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.

For more information about the GeoGebra CAS commands and their syntax, read the GeoGebraCAS documentation.

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.
    Following your indications I made some further tests.
    If I correctly understand, the issue arises from the fact that Geogebra CAS understand expressions as “xxx” or “xyz” as variable names, not products. So now the behaviuor I obtained is clear. I noticed that actually Geogebra indicated in different ways variables and products in the results: xyx is a variable, x y z (with the spaces between the letters) is the product of x, y and z.
    I only have a doubt: I suspect that this notation can lead to some trouble for not expert users. Usually in algebra textbooks and practice, expressions as xyz are intended as product, not a single variable name. So at first some users, like it happened to me, can be mislead. In particular, showing the results, probably it would be better if Geogebra would indicate the product with some symbols, as a point, instead thatn simply with the spaces, that are at first less recognizable.
    What do you think, is it only of problem of mine related to having still little confidence with the program?
    Thanks again, ciao.

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