal point is selected :

Then you may :

- choose the foreground color and the background color : select foreground or background and choose a color
- choose a label : enter a text in the textfield label and select formula or text

You validate the datas with a line's end in the textfield or a click on the Apply button. The Ok button validate the datas and hide the dialog.

Every object has a foreground color. Only points and domains have a background color. You can see the foreground and the background radiobuttons only if a point or a domain is selected.

Whenever the text button is selected, the label is an ordinary string.
Whenever the formula button is selected, the application try to parse the text as a mathematical expression. See Curves for valid expressions.
Furthermore you can use :

- the underscore operator "_" to define an index
- the functions "pth(…)" and "bra(…)" to enclose any expression between parenthesis or brackets.

When a label is created, its possible to change the label's color. Press on Shift, click on the label and choose a color in the Appearance dialog.

The label's location in the main window is relative to an anchor point which depends of the labeled object and of the last click : usually, the label is near the last click.
You can move the anchor point : press on Shift and click on the labeled object.

Finally, clicking on a label, you select the object it refers to.
Abstract

- if you click on an object, the dialog bar is displayed and you can modify some properties of this object
- if you click on the Appearance button, a new dialog is displayed and you can modify the label and the color of the selected object (including mathematical expressions)
- if you click on an object with Shift pressed, you move the anchor point of this object's label to the click
- if you click on a label, you select the labeled object
- if you click on a label with Shift pressed, you can choose the label's color in the Appearance dialog

Labels samples :
contents

# 3. Changes

### 3.1 Changing objects' properties

Select an object : the dialog bar is displayed and you can modify the registered datas.
Click on the button in the tools bar : the Appearance dialog is displayed and you can modify the label or the color of the selected object.
See Objets' creation for more informations.

### 3.2 Moving objects

Only can be moved

- normal points
- points on a line or a curve
- lines which are not defined with an equation
- tangents defined with a click
- recurring sequences
- equations
- labels

To move an object , press the mouse on this object and drag the mouse. You can see the changes in the main window and in the dialog bar.
Labels are moved relatively to an anchor point. To move the anchor point on the labeled object, press Shift and click on this object.

### 3.3 Settings

You can show or hide the axis and the grids with the approriate option of the Edit menu.
You can also move the whole graph : press the mouse on one of the axis and drag the mouse.

In order to change the settings, click on the button in the tools bar : the Settings dialog is displayed. Here is a snapshot :

Then you may :

- choose the left X-coordinate (xl) and the right X-coordinate (xr) of the main window
- choose the bottom Y-coordinate (yb) and the top Y-coordinate (yt) of the main window
- show/hide the axis or the grids with the approriate checkbox
- scale the axis' units (ux and uy) ; the default unit is multiplied by this number
- scale the grids' units (gx and gy) ; the distance between two parallels is equal to this number of units
- define the inner grid (gr) : the coordinates of the normal points are rounded at this precision
- choose round-offs (ro) : the values displayed in the dialog bar and in this dialog are rounded at this precision
- show the color panel when you click on the axis button or the grids button , choose a color and hide the panel when you click on the hide button
- choose a font and a font's size with the two appropriate comboboxes : the changes apply to the dialog bar, the Appearance dialog, the labels and the additional results displayed in the main window
- validate the datas with the Apply button and hide the dialog with the Ok button

Please, note the two ways the application validate coordinates and units :

- after a line's end in a coordinates' textfield or a click on the Apply button, first the application register the coordinates and then compute new units
- after a line's end in a units' textfield , first the application register the units and then compute new coordinates

Use one of the tree Zoom buttons in the tools bar for quick and easy changes :

- select a box in the main window and zoom with
- zoom+ with
- zoom- with

contents

# 4. Saving the graph

You can save your job under various formats. Choose a format with the Save as option in the File menu.

### 4.1 tsm format

This format is specific to edugraphe and allows you to reuse the graphs you created. The Save option in the File menu use this default format.

