CAS venster

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Dit artikel betreft van de GeoGebra gebruikers interface.

Hoofdcomponenten

• Menubalk
• Gereedschappenbalk
• Invoerveld
• Context Menu
• Navigatiebalk
• Virtueel Keyboard

Views

• Algebra venster
• CAS venster
• Tekenvenster
• Rekenblad
• Schermindelingen

Menu's

• Bestandsmenu
• Menu bewerken
• Bekijk Menu
• Opties Menu
• Macromenu
• Venster Menu
• Helpmenu

Dialogen

• Eigenschappen dialoogvenster
• Constructie Protocol
• Macro dialoogvenster
• Macro Manager dialoogvenster
• Verfijn dialoogvenster
• Opties uitleg
• Exporteer uitleg bij tekenvenster
• Exporteer werkblad uitleg
• Afdrukvoorbeeld

CAS venster

Standaard wordt het CAS venster geopend naast het Tekenvenster. Naargelang welk van de twee vensters actief is, staat de Knoppenbalk van het CAS venster of het Tekenvenster bovenaan in het GeoGebra-scherm met de knoppen Ongedaan maken / Opnieuw rechtsboven.

CAS venster

Het CAS venster is een deel van de Schermindeling CAS, maar je kunt het CAS venster ook openen in andere schermindelingen via het menu Beeld.

Wiskundige Objecten creëren

Rechtstreekse invoer

In het CAS venster kan je met het CAS (Computer Algebra Systeem) van GeoGebra symbolisch rekenen. Het is opgebouwd uit cellen met een Invoerveld bovenaan en een toonveld onderaan. Je kunt deze Invoervelden op dezelfde manier gebruiken als het gewone Invoerveld, met volgende verschillen:

• Je kunt variabelen gebruiken waaraan geen waarde werd toegekend.
  Voorbeeld: Typ (a+b)^2 in een Invoerveld en klik op de Sjabloon:KeyCode-toets. Je krijgt als resultaat a²+2ab+b².
• = wordt gebrukt in vergelijkingen en := voor toewijzingen. Dit betekent dat de invoer a=2 de waarde 2 niet toekent aan de variabele a. Je doet dit wel met de invoer a:=2.
• Vermenigvuldiging moet je expliciet vermelden. In het Invoerveld kan je zowel a(b+c) als a*(b+c) typen voor een vermenigvuldiging, in het CAS venster is enkel a*(b+c) geldig.

Keyboard Shortcuts for Direct Input

In the CAS View the following keyboard shortcuts help you to evaluate or check your input.

Nota: Instead of using these keyboard shortcuts, you may also use the corresponding Tools of the CAS View Toolbar.

• Sjabloon:KeyCode: Evaluates you input
• Sjabloon:KeyCode: Evaluates your input numerically
  Voorbeeld: sqrt(2) yields 1.41
• Sjabloon:KeyCode: Checks your input but does not evaluate it.
  Voorbeeld: b + b stays as b + b.
  Nota: Assignments are always evaluated, e.g. a := 5

In the CAS View the following keyboard shortcuts help you to reuse previous input or output in a new row if you enter them into an empty Input Field:

• Sjabloon:KeyCode bar: Inserts the previous output into the new row.
• ): Inserts the previous output in parentheses.
• =: Inserts the previous input into the new row.

Nota: You may suppress any output with a semicolon at the end of your input, e.g. a := 5;.

Variable Assignments and Connection with other Views

You may use the := notation for assignments, e.g. b := 5, a(n) := 2n + 3.

• Free up a name: Use Delete[b] in order to free up a variable name again.
• Redefine a variable or function: You may redefine a variable or function, but you must do so in the same cell, otherwise it will be treated as a new variable and automatically renamed.

Variables and functions are always shared between the CAS View and the other Views if possible. For example:

• If you define b:=5 in the CAS View, then you can use b in all the other Views of GeoGebra.
• If you define a function f(x)=x^2 in another View, you can also use this function in the CAS View.

