# 3 suggestions: a Exponent and a Root command and a command to reduce/simplify formulas

I’m working on a GeoGebra-app where the students are going to learn how to solve equations and isolate letters in formulas by choosing which operations they would like to make on the left and right side of the equal sign.

But when it comes to more complex equations like 2^(3x) = 64 and so on, I need GeoGebra to be able to identify the exponent 3x and the root 2 for the function 2^(3x). Therefore I will suggest to make an Exponent and a Root command which has this as an output.

And when it comes to formulas, I miss the possibility to only reduce the formula when the same letter appear on the same side of the equal sign but with the opposite operation sign beside it.

Like for example: A = a + b <=> A - a = a - a + b <=> A - a = b

Or K = (1 + r)^n <=> lg(K) = lg( (1 + r)^n ) <=> lg(K) = lg(1 + r) * n <=> lg(K) / lg(1 + r) = lg(1 + r) * n / lg(1 + r) <=> lg(K) / lg(1 + r) = n

I use one function for each side.

By now when a function contain letters and you use the command “Simplify” then a + b + c - c will be 7 when a = 3 and b = 4 instead of just a + b.

Maybe this would require some special object for entering and reducing formulas. Or you could make a special command for reducing formulas according to my description above.

It would be very nice if it would be possible to enter and reduce formulas in GeoGebra in this way.

Else I can’t see how I can make a GeoGebra-app that can learn the students how to isolate letters in formulas and get there isolation checked by the pc which is a much more effective way to learn it than any other way I know.

In CAS of Classis it's even more easy since you can refer to an expression in whatever line with e.g. $1 and things as $1 - a to substract a from the result of line 1

There's a Command Simplyfy ( a + b + c - c) or you can type a + b + c - c and click on the = Tool on the CAS Toolbar.Conserning lists, you can apply all list commands and so picking out elements out of the lists, and creating others.

chris

Did you try the CAS app?

1) Can I do the same in GeoGebra Classic 5 in its CAS-section ?

2) Is it possible to insert a formula expression in the CAS-view from a list or by using a script, get it simplified there and insert the result in a list ?

In CAS of Classis it's even more easy since you can refer to an expression in whatever line with e.g. $1 and things as $1 - a to substract a from the result of line 1

There's a Command Simplyfy ( a + b + c - c) or you can type a + b + c - c and click on the = Tool on the CAS Toolbar.Conserning lists, you can apply all list commands and so picking out elements out of the lists, and creating others.

chris

Okay, I didn’t know that.

Both thanks a lot.

I have tried to make it work by the use of a button script, but I can’t seem to make it all work. Hope you can help me further...

I can import a LaTex string from a list to a row in the CAS-view by writing this in the first row:

Element[ List, n ] , where n is the position of the last element in the list and which value is increased by 1 for every click on a button.

And I seem to be able to manipulate the expression and get it simplified, although I would prefer to see the expression before and after the simplification.

But more importantly, I can’t seem to insert the simplified expression into the same list that the expression came from in the first row.

I have tried these methods:

List = Insert[ SimplifiedExpression, List, Length( List ) + 1 ]

SetValue[ List, Insert[ SimplifiedExpression, List, Length( List ) + 1 ]

As the SimplifiedExpression, I have tried to use either $2, LaTex($2) or make a new text object that is defined as LaTex($2). But none of these methods worked.

So I hope you have some suggestions for how I can get the simplified expression inserted in the original list.

I need this as I would like to get the whole manipulation of the formula viewed in a table with the equation signs aligned under each other and with a explanation of the operation shown next to it.

have you tried formulatext() and tabletext()?

The simplified expression can be inserted in the original list, by first combining the original list and the simplified expression in a new list and then set the original list equal to this new list:

SetValue[ NewList, Insert[ SimplifiedExpression, OriginalList, Length( OriginalList ) + 1 ]

SetValue[ OriginalList, NewList ]

Mathmagic: I would like your idea if it was possible to align the equal signs.

I have done it by separate the right and the left side of the equation and make a list with equal signs between the two sides of the equation. And use the TableText command as you also suggested.

My next challenge is to use a dropdown-menu for the students to choose which operation they would like to make on both sides of the equal sign.

I have managed to get it to work for solving equations. But I can’t seem to find out how I can get it to work with entering a formula in the CAS-view...

How can I in a button script combine a IF-sentence with a formula in a row in the CAS-view, so if a student choose “+” in the dropdown-menu, then a written letter (in a input field or dropdown-menu) will be added to both sides of the formula, and if a “*” is chosen in the dropdown-menu, then the written letter will be multiplied on both sides of the formula, an so on. How can I do that ?

Loading...Comments have been locked on this page!