Quantum Mechanics with HV is Local!

[Joy Christian]

What they mean with



is that you can just replace with in the expression that follows.

And yes, I know it's silly.

There is nothing silly or (as Gill claims) unconventional about it. The limit operation is highschool calculus applied to ordinary vectors in a 3D space.

***

[Heinera]

There is nothing silly or (as Gill claims) unconventional about it. The limit operation is highschool calculus applied to ordinary vectors in a 3D space.

The silliness lies in the notation being wholly unnecessary; it's only there to make the formulas look "advanced". Which they are not.

[Joy Christian]

There is nothing silly or (as Gill claims) unconventional about it. The limit operation is highschool calculus applied to ordinary vectors in a 3D space.

The silliness lies in the notation being wholly unnecessary; it's only there to make the formulas look "advanced". Which they are not.

The silliness of your comment lies in your lack of understanding of what the model is about. High school mathematics is hardly "advanced" unless one does not have a high school diploma.

***

[Heinera]

The silliness of your comment lies in your lack of understanding of what the model is about. High school mathematics is hardly "advanced" unless one does not have a high school diploma.

But the formulas don't even require high school mathematics.

[FrediFizzx]

So these functions,

,
,

work without the HV, , to give the correct QM predictions for outcome possibilities and also gives the result of via the product calculation.
.

I'm sorry to tell you, but you guys completely botched up the math. When fed into a computer (you should try it sometime) these functions give the classical triangle correlations.

But I guess you don't belive in computers.

Nice try but no dice. I've run it on a computer and it works perfectly to give -a.b just as our analytical formulas say. But please demonstrate otherwise if you can.
.

[gill1109]

So these functions,

,
,

work without the HV, , to give the correct QM predictions for outcome possibilities and also gives the result of via the product calculation.
.

I'm sorry to tell you, but you guys completely botched up the math. When fed into a computer (you should try it sometime) these functions give the classical triangle correlations.

But I guess you don't belive in computers.

Nice try but no dice. I've run it on a computer and it works perfectly to give -a.b just as our analytical formulas say. But please demonstrate otherwise if you can.
.

Please show us the code, or perhaps better, well commented pseudo-code.

[FrediFizzx]

The code's been on the forum for a long time. search for it you will find it. Otherwise I will find it in the morning.

[gill1109]

The code's been on the forum for a long time. Search for it you will find it. Otherwise I will find it in the morning.

Code which implements the *current version* of your key definitions?

I'm not interested in code which corresponds to earlier versions of those two formulas.

But if you already have that, please locate it for me! No hurry ... thanks in advance.

[FrediFizzx]

Hmm... seems like I never posted the 3D code. I will have to find it. But I am going to tell you now that it is QM mapped to geometric algebra for validation of the product calculation.

Here is a link to the GHZ code to amuse yourself with in the meantime.
viewtopic.php?f=6&t=324
.

[FrediFizzx]

Hmm... seems like I never posted the 3D code. I will have to find it. But I am going to tell you now that it is QM mapped to geometric algebra for validation of the product calculation.

Here is a link to the GHZ code to amuse yourself with in the meantime.
viewtopic.php?f=6&t=324
.

I guess I never did the 3-sphere with 3D vectors code so I will have to do that. In the meantime,

viewtopic.php?f=6&t=388
.

[FrediFizzx]

The silliness of your comment lies in your lack of understanding of what the model is about. High school mathematics is hardly "advanced" unless one does not have a high school diploma.

But the formulas don't even require high school mathematics.

Oh, so I guess kids learn about in grade school. Give us a break. Sheesh. Here is another one for you that you probably never learned.
.

[gill1109]

Hmm... seems like I never posted the 3D code. I will have to find it. But I am going to tell you now that it is QM mapped to geometric algebra for validation of the product calculation.

Here is a link to the GHZ code to amuse yourself with in the meantime.
viewtopic.php?f=6&t=324
.

I guess I never did the 3-sphere with 3D vectors code so I will have to do that. In the meantime,

viewtopic.php?f=6&t=388
.

GAviewer code would be fine. But please make sure that it is code which recognisably implements your current two formulas defining A(a, lambda) and B(b, lambda). We would like to see what you really do mean by your non-standard limit notation and your non-standard linking of the dummy variables in two separate equations. If I try to implement it, I will end up getting the wrong answer, *and* you guys will accuse me of doing a straw-man attack, and it will all have been a waste of time.

Example. Already some years ago I tried to understand Python code of Michel and wrote "my own" version of his algorithm in R, but of course, he could not accept what I then wrote about "his" algorithm. He had published Python code only. He gave no literature reference and gave no clue where he had got the ideas from. If he had published a mathematical article using conventional mathematical notations, then the Python code could have been an implementation of his published mathematical formulas. And other people could have made other implementations. And everyone could openly discuss the maths and the implementations and the interpretations.

I think we need to come to some minimal requirements of simulation programs. The important thing is that one can experiment with them. And experiments must be reproducible. And for these reasons, I think the programs must have the following minimal requirements:

1) "save random seed" and "restore random seed" facilities
2) the user can freely submit their own *settings*
3) the user can demand that only one "trial" is done (one trial = two settings and two outcomes)

Any comments on these requirements? I think they are reasonable. If you think they are unreasonable, why?

I want to be able to test such software on a single computer, and not have to go to the trouble of setting up a computer network. But the computer program must in principle be so modular with modules for the source, for Alice's detector, and for Bob's detector.

[FrediFizzx]

Hmm... seems like I never posted the 3D code. I will have to find it. But I am going to tell you now that it is QM mapped to geometric algebra for validation of the product calculation.

Here is a link to the GHZ code to amuse yourself with in the meantime.
viewtopic.php?f=6&t=324
.

I guess I never did the 3-sphere with 3D vectors code so I will have to do that. In the meantime,

viewtopic.php?f=6&t=388
.

GAviewer code would be fine. But please make sure that it is code which recognisably implements your current two formulas defining A(a, lambda) and B(b, lambda). We would like to see what you really do mean by your non-standard limit notation and your non-standard linking of the dummy variables in two separate equations. If I try to implement it, I will end up getting the wrong answer, *and* you guys will accuse me of doing a straw-man attack, and it will all have been a waste of time.
…

There is nothing non-standard about . I can't believe a math professor would call that non-standard. And there is no non-standard linking of the vector s between A and B. s_A = -s_B is required by the physics of the original singlet after it splits. You must be trying to mentally block yourself from the truth.

But the limits don't matter for the product calculation anyway as they are not used in it when QM is mapped to GA. I will have the validation of the product calculation via GAViewer done soon.
.

[FrediFizzx]

Here is a sample output with 1000 trials,

Code: Select all

correlation = 0.061235
negcos = 0.061235
correlation = -0.678012
negcos = -0.678012
correlation = -0.167233
negcos = -0.167233
correlation = 0.880062
negcos = 0.880062
correlation = -0.275535
negcos = -0.275535
correlation = -0.401002
negcos = -0.401002
correlation = -0.484143
negcos = -0.484143
correlation = -0.428842
negcos = -0.428842
correlation = 0.497313
negcos = 0.497313
correlation = 0.602708
negcos = 0.602708
correlation = -0.998583
negcos = -0.998583
correlation = 0.022876
negcos = 0.022876
correlation = 0.282134
negcos = 0.282134
correlation = -0.281004
negcos = -0.281004
correlation = -0.508342
negcos = -0.508342
correlation = 0.312666
negcos = 0.312666
correlation = -0.297470
negcos = -0.297470
correlation = -0.121253
negcos = -0.121253
mean = -0.013428 + -0.005777*e2^e3 + -0.001460*e3^e1 + 0.016000*e1^e2
aveA = 0.024000
aveB = -0.024000

You can see that the correlations are matching the negative cosine to 6 decimal places event by event. I'm just trying to correctly extract the angle between a and b so that I can plot the data. It is a bit tougher since the vectors are in 3D.
.

[gill1109]

Hmm... seems like I never posted the 3D code. I will have to find it. But I am going to tell you now that it is QM mapped to geometric algebra for validation of the product calculation.

Here is a link to the GHZ code to amuse yourself with in the meantime.
viewtopic.php?f=6&t=324
.