Nota:

The output will always be just the expression after the :=, e.g. if you type b:=5 the output will be 5. Please also note, that for clarification actually b := 5 will be displayed.

Equations

• You may write equations using the simple Equals sign, e.g. 3x + 5 = 7.
• Arithmetic operations: You can perform arithmetic operations on equations, which is useful for manual equation solving.
  Voorbeeld: (3x + 5 = 7) - 5 subtracts 5 from both sides of the equation.
• Extracting one Side: You may extract either the left or right side of an equation by using the commands LeftSide[] and RightSide[].
  Voorbeeld: LeftSide[3x + 5 = 7] returns 3 x + 5 and RightSide[3x + 5 = 7] returns 7

Row References

You can refer to other rows in the CAS View in two ways:

• Static row references copy the output and won't be updated if the referenced row is subsequently changed
  • #: Copies the previous output.
  • #5: Copies the output of row 5.
• Dynamic row references insert a reference to another row instead of the actual output and therefore will be updated if the referenced row is subsequently changed
  • $: Inserts a reference to the previous output.
  • $5: Inserts a reference to the output of row 5

CAS Commands

GeoGebra also offers a wide range of CAS Commands that can be used to create objects in the CAS View. Just start typing the name of a Command into the Input Field and GeoGebra will offer you a list of Commands that match your input.

Nota: For a complete list of Commands see section CAS Commands.

Nota: From GeoGebra 4.9.170.0 on, the CAS View supports exact versions of some Geometry Commands

.

CAS View Toolbar

The CAS View Toolbar provides a range of CAS Tools that can be operated with the mouse and allow you to evaluate input and perform calculations. Just enter your input and use the mouse to click on the corresponding CAS Tool afterwards in order to apply it to your input.

Nota: For a complete list of Tools see CAS Tools.

Context Menus

Row Header Context Menu

Right click (MacOS: Sjabloon:KeyCode-click) on a row header in order to show a Context Menu with the following options:

• Insert Above: Inserts an empty row above the current one.
• Insert Below: Inserts an empty row below the current one.
• Delete Row: Deletes the contents of the current row.
• Text: Toggles between the current result and a text showing the current result contained in the row, which allows the user to insert comments.
• Copy as LaTeX (GeoGebra Desktop): Copies the contents of the current row to your computer’s clipboard, allowing you to paste the contents e.g. in a Text object.

Nota: To copy the contents of more than one CAS row as LaTeX, select the rows you want with Sjabloon:KeyCode-click (MacOS: Sjabloon:KeyCode-click), then right-click (MacOS: Sjabloon:KeyCode-click) on the row header and select Copy as LaTeX.

Cell Context Menu

In GeoGebra Desktop, right click (MacOS: Sjabloon:KeyCode-click) on a CAS output cell in order to show a Context Menu with the following options:

• Copy: Copies the cell contents to the your computer’s clipboard. Then, right click on a new cell in order to show the Paste option.
• Copy as LaTeX: Copies the cell contents in LaTeX format to the your computer’s clipboard, so it can be pasted into a Text object or a LaTeX editor.
• Copy as LibreOffice Formula: Copies the cell contents in LibreOffice formula format to your computer’s clipboard, so it can be pasted in a word processing document.
• Copy as Image: Copies the cell contents in PNG format to your computer’s clipboard, so it can be pasted into an Image object or in a word processing document.

Display of Mathematical Objects

CAS View Style Bar

The CAS View Style Bar provides buttons to

• change the text style ( bold and italics) and color
• display a virtual keyboard (GeoGebra Desktop)
• display additional Views in the GeoGebra window (GeoGebra Web and Tablet Apps)

Showing CAS Objects in the Graphics View

In the CAS View, the icon to the left of every row shows the current visibility state (shown or hidden) of the object defined in it (when possible). You may directly click on the little Show / Hide Object icon in order to change the visibility status of the object in the Graphics View.