GeoGebra 4.0 Sneak Peek 5: The Computer Algebra System

This is the fifth post of the GeoGebra 4.0 Sneak Peek Series.

One of the major enhancements of GeoGebra 4.0 is the integration of Computer Algebra System (CAS).  The GeoGebra CAS window can be viewed by clicking the View>CAS from the menu bar. The CAS toolbar includes the following tools as shown in the first figure:  Evaluate (exact evaluation), Numeric (numeric evaluation; e.g. sin(1)), Keep Input, Factor, Expand, Substitute, Solve, and Differential/ Integral.

You can enter  expressions/equations at the CAS window (see black texts below) and click the buttons at the toolbar to perform a command. The output of a command is shown in blue texts. Line 1, for example, used the Evaluate button to simplify 2x + 4x – 3y + 2y.

The GeoGebra CAS also accepts keyboard input; type the command and then the expression. For example, typing solve[x^2-3x + 5 = 10, x] in the CAS window is just the same as typing the equation x^2-3x + 5 = 10 and then clicking the Solve button.

In the next post, we are going to discuss about the Function Inspector tool.

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7 thoughts on “GeoGebra 4.0 Sneak Peek 5: The Computer Algebra System”

1. Hi from Italy.
First of all congratulations, your series of tutorials about Geogebra are really clear and interesting.
I am experimenting a bit with the CAS in the beta of 4.0 and 5.0, and I would like to ask a pair of questions:

1) Is there a way to tell the program to tranform products of the same variable in a power, as xxx->x^3 ? I don’t find the appropriate command in the toolbar. It makes the trasformation if I write the product with the symbol, x*x*x

2) It seems that Geogebra has some problems with commutative property of multiplication of more than two factors, for example it is able to simplify xy+yx -> 2xy, but not xyz+yxz. Also in this case it makes the simplification if I use the symbol, x*y*z

Do you have any advice on these points?
Thanks

• Hi Antlab,

Thank you. I am glad that you have used my tutorial. The GeoGebra 4.0 is still in Beta form, so it is not yet very stable. There are still a few bugs. For your questions.

For x*x*x, you use the Exact evaluation tool, the one with the equal sign. I’ve tried it and it’s functioning correctly.

2. Hi Antlab,

(1) xxx is valid as a name for a GeoGebra variable, so you need to type x*x*x or just x then 3

(2) is not a bug. As above, for xyz you need to type x*y*z

3. Thanks Guillermo and Michael for the answers and clarifications.