CAS
(Computer Algebra System) is the calculator in GeoGebra
, and has its own view. Open it by clicking CAS
under View
in Menu
.
In this entry, we’ll take a look at the basics of CAS
. If you want to learn how to use CAS
for a specific task in a given subject, like solving systems of equations or differentiation, check out the respective GeoGebra
entries. The entries are categorized by subject.
By typing your calculation into an empty row in CAS
and pressing Enter
, CAS
will do the calculation for you.
GeoGebra
Instruction 1
Open CAS
under View
in Menu
.
To add $36+87$, type
36 + 87
and press Enter
.
To subtract $143-46$, type
143 - 46
and press Enter
.
To multiply $13\times 15$, type
13 * 15
and press Enter
.
To divide $132\xf712$, type
132 / 12
and press Enter
.
GeoGebra
Instruction 2
CAS
under View
in Menu
. To calculate ${x}^{p}$, type x^p
and press Enter
.
Roots:
To calculate ${x}^{\frac{1}{n}}$, type x^1/n
and press Enter
.
If want to compute a square root, you can use the command sqrt(<x>)
instead. sqrt
is short for “square root”.
Note! GeoGebra
only prints the positive root, even if there’s a negative root too.
Algebraic expressions work the same way, but make sure that you use the multiplication symbol (*
) between the individual symbols. If you for example type ab
, GeoGebra
will interpret it as an object with the name “ab
”, and not $a\cdot b$.
GeoGebra
Instruction 3
Open CAS
under View
in Menu
.
To compute $2a+3a$, type
2a + 3a
and press Enter
.
To compute $ab\cdot {b}^{2}$, type
a * b * b^2
and press Enter
. You get $a{b}^{3}$. If you type
ab * b^2
you get $ab\cdot {b}^{2}$, because GeoGebra
interprets ab
as an object, and not the product $a\cdot b$.
If you want to type a fraction in CAS
, you need to add a fraction bar (also known as “vinculum”). Here’s how you do it:
GeoGebra
Instruction 4
CAS
under View
i Menu
. /
. A fraction bar should appear, which consists of two empty fields for the numerator and the denominator, respectively. Type the numerator of your fraction first, and then click on the second field and type your denominator. Press Enter
when you’re done. Note! CAS
simplifies fractions automatically.
CAS
can also be used for rounding numbers.
GeoGebra
Instruction 5
CAS
under View
i Menu
. round(<x>)
where you replace <x>
with your number.
round(<x>, <y>)
where you replace <x>
with your number, and <y>
with the number of decimal places.
You can also calculate powers and roots in CAS
.
By clicking Expand
in the CAS
Toolbar
, you can expand parentheses.
GeoGebra
Instruction 6
CAS
under View
in Menu
. CAS
and click Expand
from Toolbar
.
CAS
can be used to factorize an expression. If it doesn’t change after clicking Factor
, it can’t be factorized.
Note! GeoGebra
uses the term factor instead of factorize.
GeoGebra
Instruction 7
CAS
under View
in Menu
. CAS
and click Factor
in Toolbar
.