Each session is a numbered collection of levels, each level has a type: command line, comment, expression editor, spreadsheet, program, 2-d or 3-d geometry, or logo-like turtle.
If no command line is available, you can get a new one by the
Toolbox->New entry
menu. You can modify existing command lines or write in a new
command line. The following shortcuts are available.
When you evaluate a command line, a log output may be displayed (written in blue over white by default), followed by the answer, which might be an expression or a graphic (2-d or 3-d) widget if the answer is a graphic object (for lists, the widget type corresponds to the type of the last evaluated object).
If you do not want to see the answer displayed (for example if
you store a large matrix in a variable), just finish
your command line with :;
Comments are inserted using the Toolbox->New comment menu.
They are by default written in green instead of red over white.
Comments are not evaluated when pressing Enter (the effect is to
put the cursor to the next level).
Typing the shortcut Alt-e or using the menu Expression->New expression will open an expression editor above the current level. The scientific keyboard should automatically appear (press the x button at the top right of the keyboard if you don’t want it).
The expression editor lets you enter complex mathematical expression in 2-d like on a paper. For example, suppose you want to enter
| ⎛ ⎜ ⎜ ⎝ |
| ⎞ ⎟ ⎟ ⎠ | · | ⎛ ⎜ ⎜ ⎝ | 3+ |
| ⎞ ⎟ ⎟ ⎠ |
|
Open an expression editor (Alt-e) then type
/ (for the division)
^ 5
You can now move the selection in the tree of the expression with the arrows keys :
Another example, let’s enter
| ∫ |
|
|
Type Alt-e to open a new expression editor.
, key to switch to a definite integral. (To do the
reverse operation, you can select each bound and press the backspace
key).
1/(1+x^2).We now list the other special keys in the expression editor:
":
Outside editor mode (no visible cursor),
edit the selection like in a command line, this is especially
useful if you want to edit a function name.
In editor mode, switch between considering the edit as a string
and as a normal edit.
,: if a sequence is selected, add a 0 to the end of the
sequence and select it. If the selection is not a sequence, creates
a sequence of size 2 with first element the selection, init the second
element to 0 and select it. You can move the newly created 0 in the
sequence with Ctrl-→ and Ctrl-←.
(: if a sequence is selected, make it the arguments to a
user function, the name of the user function is initialized
to f and selected (type the function name to replace
the f by your function name). If a vector is selected, it is replaced
by a sequence.
[: if a sequence is selected, it is replaced by a vector,
if a vector is selected, an indexed vector/matrix position is created
where the variable name of the vector/matrix is initialized to
m and selected (type the matrix/list name to replace m).
Msg output, click
on the Msg button to make it visible or hide it).
Programs may be written in a command line if they are one or two
lines long, but for more complex programs, it is a good idea to
put them in a separate program level, using the
Prg->New program menu. This will open an editor in
a new level. Type your program (the Prg menu may help you
for the syntax of tests, loops, function definition, etc.),
and press the OK button once completed.
If parsing is successful, you can test your program
in any command line.
The Prg menu has items to open or
import an existing (program) file inside the current text, save
or export the current program (independently from the worksheet).
You can also use the menu
to insert programming structures. There are buttons to find the
next occurence of a search string, to parse the current program
(errors are displayed in the message area) and to save the
program (the current filename is displayed at the right of the
save button).
The keywords of the language are highlighted. In Xcas programming mode, the tab key may be used for indentation (experimental feature).
Tip: before pressing the OK button, check the programming syntax by looking at the status area button in the middle at the top of the session. If you need to change the syntax, hit the status button and select the right syntax.
A graphic output is made of a 2-d or 3-d scene with controls, it corresponds to a unique command line above it. You can create some examples easily using the Graphic menu.
A geometry figure is the display of a 2-d or 3-d graphic scene representing the graphical objects of the command lines that are on its left.
The controls are common to 2-d, 3-d graphics or geometry. You can move left, right, up and down the window, redefine it using coordinates, zoom in and out, pause and restart an animation using the buttons and the M menu at the right of the graphic, or using the Graphic menu. In 2-d, the coordinates of the mouse are displayed while it is in the graphic area. You can modify the visualization window with the mouse (drag to move, use the scroll button for centered zoom in/out, or select an area with the right mouse button for an area zoom in). In 3-d, you can rotate the representation along the current x, y, z axis with a mouse drag outside of the scene rendering, or by using the x,X, y,Y and z,Z keys (if the focus is in the 3-d scene).
