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#76 2013-07-31 20:06:46
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#77 2013-07-31 21:01:45
- MathsIsFun
- Administrator
- Registered: 2005-01-21
- Posts: 7,713
Re: Implicit Equation Grapher
First thing I notice is the new warning about the flash player.
What warning?
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
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Implicit Equation Grapher
Hi;
This warning is new on mine:
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#79 2013-07-31 21:09:05
- MathsIsFun
- Administrator
- Registered: 2005-01-21
- Posts: 7,713
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
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#81 2013-08-05 11:36:46
- MathsIsFun
- Administrator
- Registered: 2005-01-21
- Posts: 7,713
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
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#83 2013-08-05 13:05:42
- MathsIsFun
- Administrator
- Registered: 2005-01-21
- Posts: 7,713
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 
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
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#85 2013-08-06 23:01:33
- MathsIsFun
- Administrator
- Registered: 2005-01-21
- Posts: 7,713
Re: Implicit Equation Grapher
You are welcome, bobby
... 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
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#87 2013-08-06 23:50:59
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
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
The knowledge of some things as a function of age is a delta function.
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