I guess I never did the 3-sphere with 3D vectors code so I will have to do that. In the meantime,

viewtopic.php?f=6&t=388
.

GAviewer code would be fine. But please make sure that it is code which recognisably implements your current two formulas defining A(a, lambda) and B(b, lambda). We would like to see what you really do mean by your non-standard limit notation and your non-standard linking of the dummy variables in two separate equations. If I try to implement it, I will end up getting the wrong answer, *and* you guys will accuse me of doing a straw-man attack, and it will all have been a waste of time.
…

There is nothing non-standard about . I can't believe a math professor would call that non-standard. And there is no non-standard linking of the vector s between A and B. s_A = -s_B is required by the physics of the original singlet after it splits. You must be trying to mentally block yourself from the truth.

But the limits don't matter for the product calculation anyway as they are not used in it when QM is mapped to GA. I will have the validation of the product calculation via GAViewer done soon.
.

Your assumptions about math professors are badly wrong. Looking forward to seeing the GA. But I want to see how you express the limits in GA! You say "the limits do not matter because they are not used when QM is mapped to GA". You promised us GA which would verify and elucidate what you mean by your limit operations.

You don't use , so I don't see why you mention it. Physics is one thing but if you want to express physics in mathematical language, the mathematics had better make sense, too. By all means expand mathematics with new features and new structures if you need them. But give them a coherent mathematical definition. Presently you expand mathematics but give no bridge between the established and accepted old stuff, and the new. So your work is not scientific. No one can reproduce your computations. Because you are the sole owner of their meaning and you simply mean them to get the right answer (which we knew in advance), but don't apparently care how you get the right answer.

[gill1109]

Where did I promise that? Don't make things up.
.

I asked you. You said you would code it. I suppose you didn't understand my question.

But there is progress, now you do understand my question! You can simply say "no" if you don't want to do it / don't know how to do it.

[FrediFizzx]

Where did I promise that? Don't make things up.
.

I asked you. You said you would code it. I suppose you didn't understand my question.

But there is progress, now you do understand my question! You can simply say "no" if you don't want to do it / don't know how to do it.

It is obvious that there is no sense for me to continue with this since you are going to refuse to understand it anyways. You saw the sample output. That will have to do it. The product calculation is validated via computer program.
.

[FrediFizzx]

Here is the output for 2,000 trials.