Note that the controls apply only to the visualization, not to the creation
of graphic objects. For example, if you create a plot of a function,
the discretisation parameters for this plot (e.g. minimal value for
x) are fixed and will not change if you move the minimal visualisation
value using the controls. You must recreate a graphical object if
you did not correctly choose the parameters. For example if you
run the command plot(sin(x)), the minimal value for computation
of x will be the default value
(Xmin from the Geo configuration, -10 by default). If
you move the minimal value of x for visualization below Xmin, you will
not see the plot there. To see the plot below Xmin, you would have
to specify something like plot(sin(x),x=-20..0) and validate
the command line. This limitation does not apply to geometric objects
(points, segments, lines and circles)
which will always be drawn if they are visible.
An M menu is available below the controls (its items are also available
from the top Graphic menu),
it contains items to print
and control the screen. You can export a graph to encapsulated
postscript and to PNG (you must have the converting tools
netpbm or ImageMagic
installed, this should be installed by the Xcas installer under Windows. If they
are not installed under Linux, run your software installer or
open a Terminal
and type
sudo apt-get install imagemagick
for Debian/Ubuntu distributions or
sudo yum install imagemagick
for Fedora-compatible distributions).
Titles and axis legends must be part of the command(s) that generate the graph or geometry window. For example, try this on a command line
f(t):=sin(t);title="Graph of f on a period",
labels=["t","f(t)"],legend=["cm","m"],
plot(f(t),t=-pi..pi,legend="f")
Use the Geo->New figure 2d menu to make a new 2-d geometry
session. This will open a new level with a “subsession” (group of
command lines) at the left,
a 2-d screen in the middle, and the controls at the right. If there
are parameters, they will be below the controls at the right.
The subsession is a list of command line levels. Evaluation of
a command line level will automatically reevaluate all levels
below (i.e. with a higher level number), therefore if you use
one level to define an object and modify the definition of this
object later, all objects depending on this object will be modified.
Modification of a level defining a point or a 1-d parameter can be
done interactively with the mouse either in the geometry screen or in the
parameter area (below the controls).
The geometry level has a mode, which affects how the mouse behaves.
To erase a geometrical object, right-click on it, select Delete
or select its level in the
subsession at the left, and use the Edit->Delete selected levels
menu or Backspace key.
For example, you can click three points with the mouse (in point mode),
this will create 3 levels with definitions for points A,B,C.
Then you can make the circle containing A, B, C either by selecting
the Circles->circumcircle mode and click on A,B,C
or by entering in a command line the
circumcircle command (menu Geo->Circles->circumcircle)
c:=circumcircle(A,B,C)
Remark: how to work with several figures in a tab
When you create objects in a figure with a mouse,
the name of the created object is
automatically chosen. This name is shared between figures in the same
tab so that they don’t interfere if you have several figures in the
same tab. If you want to copy a part of a figure in another figure,
enter in a level of the target figure
the instruction eval([ ],1) where you put inside the brackets
the names of the objects to be copied (e.g. eval([A,B,AB],1)
will copy A, B and AB from a previous figure to the new figure).
If you change the initial figure (where A,
etc. were defined), you must reevaluate the instruction in the target figure
to reflect the changes (press Enter in the first level of the target figure).
Parameters are real values which can move in a fixed interval, e.g. between -5 and +5. The real value may be changed by clicking on arrows below the controls at the right of the geometrical representation. There are two kinds of parameters: formal and numeric parameters. Formal parameters have a formal name which is used in all exact calculations, and a numeric value which is used for all numeric evaluations (including graphical representation of objects depending on the parameter). They can therefore be used to make an analytical proof of a geometric theorem using the CAS engine while displaying a figure. Numeric parameters always evaluate to their numeric value, they can not be used to make an analytic proof (only to make conjectures like with most interactive geometry software).
To add a new parameter, use the Geo->Edit->Add parameter menu.
For example, add a level with f(x):=a*x^2+b*x+c
then define 3 parameters named a, b, c and add the command
plot(f(x)), then move one of them to see the
influence of each parameter
on the shape of the parabola.
You could also add a level mini:=solve(diff(f(x),x)) and
M:=point(mini[0],f(mini[0])) to display the minimum.
Note that the coordinates of M are displayed in terms of a and b
under the command line defining M at the left. You would have to add a level with
evalf(coordinates(M)) to see the current numeric value.
There are several options for 3-d graph rendering that can be configured by clicking on the cfg button. First, you have to choose between intrinsic colors or a scene viewed with 1 to 8 light spots, see below.