The application create a new text file on your disk. You can read and modify the file (be careful). Take a look at the first lines of a .tsm file :
line 1 : tsm created by edugraphe 1.1 on Mon Mar 07 11:10:49 CET 2005 charset : UTF-8
Comments line as every line whose the first character is a colon .
line 2 fenetre(606,398,-5.7,7.4,-1.7,7.2,0.1,0.1,1.5,1.5,0.01,true,false,Lucida Sans,12,1.31,1.26,156,156,156,210,210,210)
Configure the main window :

- dimensions : width = 606 and height = 398
- coordinates : xg = -5.7 , xd = 7.4 , yb = -1.7 , yh = 7.2
- inner grid : gx = 0.1 , gy = 0.1
- grids' units : qx = 1.5 , qy = 1.5
- precision : ar = 0,01
- show/hide the axis (true)
- show/hide the grids (false)
- font = Lucida Sans and font's size = 12
- units : ux = 1.31 et uy = 1.26
- axis RGB color = (156,156,156) and grids RGB color = (210,210,210)

line 3 ajouter(barre)
Command : the tools bar is accessible.
line 4 barre(point,pointoncurve,intersection,mark, space,line,tangent,space,curve,euler, space,recsequence,gensequence,equation, space,domain, space,select,delete,zoom,zoomp,zoomm, tab,prefs,aspect,help)
Configure the tools bar from left to right. Every tools bar's button has a (transparent?) command . If the command space is read a small space is added before the next button. If the command tab is read, the next button is pushed to the rightmost place.
line 5 ajouter(dialogue)
Command : the dialog bar is accessible.
line 6 point(-4,4,true,false,0,[A],false,255,0,0,255,208,137)
A new normal point is created :

- X-coordinate = -4 , Y-coordinate = 4
- visible = true
- affiche = false (no additinal information displayed)
- np = 0 (parameter for computation)
- nom = A (label)
- prettyprint = false (the label is not a mathematical formula)
- foreground RGB color = (255,0,0) and background RGB color = (255,208,137)

Writing in a .tsm file may be dangerous (it's at your risk!). Save your changes using unicode ("UTF-8") charset.

### 4.2 png and eps graphics formats

The application create a new image file on your disk.
The Photo option in the File menu allows you to select and save only a rectangular box in the main window.
You will be able to reuse the images in any latex or html document. E.g. illustrations in this document are made using edugraphe and the png format .

Furthermore you can insert a eps file in any LaTeX document with desired dimensions :

- put in the preamble \usepackage{graphicx}
- insert the image in the document with the command \includegraphics{curve.eps}
- fix the dimensions with the option width of this command

Sample : You have to include your job with exactly 1cm for the X-axis' unit.

- choose the Photo option in the File menu
- select a box with left X-coordinate = -4 and right X-coordinate = 4
- save it under the eps format
- include the file with \includegraphics[width=8cm]{curve.eps}

### 4.3 html format

With this option you directly create an applet in a new web page : you can view the page and the graph using your navigator.
You can also edit and modify the file : for example, it is easy to change the tools bar configuration. The commands' separator is the colon character. Don't remove them and remember that no comments are allowed.
See the tsm format section for more informations.
When the web page is created, you get a new worksheet : simply write your comments or questions before or after the two applet's tags.
contents

# 5. Menus

Most options in the menus are known. For completion, you can use following options.

- File menu
  - New : open a new file
  - Open : open an existing file
  - Print : print the current file
  - Page-setting : configure the page-setting
  - About : display the "About" window
  - Quit : close the program
- Edit menu
  - Select : turns to the select mode
  - Clear : remove all objects
- Window menu
  - Settings : show/hide the "Settings" dialog
  - Appearance : show/hide the "Appearance" dialog
  - Axis : show/hide the axis
  - Grids : show/hide the grids
  - Equal scale : reset units to default values
  - Tools bar : show/hide the tools bar
  - Dialog : show/hide the dialog bar
- Help menu
  - Manual : show/hide the window where you can read this document

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