Code: Select all

Correlations  neg cosine   Difference
-0.999636   -0.999636   0
-0.999209   -0.999209   0
-0.998494   -0.998494   0
-0.997928   -0.997928   0
-0.99716   -0.99716   0
-0.995499   -0.995499   0
-0.994493   -0.994493   0
-0.993795   -0.993795   0
-0.992287   -0.992287   0
-0.992011   -0.992011   0
-0.991293   -0.991293   0
-0.990372   -0.990372   0
-0.989181   -0.989181   0
-0.988348   -0.988348   0
-0.987466   -0.987466   0
-0.986844   -0.986844   0
-0.986135   -0.986135   0
-0.984871   -0.984871   0
-0.983396   -0.983396   0
-0.983201   -0.983201   0
-0.98249   -0.98249   0
-0.982458   -0.982458   0
-0.982257   -0.982257   0
-0.98104   -0.98104   0
-0.980796   -0.980796   0
-0.980081   -0.980081   0
-0.976796   -0.976796   0
-0.974053   -0.974053   0
-0.973911   -0.973911   0
-0.972942   -0.972942   0
-0.97191   -0.97191   0
-0.971406   -0.971406   0
-0.970998   -0.970998   0
-0.970329   -0.970329   0
-0.970252   -0.970252   0
-0.969467   -0.969467   0
-0.969245   -0.969245   0
-0.967542   -0.967542   0
-0.965849   -0.965849   0
-0.963887   -0.963887   0
-0.963784   -0.963784   0
-0.963345   -0.963345   0
-0.958199   -0.958199   0
-0.957994   -0.957994   0
-0.956231   -0.956231   0
-0.955782   -0.955782   0
-0.952206   -0.952206   0
-0.951974   -0.951974   0
-0.951025   -0.951025   0
-0.950994   -0.950994   0
-0.950699   -0.950699   0
-0.948913   -0.948913   0
-0.948858   -0.948858   0
-0.948782   -0.948782   0
-0.947755   -0.947755   0
-0.947605   -0.947605   0
-0.94731   -0.94731   0
-0.944082   -0.944082   0
-0.943689   -0.943689   0
-0.943   -0.943   0
-0.942849   -0.942849   0
-0.942295   -0.942295   0
-0.941137   -0.941137   0
-0.941004   -0.941004   0
-0.939767   -0.939767   0
-0.939459   -0.939459   0
-0.937386   -0.937386   0
-0.936653   -0.936653   0
-0.936472   -0.936472   0
-0.936374   -0.936374   0
-0.936117   -0.936117   0
-0.935176   -0.935176   0
-0.934418   -0.934418   0
-0.932191   -0.932191   0
-0.932079   -0.932079   0
-0.932062   -0.932062   0
-0.930468   -0.930468   0
-0.928041   -0.928041   0
-0.924905   -0.924905   0
-0.923071   -0.923071   0
-0.921182   -0.921182   0
-0.921177   -0.921177   0
-0.920897   -0.920897   0
-0.91962   -0.91962   0
-0.918315   -0.918315   0
-0.918057   -0.918057   0
-0.917742   -0.917742   0
-0.917162   -0.917162   0
-0.916817   -0.916817   0
-0.91646   -0.91646   0
-0.914666   -0.914666   0
-0.914295   -0.914295   0
-0.913828   -0.913828   0
-0.912723   -0.912723   0
-0.911104   -0.911104   0
-0.909875   -0.909875   0
-0.909782   -0.909782   0
-0.908353   -0.908353   0
-0.907335   -0.907335   0
-0.907131   -0.907131   0
-0.906857   -0.906857   0
-0.906856   -0.906856   0
-0.906211   -0.906211   0
-0.905804   -0.905804   0
-0.905284   -0.905284   0
-0.904831   -0.904831   0
-0.904718   -0.904718   0
-0.901867   -0.901867   0
-0.899602   -0.899602   0
-0.899251   -0.899251   0
-0.898273   -0.898273   0
-0.897495   -0.897495   0
-0.897415   -0.897415   0
-0.896167   -0.896167   0
-0.895767   -0.895767   0
-0.894937   -0.894937   0
-0.893924   -0.893924   0
-0.893076   -0.893076   0
-0.891287   -0.891287   0
-0.890735   -0.890735   0
-0.890633   -0.890633   0
-0.888784   -0.888784   0
-0.887359   -0.887359   0
-0.884777   -0.884777   0
-0.884444   -0.884444   0
-0.883042   -0.883042   0
-0.882687   -0.882687   0
-0.882644   -0.882644   0
-0.880601   -0.880601   0
-0.879199   -0.879199   0
-0.875791   -0.875791   0
-0.874257   -0.874257   0
-0.872604   -0.872604   0
-0.872316   -0.872316   0
-0.869849   -0.869849   0
-0.869271   -0.869271   0
-0.867636   -0.867636   0
-0.867245   -0.867245   0
-0.867098   -0.867098   0
-0.863257   -0.863257   0
-0.86238   -0.86238   0
-0.862073   -0.862073   0
-0.861903   -0.861903   0
-0.861246   -0.861246   0
-0.861131   -0.861131   0
-0.860849   -0.860849   0
-0.860272   -0.860272   0
-0.858167   -0.858167   0
-0.857322   -0.857322   0
-0.855697   -0.855697   0
-0.855183   -0.855183   0
-0.854997   -0.854997   0
-0.852258   -0.852258   0
-0.851819   -0.851819   0
-0.850576   -0.850576   0
-0.84958   -0.84958   0
-0.849413   -0.849413   0
-0.84901   -0.84901   0
-0.848865   -0.848865   0
-0.848471   -0.848471   0
-0.846872   -0.846872   0
-0.846653   -0.846653   0
-0.846028   -0.846028   0
-0.842832   -0.842832   0
-0.842487   -0.842487   0
-0.841344   -0.841344   0
-0.839833   -0.839833   0
-0.838553   -0.838553   0
-0.838391   -0.838391   0
-0.837817   -0.837817   0
-0.837716   -0.837716   0
-0.837241   -0.837241   0
-0.837173   -0.837173   0
-0.836138   -0.836138   0
-0.83564   -0.83564   0
-0.83428   -0.83428   0
-0.830256   -0.830256   0
-0.829669   -0.829669   0
-0.829098   -0.829098   0
-0.828524   -0.828524   0
-0.827764   -0.827764   0
-0.821528   -0.821528   0
-0.821177   -0.821177   0
-0.819763   -0.819763   0
-0.819233   -0.819233   0
-0.819193   -0.819193   0
-0.818658   -0.818658   0
-0.818205   -0.818205   0
-0.817743   -0.817743   0
-0.816621   -0.816621   0
-0.812511   -0.812511   0
-0.812018   -0.812018   0
-0.811966   -0.811966   0
-0.810384   -0.810384   0
-0.810277   -0.810277   0
-0.809787   -0.809787   0
-0.807756   -0.807756   0
-0.807173   -0.807173   0
-0.806998   -0.806998   0
-0.804945   -0.804945   0
-0.80396   -0.80396   0
-0.803517   -0.803517   0
-0.802642   -0.802642   0
-0.7986   -0.7986   0
-0.797011   -0.797011   0
-0.796754   -0.796754   0
-0.796704   -0.796704   0
-0.796531   -0.796531   0
-0.793263   -0.793263   0
-0.793105   -0.793105   0
-0.791691   -0.791691   0
-0.790286   -0.790286   0
-0.789   -0.789   0
-0.788181   -0.788181   0
-0.788071   -0.788071   0
-0.787458   -0.787458   0
-0.787333   -0.787333   0
-0.786526   -0.786526   0
-0.784281   -0.784281   0
-0.780943   -0.780943   0
-0.779534   -0.779534   0
-0.778696   -0.778696   0
-0.778681   -0.778681   0
-0.777595   -0.777595   0
-0.777217   -0.777217   0
-0.77671   -0.77671   0
-0.776221   -0.776221   0
-0.77544   -0.77544   0
-0.775352   -0.775352   0
-0.774909   -0.774909   0
-0.774754   -0.774754   0
-0.773903   -0.773903   0
-0.773581   -0.773581   0
-0.773395   -0.773395   0
-0.771406   -0.771406   0
-0.770199   -0.770199   0
-0.770193   -0.770193   0
-0.767253   -0.767253   0
-0.766598   -0.766598   0
-0.766061   -0.766061   0
-0.765186   -0.765186   0
-0.764623   -0.764623   0
-0.764113   -0.764113   0
-0.763228   -0.763228   0
-0.763101   -0.763101   0
-0.762257   -0.762257   0
-0.761026   -0.761026   0
-0.760578   -0.760578   0
-0.757326   -0.757326   0
-0.75688   -0.75688   0
-0.756815   -0.756815   0
-0.756737   -0.756737   0
-0.7527   -0.7527   0
-0.74867   -0.74867   0
-0.744133   -0.744133   0
-0.744104   -0.744104   0
-0.742716   -0.742716   0
-0.741963   -0.741963   0
-0.740534   -0.740534   0
-0.738092   -0.738092   0
-0.734757   -0.734757   0
-0.733604   -0.733604   0
-0.731703   -0.731703   0
-0.728243   -0.728243   0
-0.727182   -0.727182   0
-0.726745   -0.726745   0
-0.725285   -0.725285   0
-0.725268   -0.725268   0