Then you can choose the x, y, z range that will be visible. The position of the eye visualizing the scene can be changed by specifying a plane equation (normal to the vision direction). You can also easily change the viewpoint outside of the cfg configuration window either with the mouse (push outside of the parallelepiped, drag the mouse and release it at your option) or with the x,X, y,Y, z,Z keys to rotate around the x, y or z axis.
By using the r key or by selecting
M->3-d->Rotate animation,
you can get a visualization animation by rotation around the
origin. By default, it will rotate the viewpoint around the z axis
but this is configurable from the cfg button. You can configure:
Anim: what will be animated, viewpoint if bit 8 is 1,
spot number 7 to 0 if bit 7 to 0 are set to 1. For example, 255 will
move all spots leaving the viewpoint unchanged.
t: interval between 2 redrawings.
n: number of steps for a round trip.
x, y, z: coordinates of the axes.
d: normally 0, may be nonzero if you want also to move the
number of images of a programmed animation.
You can specify the axis of rotation in the command line defining the scene by
gl_rotation_axis=[x,y,z]
where x,y,z
are the coordinates of the axis of rotation.
Do not confuse visualization animation with programmed animation
obtained by instructions like animate, animate3d, animation.
If you enable Lights in the cfg configuration of a 3-d
graph, the scene will be rendered by the OpenGL lighting
algorithm. You can enable 1 to 8 spots of light, each is configurable
(buttons L0 to L7).
Each spot has geometric properties: it may be a positional spot if w=1 or a directional spot if w=0
x->, y->, z->. Light coming from a positional spot may
be attenuated, the attenuation may depend on the distance between
the spot and the object (with a quadratic,
att0, att1, att2 in the spot configuration), and by the
cosine of the angle between the spot direction and the segment
spot-object to an exponent (exp in the spot configuration).
In addition, the spot may light only inside a cone of angle
configurable by the cutoff value (in degrees, use 180
for no cutoff or a value between 0 and 90). An additional attenuation
comes from the cosine of the angle incoming direction-normal to the
object, so that zenithal lighting is maximal.
Objects from the scene may have their own properties with respect to three kinds of light:
In addition, an object may have intrinsic light, called emission.
Each property must be specified for 4 channels: r (red), b (blue)
and g (green) for the colors, and a (alpha) for transparency (if
you enable Blending).
Object properties must be specified in their definition (on
the command line):
gl_material=[gl_front,gl_ambient,[r,g,b,a]]gl_diffuse, gl_specular or gl_emission
instead of gl_ambient for diffuse, specular or intrinsic
light. Default is 0.2 for ambient, 0.8 for diffuse and 0 for emission
on r,g,b channels and 1 on alpha channels.
gl_material=[gl_front,gl_shininess,n]gl_texture="filename" specify an image filename that
will be mapped on a sphere or a polygon or a parametric
defined surface.
Summing up, the formula for light on each channel is :
|
where :
3-d geometry is based on the same principles as 2-d geometry: a subsession at the left and the representation in the middle. Mouse interaction outside the representation will change the viewpoint, inside the representation it will depend on the mode: draw a point, a segment, ... according to the mouse plane displayed above (all mouse clicks are supposed to refer to this plane, which is perpendicular to the visualisation axis).
Use the Spreadsheet->new spreadsheet menu to add a spreadsheet level.
You will see a small configuration screen where you can change
the number of rows/columns, if an attached graph is displayed,
and also a variable name that you can use to get values
from command lines outside of the spreadsheet (using the matrix notation,
e.g. a[1,2] will return the value of the cell at row 2, column 3
in xcas syntax mode, or at row 1, column 2 in other syntax modes).
You can modify the spreadsheet configuration by clicking on the
status line above the cells or with the
spreadsheet File->variable name menu later).
If you have chosen to display the graph inside the spreadsheet
configuration, it will dynamically
display all cells that evaluate to a graphic object.
You may also display all the graphic
objects of the spreadsheet in a separate window, either in 2-d or in 3-d by
clicking on the 2d or 3d button at the right of
the spreadsheet menu.
A cell may contain
a fixed value (any valid Xcas object: integers, reals, symbols,
algebraic objects, strings, ...) or a formula depending on other
cells. The syntax for formulas is the same as for many spreadsheets,
begin with an =, then enter an algebraic expression where
other cells are represented using a symbol made of the column
name (e.g. A) and the row number (e.g. 1). When copying cells,
cell dependance in a formula is considered relative
unless you write a dollar ($) sign before the column name or
row number. You can enter an area instead of a cell name, an area
is always a rectangular area, it is made of two cell names separated
by .. representing opposite vertices of the rectangular area.
