local variables for repeated occurrences of subexpressions

Niek Sprakel shared this question 8 months ago
Answered

Hi.

Is there any way in GeoGebra to work with local variables to compactify expressions?

Things get really unwieldy if you have a large subexpression that occurs multiple times within a larger expression.

For instance, in the following expression, it's cumbersome to repeat certain subexpressions like "(0,f(p)Element(Element(m1,p),3))" multiple times, so it would be nice if you could have something like a local variable to substitute for that repeated subexpression to take care of that:

Sequence({Segment(Element(Element(m1,p),1),Element(Element(m1,p),1)+ (0,f(p)Element(Element(m1,p),3))),Segment(Element(Element(m1,p),2),Element(Element(m1,p),2)+ (0,f(p)Element(Element(m1,p),3))),Semicircle(Element(Element(m1,p),1)+ (0,f(p)Element(Element(m1,p),3)),Element(Element(m1,p),2)+ (0,f(p)Element(Element(m1,p),3)))},p,1,v)


The attached ggb file is an experiment to visualize gaps between prime numbers where I ran into this issue.

greetings and thanks in advance for any suggestions, Niek

Comments (4)

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This doesn't directly answer your question about local variables, but one thing you can do to shorten your code is to avoid using the Element() command. A better way to access list elements is to use the list name directly. Say you have L = { {1,2}, {3,4}, {5,6}, {7,8} }. Then you can call L(3) to get {5,6}, and if you call L(3,1), you get 5.

So, in your code, you have Element(Element(m1,p),1), but this could be shortened to m1(p,1).

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Ah, thanks. I also noticed this more compact way to refer to elements of a list in the wiki pages of GeoGebra and it does reduce the expressions quite a bit. Though it seems that sometimes it interprets a list of lists as a matrix, if the elements have the same length. I guess using a list of tuples would also be an option, where x(t), y(t) and z(t) can be used to refer to the components of a tuple t.

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I do not know if there is a way; I use the replacement feature of word or another editor

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You can abuse the Zip function to effectively create local computed constants from single-item lists, then use Join to remove the outer layer of nesting created by the Zip:

Join[Zip[expression-of-a-and-b, a, {formula-for-a}, b, {formula-for-b}]]


Note that the an index variable named “i” which works in the Sequence command does not work in a Zip command (except for an enclosing Sequence construct). Use something like “ix” instead.

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