-0.723195   -0.723195   0
-0.722108   -0.722108   0
-0.721404   -0.721404   0
-0.721223   -0.721223   0
-0.719801   -0.719801   0
-0.718071   -0.718071   0
-0.717126   -0.717126   0
-0.716533   -0.716533   0
-0.715532   -0.715532   0
-0.714391   -0.714391   0
-0.713269   -0.713269   0
-0.713214   -0.713214   0
-0.712713   -0.712713   0
-0.71142   -0.71142   0
-0.711147   -0.711147   0
-0.710838   -0.710838   0
-0.709537   -0.709537   0
-0.709085   -0.709085   0
-0.70852   -0.70852   0
-0.70748   -0.70748   0
-0.706364   -0.706364   0
-0.703441   -0.703441   0
-0.701334   -0.701334   0
-0.700656   -0.700656   0
-0.700524   -0.700524   0
-0.700514   -0.700514   0
-0.700332   -0.700332   0
-0.698694   -0.698694   0
-0.69691   -0.69691   0
-0.696477   -0.696477   0
-0.695531   -0.695531   0
-0.694968   -0.694968   0
-0.694861   -0.694861   0
-0.693431   -0.693431   0
-0.69341   -0.69341   0
-0.691557   -0.691557   0
-0.689137   -0.689137   0
-0.685901   -0.685901   0
-0.685633   -0.685633   0
-0.684737   -0.684737   0
-0.684012   -0.684012   0
-0.683339   -0.683339   0
-0.682519   -0.682519   0
-0.680603   -0.680603   0
-0.679932   -0.679932   0
-0.679701   -0.679701   0
-0.679683   -0.679683   0
-0.679529   -0.679529   0
-0.679458   -0.679458   0
-0.676404   -0.676404   0
-0.673387   -0.673387   0
-0.673057   -0.673057   0
-0.672738   -0.672738   0
-0.670443   -0.670443   0
-0.669296   -0.669296   0
-0.668861   -0.668861   0
-0.668768   -0.668768   0
-0.668698   -0.668698   0
-0.666147   -0.666147   0
-0.665925   -0.665925   0
-0.664772   -0.664772   0
-0.66413   -0.66413   0
-0.662681   -0.662681   0
-0.661906   -0.661906   0
-0.661832   -0.661832   0
-0.661799   -0.661799   0
-0.661743   -0.661743   0
-0.66149   -0.66149   0
-0.660421   -0.660421   0
-0.659042   -0.659042   0
-0.654311   -0.654311   0
-0.653682   -0.653682   0
-0.653118   -0.653118   0
-0.651984   -0.651984   0
-0.649813   -0.649813   0
-0.649757   -0.649757   0
-0.648342   -0.648342   0
-0.647301   -0.647301   0
-0.647087   -0.647087   0
-0.646649   -0.646649   0
-0.646538   -0.646538   0
-0.646531   -0.646531   0
-0.646416   -0.646416   0
-0.646107   -0.646107   0
-0.644288   -0.644288   0
-0.643311   -0.643311   0
-0.641458   -0.641458   0
-0.640881   -0.640881   0
-0.640775   -0.640775   0
-0.640519   -0.640519   0
-0.639454   -0.639454   0
-0.638117   -0.638117   0
-0.63618   -0.63618   0
-0.636138   -0.636138   0
-0.636077   -0.636077   0
-0.635532   -0.635532   0
-0.634962   -0.634962   0
-0.633458   -0.633458   0
-0.633206   -0.633206   0
-0.630269   -0.630269   0
-0.629319   -0.629319   0
-0.629088   -0.629088   0
-0.628133   -0.628133   0
-0.626142   -0.626142   0
-0.626038   -0.626038   0
-0.625795   -0.625795   0
-0.625121   -0.625121   0
-0.624413   -0.624413   0
-0.623344   -0.623344   0
-0.622734   -0.622734   0
-0.622022   -0.622022   0
-0.620315   -0.620315   0
-0.618644   -0.618644   0
-0.618299   -0.618299   0
-0.615963   -0.615963   0
-0.614139   -0.614139   0
-0.612481   -0.612481   0
-0.611685   -0.611685   0
-0.610702   -0.610702   0
-0.607811   -0.607811   0
-0.607509   -0.607509   0
-0.607419   -0.607419   0
-0.606655   -0.606655   0
-0.604859   -0.604859   0
-0.604674   -0.604674   0
-0.604634   -0.604634   0
-0.604127   -0.604127   0
-0.601486   -0.601486   0
-0.601018   -0.601018   0
-0.600916   -0.600916   0
-0.600729   -0.600729   0
-0.600504   -0.600504   0
-0.599347   -0.599347   0
-0.599179   -0.599179   0
-0.598857   -0.598857   0
-0.598252   -0.598252   0
-0.597322   -0.597322   0
-0.596478   -0.596478   0
-0.596372   -0.596372   0
-0.595341   -0.595341   0
-0.595272   -0.595272   0
-0.595073   -0.595073   0
-0.592141   -0.592141   0
-0.591994   -0.591994   0
-0.591703   -0.591703   0
-0.590449   -0.590449   0
-0.587235   -0.587235   0
-0.586961   -0.586961   0
-0.586829   -0.586829   0
-0.586369   -0.586369   0
-0.586119   -0.586119   0
-0.585638   -0.585638   0
-0.584158   -0.584158   0
-0.584141   -0.584141   0
-0.580844   -0.580844   0
-0.580619   -0.580619   0
-0.578937   -0.578937   0
-0.57855   -0.57855   0
-0.578052   -0.578052   0
-0.577206   -0.577206   0
-0.575241   -0.575241   0
-0.575193   -0.575193   0
-0.575019   -0.575019   0
-0.57476   -0.57476   0
-0.573673   -0.573673   0
-0.573312   -0.573312   0
-0.568932   -0.568932   0
-0.568123   -0.568123   0
-0.566914   -0.566914   0
-0.56532   -0.56532   0
-0.564155   -0.564155   0
-0.563968   -0.563968   0
-0.563846   -0.563846   0
-0.563195   -0.563195   0
-0.563139   -0.563139   0
-0.562779   -0.562779   0
-0.561248   -0.561248   0
-0.56073   -0.56073   0
-0.560419   -0.560419   0
-0.559964   -0.559964   0
-0.559961   -0.559961   0
-0.559763   -0.559763   0
-0.559647   -0.559647   0
-0.559609   -0.559609   0
-0.559205   -0.559205   0
-0.55776   -0.55776   0
-0.554688   -0.554688   0
-0.55445   -0.55445   0
-0.554022   -0.554022   0
-0.55345   -0.55345   0
-0.552925   -0.552925   0
-0.552531   -0.552531   0
-0.550509   -0.550509   0
-0.548455   -0.548455   0
-0.548097   -0.548097   0
-0.54748   -0.54748   0
-0.547108   -0.547108   0
-0.546495   -0.546495   0
-0.545915   -0.545915   0
-0.545171   -0.545171   0
-0.543205   -0.543205   0
-0.542665   -0.542665   0
-0.541791   -0.541791   0
-0.541555   -0.541555   0
-0.540525   -0.540525   0
-0.540093   -0.540093   0
-0.539633   -0.539633   0
-0.538544   -0.538544   0
-0.535795   -0.535795   0
-0.535468   -0.535468   0
-0.534882   -0.534882   0
-0.533817   -0.533817   0
-0.533141   -0.533141   0
-0.532721   -0.532721   0
-0.531382   -0.531382   0
-0.526781   -0.526781   0
-0.526444   -0.526444   0
-0.523892   -0.523892   0
-0.522089   -0.522089   0
-0.521354   -0.521354   0
-0.519701   -0.519701   0
-0.519699   -0.519699   0
-0.518942   -0.518942   0
-0.51846   -0.51846   0
-0.518084   -0.518084   0
-0.517552   -0.517552   0
-0.517244   -0.517244   0
-0.51516   -0.51516   0
-0.514245   -0.514245   0
-0.513317   -0.513317   0
-0.512065   -0.512065   0
-0.511721   -0.511721   0
-0.510374   -0.510374   0
-0.510363   -0.510363   0
-0.509737   -0.509737   0
-0.509307   -0.509307   0
-0.50865   -0.50865   0
-0.507964   -0.507964   0
-0.505006   -0.505006   0
-0.504188   -0.504188   0
-0.504171   -0.504171   0
-0.503706   -0.503706   0
-0.502015   -0.502015   0
-0.501856   -0.501856   0
-0.5011   -0.5011   0
-0.500733   -0.500733   0
-0.50041   -0.50041   0
-0.49974   -0.49974   0
-0.499643   -0.499643   0
-0.497885   -0.497885   0
-0.497471   -0.497471   0
-0.495647   -0.495647   0
-0.495576   -0.495576   0
-0.494978   -0.494978   0
-0.494399   -0.494399   0
-0.492589   -0.492589   0
-0.491878   -0.491878   0
-0.491267   -0.491267   0
-0.489576   -0.489576   0
-0.487915   -0.487915   0
-0.485718   -0.485718   0
-0.484457   -0.484457   0
-0.483949   -0.483949   0
-0.483916   -0.483916   0
-0.483493   -0.483493   0
-0.483244   -0.483244   0
-0.48165   -0.48165   0
-0.479787   -0.479787   0
-0.477954   -0.477954   0
-0.473516   -0.473516   0
