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#76 2013-07-31 20:06:46

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,598

Re: Implicit Equation Grapher

Hi;

First thing I notice is the new warning about the flash player.

It is funny about the known bug. That is just y = x and should graph as a straight line. Mathematica will graph it like that, Geogebra too, but other graphers like this one have the same problem.

http://kevinmehall.net/p/equationexplorer/

http://www.flashandmath.com/mathlets/ca … licit.html


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#77 2013-07-31 21:01:45

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,535

Re: Implicit Equation Grapher

bobbym wrote:

First thing I notice is the new warning about the flash player.

What warning?

bobbym wrote:

It is funny about the known bug. That is just y = x and should graph as a straight line. Mathematica will graph it like that, Geogebra too, but other graphers like this one have the same problem

Mathematica and Geogebra may do something analytical with the equation first.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#78 2013-07-31 21:04:58

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,598

Re: Implicit Equation Grapher

Hi;

This warning is new on mine:

View Image: 2013-07-30_085603.gif

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#79 2013-07-31 21:09:05

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,535

Re: Implicit Equation Grapher

Is that because you have Flash disabled?


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#80 2013-07-31 21:10:51

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,598

Re: Implicit Equation Grapher

Yes, when I enable it everything works as it should.

You might consider a Newton type iteration to find your points instead of a change of sign.

The differentiations would be done numerically and there would be no algebraic manipulations. You could use it when the sign change algorithm you are using failed to find a point.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#81 2013-08-05 11:36:46

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,535

Re: Implicit Equation Grapher

Breakthrough!

Was finally able to get Newton-Raphson to work.

Latest version (v0.90) now posted: Implicit Equation Grapher
You can still access the old algorithm (called "SignChange").

The "extra lines" seem to have gone, and (x-y)^2=0 works now.

Would really appreciate everyone testing it (try different functions) to make sure it does the best it can.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#82 2013-08-05 11:43:20

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,598

Re: Implicit Equation Grapher

Did you see post #80? And they say telepathy is kaboobly doo!

I will look at it now, but you probably sensed that already.

Runs really nice and quick. Worked on all of mine. I especially liked this one (x - y)^2 + x^2 = 0.

There is one weird effect I am getting.

When I plot this exp(x-y)=0 which should have no solution among the Reals. I get an empty graph but when I hit 2x or 10x I get a surprise.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#83 2013-08-05 13:05:42

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,535

Re: Implicit Equation Grapher

I started working on this recently because I wanted to improve it.

I knew that Newton was a possible approach but wasn't convinced. So I started off to see if I could find the slope at any point ... hence the "shaded" plot types. Once I mastered slope I knew it was but a few small steps to Newton.

I was pleasantly surprised by the results, but it was very slow. After some work I was able to speed it up and you see the results.

You and some others over the past 2 years have suggested Newton to me, it just took a while for me to get around to it smile


exp(x-y)=0 seems to suffer under the Newton algorithm, values below around exp(-7.5)=5.5e-4 lead to Newton heading towards zero. I will investigate.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#84 2013-08-05 22:32:15

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,598

Re: Implicit Equation Grapher

I use the grapher and it is a good tool. Thanks for writing it.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#85 2013-08-06 23:01:33

MathsIsFun
Administrator
Registered: 2005-01-21
Posts: 7,535

Re: Implicit Equation Grapher

You are welcome, bobby

bobbym wrote:

... Maybe the ability to graph 2 or more equations.

You asked for it, and I have (I hope) managed to do it in the new v0.91  Implicit Equation Grapher

It is quite fun to overlay plots and find similarities between them.

Let me know if it doesn't behave nicely.


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

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#86 2013-08-06 23:30:42

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,598

Re: Implicit Equation Grapher

Hi MIF;

Thanks for the new feature. It is working well.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#87 2013-08-06 23:50:59

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,392

Re: Implicit Equation Grapher

The thing I noticed about Sign Change is that, when I plot y=ceil(x), for example, extra lines appear.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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