To enter a new value or formula in a cell, click on the cell, then enter your value or formula with the keyboard. As soon as you type a normal character, the focus will move from the sheet to the command line above the sheet. To help enter formula, you can use the mouse to select a cell or a cell area. Once the value or formula is correct press the enter key to validate it. You can cancel your edit at any time by clicking on a different cell.
To modify a cell value, click on the cell so that the value or formula is displayed in the command line above, then click in the command line, modify it and press Enter.
You can move in the sheet using the mouse or the direction keys, or
using the “goto” input value at the topleft of the sheet. Just enter
a cell name then enter to move there. If the cell does not exist,
the sheet will be enlarged to make it exist. You can also enter
an area in the “goto” input value to select this area without the
mouse. You must use the “goto” input value to make special
selections that are not connected areas, for example A1..B3,D,F will
“select” the subtable with rows 1 to 3 and columns A, B, D and F.
You can copy and paste a rectangular area with the mouse like this:
select the rectangular area with the mouse, click on the target cell,
click on the command line, type Ctrl-U to erase the previous
value then click on the middle button and type enter.
If you want to copy a cell formula to an area of the spreadsheet,
press at the right bottom part of the cell (when the mouse is on the
correct area of the cell, it will display a different cursor)
and move the mouse over the area you want to
copy, then release the mouse.
You can also copy cells using a menu item in the spreadsheet
Edit menu, you can either copy to the left, or to the bottom,
or to a rectangular area previously selected with the mouse (in this
case the cell which was below the mouse when you pressed the button
will be copied to the rectangular area).
The spreadsheet can be saved, exported, imported, etc. using the
spreadsheet File menu. The spreadsheet is also saved
as part of the session (but not as a standalone spreadsheet)
when you save the whole session. When you load a session, the
spreadsheet will not be evaluated automatically, you must reevaluate
it with the reeval button explicitly (or modify one cell).
Xcas does not provide filters for native binary spreadsheet formats,
but you can import spreadsheets from other software or data using
copy/paste or by saving them in the CSV (comma separated values) text format:
cells values must always be separated by the same character e.g. a comma, and
another character should be used to start a new row like a newline.
For example, you can select a spreadsheet area inside Open Office
and paste it inside Xcas.
If you want to import formulas instead of values,
use the Tools->Option menu of Open Office, find the spreadsheet Display item
and check Formulas. Select the area inside Open Office, then
paste at the same upper left cell position inside Xcas.
Alternatively you can save the spreadsheet in CSV format inside
Open Office with the File->Save as
menu item, then select CSV in the choosebox below.
Then inside Xcas, use the File->Insert CSV menu item,
select the file, change the separators if Xcas made a bad guess.
Note that Xcas must use row notation starting
at 1 instead of 0 for Open Office CSV formula import (this is the default).
Click on the status line or select inside the Edit menu
for configuration and sheet modification operations. Configuration
operations should be self-explanatory, except for matrix fill cells :
when entering a matrix in the command line,
you can choose between two modes, either the matrix will fill
a rectangular area of cells, or it will fill only one cell.
The Stats
menu is useful to make statistical plots in the corresponding graph.
When you make a graph using this menu, you will have to select
the data area where the statistic function will be applied (e.g.
a polygonplot on A1..B10) and a target cell. The target
cell is a regular cell which was empty and will contain the formula
defining the graphic object that will be displayed. If you check the
value box, the graph will not change later, but if you don’t check
the value box and modify
one data cell later, the graph will be updated like any cell
depending on this data cell would be.
To add a turtle session, use the Turtle-> new turtle menu.
A logo level is made of three parts, the graphic display
in the middle, a subsession of command lines at the left
and an editor at the right. Command lines are executed as in
a main session (command lines below an evaluated command
are not reevaluated unlike in a geometry session). The editor
records all commands.
In a logo level, you can pilot a turtle, giving it orders like forward
10 steps, turn left or right, etc. It will display a trace
using a pen with a defined color.
You can use any language construction of Xcas to program the
turtle’s moves. The current language uses French command names
(e.g. avance=move forward, etc.), the most important commandnames
are available by clicking on the buttonbar below the turtle screen
(check that the cursor is on a command line before clicking on
the button corresponding to the command you want to enter).
Most commands have a default argument (e.g. 10 for avance),
if you want to add parameters, do not add parentheses. Logo
commands use the same syntax as the return statement,
if you want to specify priorities, put parenthesis around
the command and arguments, like this: (hasard 10).