-0.472407   -0.472407   0
-0.472184   -0.472184   0
-0.472168   -0.472168   0
-0.47174   -0.47174   0
-0.468659   -0.468659   0
-0.467175   -0.467175   0
-0.466971   -0.466971   0
-0.464289   -0.464289   0
-0.463977   -0.463977   0
-0.463804   -0.463804   0
-0.463526   -0.463526   0
-0.462587   -0.462587   0
-0.462349   -0.462349   0
-0.460696   -0.460696   0
-0.460171   -0.460171   0
-0.458594   -0.458594   0
-0.45838   -0.45838   0
-0.457186   -0.457186   0
-0.455234   -0.455234   0
-0.455065   -0.455065   0
-0.454416   -0.454416   0
-0.453699   -0.453699   0
-0.452851   -0.452851   0
-0.452806   -0.452806   0
-0.452079   -0.452079   0
-0.446423   -0.446423   0
-0.446361   -0.446361   0
-0.445581   -0.445581   0
-0.445501   -0.445501   0
-0.445152   -0.445152   0
-0.444425   -0.444425   0
-0.443179   -0.443179   0
-0.443003   -0.443003   0
-0.441934   -0.441934   0
-0.441567   -0.441567   0
-0.441314   -0.441314   0
-0.440789   -0.440789   0
-0.440591   -0.440591   0
-0.440319   -0.440319   0
-0.437813   -0.437813   0
-0.437714   -0.437714   0
-0.436634   -0.436634   0
-0.435863   -0.435863   0
-0.435689   -0.435689   0
-0.43546   -0.43546   0
-0.434962   -0.434962   0
-0.432487   -0.432487   0
-0.431605   -0.431605   0
-0.430423   -0.430423   0
-0.42798   -0.42798   0
-0.427627   -0.427627   0
-0.427576   -0.427576   0
-0.42708   -0.42708   0
-0.426306   -0.426306   0
-0.424014   -0.424014   0
-0.423483   -0.423483   0
-0.420941   -0.420941   0
-0.420388   -0.420388   0
-0.419736   -0.419736   0
-0.419707   -0.419707   0
-0.419048   -0.419048   0
-0.417701   -0.417701   0
-0.417325   -0.417325   0
-0.416662   -0.416662   0
-0.41624   -0.41624   0
-0.415281   -0.415281   0
-0.414966   -0.414966   0
-0.412465   -0.412465   0
-0.411652   -0.411652   0
-0.409878   -0.409878   0
-0.409149   -0.409149   0
-0.408848   -0.408848   0
-0.406674   -0.406674   0
-0.406098   -0.406098   0
-0.405056   -0.405056   0
-0.404873   -0.404873   0
-0.404087   -0.404087   0
-0.403269   -0.403269   0
-0.402629   -0.402629   0
-0.402181   -0.402181   0
-0.400797   -0.400797   0
-0.399417   -0.399417   0
-0.398955   -0.398955   0
-0.398721   -0.398721   0
-0.398616   -0.398616   0
-0.397761   -0.397761   0
-0.397325   -0.397325   0
-0.396068   -0.396068   0
-0.393302   -0.393302   0
-0.393227   -0.393227   0
-0.392791   -0.392791   0
-0.392582   -0.392582   0
-0.390708   -0.390708   0
-0.389356   -0.389356   0
-0.386808   -0.386808   0
-0.386534   -0.386534   0
-0.385602   -0.385602   0
-0.385087   -0.385087   0
-0.380995   -0.380995   0
-0.37924   -0.37924   0
-0.376765   -0.376765   0
-0.375642   -0.375642   0
-0.374604   -0.374604   0
-0.373266   -0.373266   0
-0.372633   -0.372633   0
-0.369539   -0.369539   0
-0.367554   -0.367554   0
-0.367387   -0.367387   0
-0.366772   -0.366772   0
-0.366205   -0.366205   0
-0.365878   -0.365878   0
-0.365254   -0.365254   0
-0.364924   -0.364924   0
-0.364488   -0.364488   0
-0.364294   -0.364294   0
-0.364178   -0.364178   0
-0.361542   -0.361542   0
-0.360436   -0.360436   0
-0.360264   -0.360264   0
-0.359113   -0.359113   0
-0.358606   -0.358606   0
-0.357559   -0.357559   0
-0.35688   -0.35688   0
-0.356174   -0.356174   0
-0.355889   -0.355889   0
-0.355597   -0.355597   0
-0.355243   -0.355243   0
-0.354911   -0.354911   0
-0.354376   -0.354376   0
-0.354257   -0.354257   0
-0.352253   -0.352253   0
-0.351937   -0.351937   0
-0.351337   -0.351337   0
-0.350487   -0.350487   0
-0.350336   -0.350336   0
-0.349977   -0.349977   0
-0.349549   -0.349549   0
-0.349045   -0.349045   0
-0.347718   -0.347718   0
-0.347394   -0.347394   0
-0.346474   -0.346474   0
-0.34422   -0.34422   0
-0.342505   -0.342505   0
-0.340727   -0.340727   0
-0.340185   -0.340185   0
-0.340104   -0.340104   0
-0.339317   -0.339317   0
-0.339231   -0.339231   0
-0.338812   -0.338812   0
-0.338368   -0.338368   0
-0.338146   -0.338146   0
-0.337049   -0.337049   0
-0.336372   -0.336372   0
-0.335965   -0.335965   0
-0.332949   -0.332949   0
-0.331916   -0.331916   0
-0.330103   -0.330103   0
-0.329451   -0.329451   0
-0.328826   -0.328826   0
-0.327408   -0.327408   0
-0.326338   -0.326338   0
-0.326284   -0.326284   0
-0.325786   -0.325786   0
-0.323743   -0.323743   0
-0.321291   -0.321291   0
-0.320923   -0.320923   0
-0.319756   -0.319756   0
-0.319108   -0.319108   0
-0.31575   -0.31575   0
-0.31545   -0.31545   0
-0.313476   -0.313476   0
-0.311944   -0.311944   0
-0.311733   -0.311733   0
-0.311036   -0.311036   0
-0.310679   -0.310679   0
-0.310397   -0.310397   0
-0.309678   -0.309678   0
-0.309297   -0.309297   0
-0.309127   -0.309127   0
-0.308853   -0.308853   0
-0.308328   -0.308328   0
-0.30797   -0.30797   0
-0.307865   -0.307865   0
-0.307423   -0.307423   0
-0.30584   -0.30584   0
-0.305434   -0.305434   0
-0.304585   -0.304585   0
-0.302931   -0.302931   0
-0.301305   -0.301305   0
-0.300939   -0.300939   0
-0.299825   -0.299825   0
-0.299565   -0.299565   0
-0.29956   -0.29956   0
-0.298431   -0.298431   0
-0.292472   -0.292472   0
-0.291242   -0.291242   0
-0.290721   -0.290721   0
-0.289258   -0.289258   0
-0.288693   -0.288693   0
-0.288229   -0.288229   0
-0.287575   -0.287575   0
-0.287544   -0.287544   0
-0.285754   -0.285754   0
-0.284981   -0.284981   0
-0.284914   -0.284914   0
-0.284528   -0.284528   0
-0.281604   -0.281604   0
-0.280665   -0.280665   0
-0.280623   -0.280623   0
-0.277314   -0.277314   0
-0.276996   -0.276996   0
-0.276613   -0.276613   0
-0.275856   -0.275856   0
-0.275762   -0.275762   0
-0.275747   -0.275747   0
-0.274651   -0.274651   0
-0.273653   -0.273653   0
-0.271221   -0.271221   0
-0.267086   -0.267086   0
-0.266046   -0.266046   0
-0.264529   -0.264529   0
-0.263074   -0.263074   0
-0.262339   -0.262339   0
-0.261834   -0.261834   0
-0.26064   -0.26064   0
-0.259932   -0.259932   0
-0.259818   -0.259818   0
-0.258887   -0.258887   0
-0.258503   -0.258503   0
-0.257694   -0.257694   0
-0.256142   -0.256142   0
-0.255851   -0.255851   0
-0.255174   -0.255174   0
-0.25453   -0.25453   0
-0.254445   -0.254445   0
-0.25156   -0.25156   0
-0.251118   -0.251118   0
-0.250839   -0.250839   0
-0.250815   -0.250815   0
-0.249387   -0.249387   0
-0.249189   -0.249189   0
-0.244149   -0.244149   0
-0.243201   -0.243201   0
-0.242933   -0.242933   0
-0.242873   -0.242873   0
-0.242398   -0.242398   0
-0.239894   -0.239894   0
-0.239367   -0.239367   0
-0.238796   -0.238796   0
-0.236921   -0.236921   0
-0.232151   -0.232151   0
-0.230184   -0.230184   0
-0.229427   -0.229427   0
-0.224931   -0.224931   0
-0.222447   -0.222447   0
-0.221471   -0.221471   0
-0.220234   -0.220234   0
-0.217279   -0.217279   0
-0.217016   -0.217016   0
-0.214425   -0.214425   0
-0.214407   -0.214407   0
-0.213028   -0.213028   0
-0.212436   -0.212436   0
-0.212396   -0.212396   0
-0.211948   -0.211948   0
-0.21121   -0.21121   0
-0.209901   -0.209901   0
-0.209656   -0.209656   0
-0.209638   -0.209638   0
