Graph Implicit Function

LFS shared this question 14 years ago
Answered

Hi - Is there a way to graph an implicit function say: x^3+y^3-x y^2=5 in GeoGebra.

I also will want to draw the numerator and denominator of the derivative of this function in order to find the intersection points, i.e. the points where the tangents are horizontal and vertical respectively

Thanks for any help.

Linda

Comments (21)

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Hi Linda

Answer to the first question:

I do not know if I made a mistake but I think this is a solution "a la mathmagic"


https://ggbm.at/533569

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Hiya Piman - I really appreciate your reply!

However, I don't think this is the graph. The graph looks much different than the one I got ...

This is what I finally did - but of course I want GeoGebra and I want it to do the derivative and I want exact intersection points.

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I looked it up "graphing implicit functions" on google and got this thread: http://www.physicsforums.co.......

I downloaded graph.exe, installed it, clicked on y<x, pasted in the function (adding a * between x and y^2) and got the graph.

At least I could see that there were two points with a horizontal tangent and two points with a vertical tangent.

I found the derivative implicitly by hand: f'(x)=(-3x^2+y^2)/(3y^2-2xy). Then - still in graph.exe - I

1. clicked again on y<x and type in the numerator y^2=3x^2. The intersection points of these 2 lines and the function are the points where the tangent is horizontal.

2. clicked again on y<x and type in the denominator 3y^2=2x*y and the intersection points of these two lines (one is the x-axis) and the function are the points where the tangent is vertical.

Using my eyeballs i have - Horizontal (-0.90,1.56) and (1.16,2.04) and Vertical (1.79,1.21) and (1.70,0).

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Hi Linda

However, I don't think this is the graph. The graph looks much different than the one I got ...

There is difference because I used other coefficients. But the method of mathmagic still valid ...

With your coefficients (problem with blue locus ...) :

079fd6ee04c7b0a7c142da5ccd59f1a8

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Thanks Piman! I was swamped at work today so did not get a chance to look until now.

Not quite sure I understand, but I will look carefully tomorrow.

Best, Linda

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There is difference because I used other coefficients. But the method of mathmagic still valid ...

With your coefficients (problem with blue locus ...) :


Wow. This is incredibly slow! How long did it take you for the worksheet to finish recalculating? I am about to give up.


[edit]

I gave up after a few minutes and killed the process. :(

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Hi SharkD

I gave up using GeoGebra for implicit and just graph with graph.exe. It is quick, easy and free but all you get is the graph.

But, I don't know of any program that does anything more than just graph an implicit function (i.e. it won't find the derivative or anything), where I think this algorithm will do that for you.


But I did use this idea from piman for graphing polar functions - which are much simpler and which you saw. That worked quickly.


The real reason that I am writing is to ask you if you are using beta or pre-release? Yesterday I was doing something with the spreadsheet in beta and it was taking a while (okay there were alot of calculations, but still...). Just wondered if you were in the latest beta?

Thanks. L

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Hi

How long did it take you for the worksheet to finish recalculating?

10-12 seconds (3.0.0 , pre.release or last beta)

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Hi

Instead of the locus of points E, F, G, trace and make animation (last beta)


https://ggbm.at/533683

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10-12 seconds (3.0.0 , pre.release or last beta)


Deleting objects or reverting changes seems to take a lot longer than adding them.


Instead of the locus of points E, F, G, trace and make animation (last beta)


Yes, this is much quicker.


[edit]

I am trying to apply your method to the following worksheet. However, the program for some reason will not allow me to take the Root of f(x). There are no error messages; it simply does nothing.

https://ggbm.at/533695

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I downloaded graph.exe, installed it, clicked on y<x, pasted in the function (adding a * between x and y^2) and got the graph.


Could you provide more information on where you obtained this program? "graph.exe" is a very generic name for a program, and is not very helpful.

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Hi SharkD

I am trying to apply your method to the following worksheet. However, the program for some reason will not allow me to take the Root of f(x). There are no error messages; it simply does nothing.

This is mathmagic's method.

Root[f] only works if f is polynomial.

Idea: g(x)=TaylorPolynomial[f,x(A),12] and h(x)=TaylorPolynomial[f,x(C),12]

But the graphics of g and h don't show up because f contains expressions of type t^k(x), t slider.

If, in the expression of f, you make, for example, 0.5^k(x), then it's all right

But wen you make mathmagics method geogebra works very slowly ...


https://ggbm.at/533697

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Could you provide more information on where you obtained this program? "graph.exe"


http://sourceforge.net/proj...

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This is mathmagic's method.

Root[f] only works if f is polynomial.

Idea: g(x)=TaylorPolynomial[f,x(A),12] and h(x)=TaylorPolynomial[f,x(C),12]

But the graphics of g and h don't show up because f contains expressions of type t^k(x), t slider.

If, in the expression of f, you make, for example, 0.5^k(x), then it's all right

But wen you make mathmagics method geogebra works very slowly ...


I ended up splitting the root into four regions:


https://ggbm.at/533701


I'm not very happy with it. There are many gaps in the curve. I will try your suggestion next.


http://sourceforge.net/projects/graph


Thanks! BTW, I have also been using POV-Ray to graph the functions. It works well, but is slow and can be tricky to use.

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hello

all of us know that GG does not solve equations so somebody tryes solve equations and graph implicits sometimes

the general answer is "you must use an expressions handler" or to do it yourself

eg:

    Curve[t cbrt(5 / (t³ - t + 1)), cbrt(5 / (t³ - t + 1)), t, -100, 100]


excuse my english

saludos

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Hi MM

Finally you arrived :)

excuse my english

Your english is not important but your ideas are.

Saludos

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hello

all of us know that GG does not solve equations so somebody tryes solve equations and graph implicits sometimes

the general answer is "you must use an expressions handler" or to do it yourself

eg:

    Curve[t cbrt(5 / (t³ - t + 1)), cbrt(5 / (t³ - t + 1)), t, -100, 100]


excuse my english

saludos

Unfortunately, I am not knowledgable enough to do this. :D

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The other way, we will find a parametrization for a curve with genus 0 with maple after that draw it :smiley_cat:

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hello sarkD

simply substtitute "x=y t" and solve the equation on y variable


you can try it with "y*e^x=x*e^y" it is interesting

saludos

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hello sarkD

simply substtitute "x=y t" and solve the equation on y variable


you can try it with "y*e^x=x*e^y" it is interesting

saludos


I think I don't understand because I have forgotten most of my calculus. Step-by-step instructions might be better in this case.


-Mike

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piman's implicit.ggb file works very nicely in [ Edit: GeoGebra 3.2 ] :)

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Write the equation in standard form (i.e. f(x,y) = 0) and then use the ImplicitCurve command:

/Kzil8vZbf+oAAAAASUVORK5CYII=

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