-0.208738   -0.208738   0
-0.20873   -0.20873   0
-0.206936   -0.206936   0
-0.206731   -0.206731   0
-0.206195   -0.206195   0
-0.20588   -0.20588   0
-0.205686   -0.205686   0
-0.205014   -0.205014   0
-0.203829   -0.203829   0
-0.203051   -0.203051   0
-0.201719   -0.201719   0
-0.201651   -0.201651   0
-0.200801   -0.200801   0
-0.200712   -0.200712   0
-0.200684   -0.200684   0
-0.199841   -0.199841   0
-0.199689   -0.199689   0
-0.199383   -0.199383   0
-0.198291   -0.198291   0
-0.196227   -0.196227   0
-0.195272   -0.195272   0
-0.194881   -0.194881   0
-0.192675   -0.192675   0
-0.192637   -0.192637   0
-0.192495   -0.192495   0
-0.192085   -0.192085   0
-0.191526   -0.191526   0
-0.190473   -0.190473   0
-0.189218   -0.189218   0
-0.188988   -0.188988   0
-0.188466   -0.188466   0
-0.188372   -0.188372   0
-0.187305   -0.187305   0
-0.185401   -0.185401   0
-0.184412   -0.184412   0
-0.184174   -0.184174   0
-0.183296   -0.183296   0
-0.182921   -0.182921   0
-0.181208   -0.181208   0
-0.180342   -0.180342   0
-0.179752   -0.179752   0
-0.179424   -0.179424   0
-0.175831   -0.175831   0
-0.175036   -0.175036   0
-0.174874   -0.174874   0
-0.173455   -0.173455   0
-0.172118   -0.172118   0
-0.171769   -0.171769   0
-0.168506   -0.168506   0
-0.167849   -0.167849   0
-0.166855   -0.166855   0
-0.165807   -0.165807   0
-0.164176   -0.164176   0
-0.162982   -0.162982   0
-0.161429   -0.161429   0
-0.161208   -0.161208   0
-0.159354   -0.159354   0
-0.156592   -0.156592   0
-0.156011   -0.156011   0
-0.154649   -0.154649   0
-0.154502   -0.154502   0
-0.154451   -0.154451   0
-0.154166   -0.154166   0
-0.153496   -0.153496   0
-0.151619   -0.151619   0
-0.150979   -0.150979   0
-0.150714   -0.150714   0
-0.149927   -0.149927   0
-0.149636   -0.149636   0
-0.149033   -0.149033   0
-0.148995   -0.148995   0
-0.147874   -0.147874   0
-0.147842   -0.147842   0
-0.146956   -0.146956   0
-0.141371   -0.141371   0
-0.140905   -0.140905   0
-0.140669   -0.140669   0
-0.13901   -0.13901   0
-0.13833   -0.13833   0
-0.134583   -0.134583   0
-0.134095   -0.134095   0
-0.132972   -0.132972   0
-0.132626   -0.132626   0
-0.132431   -0.132431   0
-0.131816   -0.131816   0
-0.130951   -0.130951   0
-0.129515   -0.129515   0
-0.129125   -0.129125   0
-0.128809   -0.128809   0
-0.123824   -0.123824   0
-0.123772   -0.123772   0
-0.123643   -0.123643   0
-0.12362   -0.12362   0
-0.123321   -0.123321   0
-0.1231   -0.1231   0
-0.122401   -0.122401   0
-0.121067   -0.121067   0
-0.120581   -0.120581   0
-0.119531   -0.119531   0
-0.117563   -0.117563   0
-0.116902   -0.116902   0
-0.116888   -0.116888   0
-0.116356   -0.116356   0
-0.115177   -0.115177   0
-0.114481   -0.114481   0
-0.112579   -0.112579   0
-0.110958   -0.110958   0
-0.110901   -0.110901   0
-0.109896   -0.109896   0
-0.109787   -0.109787   0
-0.108961   -0.108961   0
-0.108949   -0.108949   0
-0.108   -0.108   0
-0.10797   -0.10797   0
-0.107027   -0.107027   0
-0.106142   -0.106142   0
-0.103514   -0.103514   0
-0.103196   -0.103196   0
-0.102827   -0.102827   0
-0.101509   -0.101509   0
-0.101454   -0.101454   0
-0.100286   -0.100286   0
-0.097612   -0.097612   0
-0.095193   -0.095193   0
-0.090877   -0.090877   0
-0.089197   -0.089197   0
-0.088846   -0.088846   0
-0.087231   -0.087231   0
-0.086982   -0.086982   0
-0.086715   -0.086715   0
-0.084793   -0.084793   0
-0.083866   -0.083866   0
-0.08344   -0.08344   0
-0.080516   -0.080516   0
-0.080435   -0.080435   0
-0.079749   -0.079749   0
-0.078384   -0.078384   0
-0.076326   -0.076326   0
-0.074287   -0.074287   0
-0.071129   -0.071129   0
-0.070747   -0.070747   0
-0.069727   -0.069727   0
-0.069708   -0.069708   0
-0.069122   -0.069122   0
-0.06903   -0.06903   0
-0.068224   -0.068224   0
-0.065069   -0.065069   0
-0.061579   -0.061579   0
-0.06144   -0.06144   0
-0.060909   -0.060909   0
-0.060084   -0.060084   0
-0.058998   -0.058998   0
-0.05853   -0.05853   0
-0.058419   -0.058419   0
-0.058115   -0.058115   0
-0.058031   -0.058031   0
-0.057958   -0.057958   0
-0.054657   -0.054657   0
-0.051756   -0.051756   0
-0.051043   -0.051043   0
-0.051005   -0.051005   0
-0.050738   -0.050738   0
-0.050443   -0.050443   0
-0.050097   -0.050097   0
-0.048324   -0.048324   0
-0.047285   -0.047285   0
-0.046839   -0.046839   0
-0.044625   -0.044625   0
-0.044224   -0.044224   0
-0.042939   -0.042939   0
-0.042908   -0.042908   0
-0.042398   -0.042398   0
-0.042233   -0.042233   0
-0.041609   -0.041609   0
-0.041086   -0.041086   0
-0.040201   -0.040201   0
-0.03998   -0.03998   0
-0.038808   -0.038808   0
-0.038419   -0.038419   0
-0.038096   -0.038096   0
-0.035367   -0.035367   0
-0.034408   -0.034408   0
-0.033967   -0.033967   0
-0.032845   -0.032845   0
-0.032505   -0.032505   0
-0.031256   -0.031256   0
-0.028827   -0.028827   0
-0.028193   -0.028193   0
-0.027357   -0.027357   0
-0.027347   -0.027347   0
-0.027107   -0.027107   0
-0.019883   -0.019883   0
-0.019643   -0.019643   0
-0.01784   -0.01784   0
-0.017601   -0.017601   0
-0.016682   -0.016682   0
-0.015831   -0.015831   0
-0.015557   -0.015557   0
-0.012097   -0.012097   0
-0.011119   -0.011119   0
-0.010428   -0.010428   0
-0.009609   -0.009609   0
-0.007491   -0.007491   0
-0.007106   -0.007106   0
-0.00552   -0.00552   0
-0.005153   -0.005153   0
-0.003609   -0.003609   0
-0.003039   -0.003039   0
-0.001842   -0.001842   0
0.002126   0.002126   0
0.002436   0.002436   0
0.002846   0.002846   0
0.003509   0.003509   0
0.00444   0.00444   0
0.004507   0.004507   0
0.007439   0.007439   0
0.007476   0.007476   0
0.008161   0.008161   0
0.00939   0.00939   0
0.010369   0.010369   0
0.011175   0.011175   0
0.012794   0.012794   0
0.013341   0.013341   0
0.014895   0.014895   0
0.01719   0.01719   0
0.017821   0.017821   0
0.019277   0.019277   0
0.019635   0.019635   0
0.020099   0.020099   0
0.020811   0.020811   0
0.021958   0.021958   0
0.026683   0.026683   0
0.026919   0.026919   0
0.02942   0.02942   0
0.030483   0.030483   0
0.030498   0.030498   0
0.031523   0.031523   0
0.03262   0.03262   0
0.037396   0.037396   0
0.03774   0.03774   0
0.039198   0.039198   0
0.042535   0.042535   0
0.047851   0.047851   0
0.048089   0.048089   0
0.048698   0.048698   0
0.049091   0.049091   0
0.049521   0.049521   0
0.053328   0.053328   0
0.05396   0.05396   0
0.054928   0.054928   0
0.055507   0.055507   0
0.057162   0.057162   0
0.057382   0.057382   0
0.057707   0.057707   0
0.059129   0.059129   0
0.059634   0.059634   0
0.061103   0.061103   0
0.061356   0.061356   0
0.062209   0.062209   0
0.062884   0.062884   0
0.064558   0.064558   0
0.065108   0.065108   0
0.066815   0.066815   0
0.070177   0.070177   0
0.070338   0.070338   0
0.070789   0.070789   0
0.072457   0.072457   0
0.073391   0.073391   0
0.073529   0.073529   0
0.074114   0.074114   0
0.077673   0.077673   0
0.079141   0.079141   0
0.080104   0.080104   0
0.081559   0.081559   0
0.084154   0.084154   0
0.08504   0.08504   0
0.086694   0.086694   0
0.088501   0.088501   0
0.089197   0.089197   0
0.089884   0.089884   0
0.091773   0.091773   0
0.093061   0.093061   0
0.094989   0.094989   0
0.0977   0.0977   0
0.097998   0.097998   0
0.09808   0.09808   0
0.098308   0.098308   0
0.098592   0.098592   0
0.101148   0.101148   0
0.10235   0.10235   0
0.104547   0.104547   0
0.105045   0.105045   0
0.107448   0.107448   0
0.107612   0.107612   0
0.107881   0.107881   0
0.108568   0.108568   0
0.10871   0.10871   0
0.109548   0.109548   0
0.109552   0.109552   0
0.110061   0.110061   0
0.11052   0.11052   0
0.110662   0.110662   0
0.11126   0.11126   0
0.114535   0.114535   0
0.1151   0.1151   0
0.115335   0.115335   0
0.115466   0.115466   0
0.1165   0.1165   0
0.11651   0.11651   0
0.119191   0.119191   0
0.120927   0.120927   0
0.121108   0.121108   0
0.123444   0.123444   0
0.123748   0.123748   0
0.124036   0.124036   0
0.125693   0.125693   0
0.126012   0.126012   0
0.126742   0.126742   0
0.127923   0.127923   0
0.128333   0.128333   0
0.130807   0.130807   0
0.131289   0.131289   0
0.13253   0.13253   0
0.13387   0.13387   0
0.135156   0.135156   0
0.13677   0.13677   0
0.138475   0.138475   0
0.138617   0.138617   0
0.139448   0.139448   0
0.140026   0.140026   0
0.14049   0.14049   0
0.142645   0.142645   0
0.144737   0.144737   0
0.145483   0.145483   0
0.147609   0.147609   0
0.148205   0.148205   0
0.14884   0.14884   0
0.148893   0.148893   0
0.150167   0.150167   0
0.150937   0.150937   0
0.153371   0.153371   0
0.154081   0.154081   0
0.155648   0.155648   0
0.15597   0.15597   0
0.156199   0.156199   0
0.156213   0.156213   0
0.159252   0.159252   0
0.160538   0.160538   0
0.161854   0.161854   0
0.163906   0.163906   0
0.164589   0.164589   0
0.166537   0.166537   0
0.166626   0.166626   0
0.167656   0.167656   0
0.168958   0.168958   0
0.170401   0.170401   0
0.171157   0.171157   0
0.174036   0.174036   0
0.174326   0.174326   0
0.174741   0.174741   0
0.175342   0.175342   0
0.175784   0.175784   0
0.175799   0.175799   0
0.176696   0.176696   0
0.179804   0.179804   0
0.180206   0.180206   0
0.180897   0.180897   0
0.18142   0.18142   0
0.182744   0.182744   0
0.183083   0.183083   0
0.185027   0.185027   0
0.18544   0.18544   0
0.187189   0.187189   0
0.187686   0.187686   0
0.188057   0.188057   0
0.188583   0.188583   0
0.188644   0.188644   0
0.189372   0.189372   0
0.189559   0.189559   0
0.189832   0.189832   0
0.190471   0.190471   0
0.19092   0.19092   0
0.19113   0.19113   0
0.191903   0.191903   0
0.192298   0.192298   0
0.19372   0.19372   0
0.200087   0.200087   0
0.20087   0.20087   0
0.200947   0.200947   0
0.200983   0.200983   0
0.201809   0.201809   0
0.203877   0.203877   0
0.203965   0.203965   0
0.205324   0.205324   0
0.207361   0.207361   0
0.208028   0.208028   0
0.208263   0.208263   0
0.208777   0.208777   0
0.208788   0.208788   0
0.209907   0.209907   0
0.210686   0.210686   0
0.212305   0.212305   0
0.215236   0.215236   0
0.215506   0.215506   0
0.215573   0.215573   0
0.21622   0.21622   0
0.217687   0.217687   0
0.222236   0.222236   0
0.222349   0.222349   0
0.222984   0.222984   0
0.223445   0.223445   0
0.224011   0.224011   0
0.225216   0.225216   0
0.226788   0.226788   0
0.227787   0.227787   0
0.228759   0.228759   0
0.231822   0.231822   0
0.231825   0.231825   0
0.233386   0.233386   0
0.234013   0.234013   0
0.23701   0.23701   0
0.238179   0.238179   0
0.238227   0.238227   0
0.23824   0.23824   0
0.238982   0.238982   0
0.239402   0.239402   0
0.240614   0.240614   0
0.242014   0.242014   0
0.242689   0.242689   0
0.242839   0.242839   0
0.24303   0.24303   0
0.243478   0.243478   0
0.243842   0.243842   0
0.244113   0.244113   0
0.245734   0.245734   0
0.24633   0.24633   0
0.250518   0.250518   0
0.250817   0.250817   0
0.251262   0.251262   0
0.252774   0.252774   0
0.254088   0.254088   0
0.255887   0.255887   0
0.257312   0.257312   0
0.25772   0.25772   0
0.258563   0.258563   0
0.260096   0.260096   0
0.260501   0.260501   0
0.261065   0.261065   0
0.262665   0.262665   0
0.263199   0.263199   0
0.263729   0.263729   0
0.264879   0.264879   0
0.266007   0.266007   0
0.26739   0.26739   0
0.267596   0.267596   0
0.2693   0.2693   0
0.270983   0.270983   0
0.27174   0.27174   0
0.271767   0.271767   0
0.272099   0.272099   0
0.272778   0.272778   0
0.272786   0.272786   0
0.274227   0.274227   0
0.274309   0.274309   0
0.274923   0.274923   0
0.276081   0.276081   0
0.277145   0.277145   0
0.277717   0.277717   0
0.279802   0.279802   0
0.280631   0.280631   0
0.281764   0.281764   0
0.282278   0.282278   0
0.282757   0.282757   0
0.283121   0.283121   0
0.283347   0.283347   0
0.283544   0.283544   0
0.285753   0.285753   0
0.286174   0.286174   0
0.286261   0.286261   0
0.288532   0.288532   0
0.289026   0.289026   0
0.289215   0.289215   0
0.290422   0.290422   0
0.291096   0.291096   0
0.291163   0.291163   0
0.291997   0.291997   0
0.293376   0.293376   0
0.293797   0.293797   0
0.294334   0.294334   0
0.294653   0.294653   0
0.296393   0.296393   0
0.296453   0.296453   0
0.296747   0.296747   0
0.298427   0.298427   0
0.299865   0.299865   0
0.299948   0.299948   0
0.300261   0.300261   0
0.301693   0.301693   0
0.302454   0.302454   0
0.302894   0.302894   0
0.303226   0.303226   0
0.306274   0.306274   0
0.307638   0.307638   0
0.308779   0.308779   0
0.308808   0.308808   0
0.308997   0.308997   0
0.310195   0.310195   0
0.310309   0.310309   0
0.311134   0.311134   0
0.313178   0.313178   0
0.3134   0.3134   0
0.313681   0.313681   0
0.313984   0.313984   0
0.314329   0.314329   0
0.315142   0.315142   0
0.315169   0.315169   0
0.315462   0.315462   0
0.315867   0.315867   0
0.31724   0.31724   0
0.317794   0.317794   0
0.319011   0.319011   0
0.319889   0.319889   0
0.320749   0.320749   0
0.323402   0.323402   0
0.323704   0.323704   0
0.323902   0.323902   0
0.324236   0.324236   0
0.325824   0.325824   0
0.326264   0.326264   0
0.329801   0.329801   0
0.332058   0.332058   0
0.332234   0.332234   0
0.333742   0.333742   0
0.335311   0.335311   0
0.335749   0.335749   0
0.336132   0.336132   0
0.336147   0.336147   0
0.3377   0.3377   0
0.337892   0.337892   0
0.338238   0.338238   0
0.340373   0.340373   0
0.343566   0.343566   0
0.347138   0.347138   0
0.349089   0.349089   0
0.350923   0.350923   0
0.351042   0.351042   0
0.351108   0.351108   0
0.352193   0.352193   0
0.35258   0.35258   0
0.352607   0.352607   0
0.354873   0.354873   0
0.355261   0.355261   0
0.356365   0.356365   0
0.360784   0.360784   0
0.361191   0.361191   0
0.361364   0.361364   0
0.361827   0.361827   0
0.362636   0.362636   0
0.363239   0.363239   0
0.363628   0.363628   0
0.365448   0.365448   0
0.37058   0.37058   0
0.371373   0.371373   0
0.372084   0.372084   0
0.373168   0.373168   0
0.376855   0.376855   0
0.380073   0.380073   0
0.384326   0.384326   0
0.384762   0.384762   0
0.385054   0.385054   0
0.385056   0.385056   0
0.386159   0.386159   0
0.386341   0.386341   0
0.386999   0.386999   0
0.389098   0.389098   0
0.390676   0.390676   0
0.390848   0.390848   0
0.392325   0.392325   0
0.392709   0.392709   0
0.393626   0.393626   0
0.394043   0.394043   0
0.396547   0.396547   0
0.3966   0.3966   0
0.396636   0.396636   0
0.397279   0.397279   0
0.398385   0.398385   0
0.398795   0.398795   0
0.39904   0.39904   0
0.399322   0.399322   0
0.399329   0.399329   0
0.400266   0.400266   0
0.400283   0.400283   0
0.405541   0.405541   0
0.406234   0.406234   0
0.40643   0.40643   0
0.406983   0.406983   0
0.408524   0.408524   0
0.408688   0.408688   0
0.409219   0.409219   0
0.409744   0.409744   0
0.410868   0.410868   0
0.410924   0.410924   0
0.412298   0.412298   0
0.413507   0.413507   0
0.414562   0.414562   0
0.41457   0.41457   0
0.415416   0.415416   0
0.416452   0.416452   0
0.416982   0.416982   0
0.41719   0.41719   0
0.417775   0.417775   0
0.417883   0.417883   0
0.419683   0.419683   0
0.421863   0.421863   0
0.423493   0.423493   0
0.423536   0.423536   0
0.42424   0.42424   0
0.425352   0.425352   0
0.426095   0.426095   0
0.428412   0.428412   0
0.429065   0.429065   0
0.430208   0.430208   0
0.431715   0.431715   0
0.432378   0.432378   0
0.433736   0.433736   0
0.43483   0.43483   0
0.4352   0.4352   0
0.435983   0.435983   0
0.4371   0.4371   0
0.437194   0.437194   0
0.440722   0.440722   0
0.44235   0.44235   0
0.442558   0.442558   0
0.4431   0.4431   0
0.443171   0.443171   0
0.443202   0.443202   0
0.443676   0.443676   0
0.445111   0.445111   0
0.448434   0.448434   0
0.448459   0.448459   0
0.448529   0.448529   0
0.448815   0.448815   0
0.448939   0.448939   0
0.449414   0.449414   0
0.450222   0.450222   0
0.450977   0.450977   0
0.45167   0.45167   0
0.452978   0.452978   0
0.454248   0.454248   0
0.45492   0.45492   0
0.455838   0.455838   0
0.456622   0.456622   0
0.456937   0.456937   0
0.456978   0.456978   0
0.458557   0.458557   0
0.459557   0.459557   0
0.460026   0.460026   0
0.463236   0.463236   0
0.463594   0.463594   0
0.464459   0.464459   0
0.465064   0.465064   0
0.466415   0.466415   0
0.467429   0.467429   0
0.468335   0.468335   0
0.46861   0.46861   0
0.469626   0.469626   0
0.471289   0.471289   0
0.471362   0.471362   0
0.471577   0.471577   0
0.472508   0.472508   0
0.472687   0.472687   0
0.473642   0.473642   0
0.475923   0.475923   0
0.476434   0.476434   0
0.477892   0.477892   0
0.478845   0.478845   0
0.479537   0.479537   0
0.481147   0.481147   0
0.481324   0.481324   0
0.481801   0.481801   0
0.482343   0.482343   0
0.483154   0.483154   0
0.483944   0.483944   0
0.484302   0.484302   0
0.485251   0.485251   0
0.48669   0.48669   0
0.488188   0.488188   0
0.488763   0.488763   0
0.488935   0.488935   0
0.48983   0.48983   0
0.494066   0.494066   0
0.499477   0.499477   0
0.500083   0.500083   0
0.503107   0.503107   0
0.504621   0.504621   0
0.505749   0.505749   0
0.506168   0.506168   0
0.506906   0.506906   0
0.507335   0.507335   0
0.507527   0.507527   0
0.510611   0.510611   0
0.5119   0.5119   0
0.513248   0.513248   0
0.515024   0.515024   0
0.515879   0.515879   0
0.519542   0.519542   0
0.519788   0.519788   0
0.520143   0.520143   0
0.520608   0.520608   0
0.520694   0.520694   0
0.524613   0.524613   0
0.52498   0.52498   0
0.525028   0.525028   0
0.526131   0.526131   0
0.526352   0.526352   0
0.526712   0.526712   0
0.527983   0.527983   0
0.528795   0.528795   0
0.529718   0.529718   0
0.53016   0.53016   0
0.530535   0.530535   0
0.53129   0.53129   0
0.532411   0.532411   0
0.533589   0.533589   0
0.533798   0.533798   0
0.533892   0.533892   0
0.533964   0.533964   0
0.534333   0.534333   0
0.534436   0.534436   0
0.537295   0.537295   0
0.538359   0.538359   0
0.538675   0.538675   0
0.538778   0.538778   0
0.538902   0.538902   0
0.539456   0.539456   0
0.539891   0.539891   0
0.541948   0.541948   0
0.541987   0.541987   0
0.542428   0.542428   0
0.544928   0.544928   0
0.546121   0.546121   0
0.548549   0.548549   0
0.550088   0.550088   0
0.55124   0.55124   0
0.552184   0.552184   0
0.552779   0.552779   0
0.553467   0.553467   0
0.553987   0.553987   0
0.555397   0.555397   0
0.558461   0.558461   0
0.558965   0.558965   0
0.561044   0.561044   0
0.561432   0.561432   0
0.561509   0.561509   0
0.561776   0.561776   0
0.563913   0.563913   0
0.564529   0.564529   0
0.565802   0.565802   0
0.567089   0.567089   0
0.568132   0.568132   0
0.568797   0.568797   0
0.568976   0.568976   0
0.569315   0.569315   0
0.569631   0.569631   0
0.572863   0.572863   0
0.573113   0.573113   0
0.573871   0.573871   0
0.575681   0.575681   0
0.577207   0.577207   0
0.577801   0.577801   0
0.578835   0.578835   0
0.579245   0.579245   0
0.583329   0.583329   0
0.584443   0.584443   0
0.586488   0.586488   0
0.58663   0.58663   0
0.586775   0.586775   0
0.587792   0.587792   0
0.589214   0.589214   0
0.589227   0.589227   0
0.589627   0.589627   0
0.59124   0.59124   0
0.591318   0.591318   0
0.591383   0.591383   0
0.592138   0.592138   0
0.592311   0.592311   0
0.594332   0.594332   0
0.595874   0.595874   0
0.59609   0.59609   0
0.596516   0.596516   0
0.596965   0.596965   0
0.597763   0.597763   0
0.59799   0.59799   0
0.598562   0.598562   0
0.598905   0.598905   0
0.59894   0.59894   0
0.599764   0.599764   0
0.600809   0.600809   0
0.603295   0.603295   0
0.603626   0.603626   0
0.604081   0.604081   0
0.604308   0.604308   0
0.606442   0.606442   0
0.60786   0.60786   0
0.610795   0.610795   0
0.614918   0.614918   0
0.615424   0.615424   0
0.61612   0.61612   0
0.617246   0.617246   0
0.623874   0.623874   0
0.624589   0.624589   0
0.625292   0.625292   0
0.625394   0.625394   0
0.625486   0.625486   0
0.626187   0.626187   0
0.626521   0.626521   0
0.628222   0.628222   0
0.629048   0.629048   0
0.629073   0.629073   0
0.629463   0.629463   0
0.633487   0.633487   0
0.633609   0.633609   0
0.634063   0.634063   0
0.634204   0.634204   0
0.63522   0.63522   0
0.635242   0.635242   0
0.636669   0.636669   0
0.638366   0.638366   0
0.638462   0.638462   0
0.638816   0.638816   0
0.639102   0.639102   0
0.639227   0.639227   0
0.639255   0.639255   0
0.640547   0.640547   0
0.640553   0.640553   0
0.640989   0.640989   0
0.641516   0.641516   0
0.643725   0.643725   0
0.644285   0.644285   0
0.64648   0.64648   0
0.646598   0.646598   0
0.647417   0.647417   0
0.648772   0.648772   0
0.649263   0.649263   0
0.64942   0.64942   0
0.649439   0.649439   0
0.650098   0.650098   0
0.651178   0.651178   0
0.651835   0.651835   0
0.652601   0.652601   0
0.654681   0.654681   0
0.656443   0.656443   0
0.65721   0.65721   0
0.657776   0.657776   0
0.658494   0.658494   0
0.661961   0.661961   0
0.665813   0.665813   0
0.666527   0.666527   0
0.669795   0.669795   0
0.671791   0.671791   0
0.673431   0.673431   0
0.674055   0.674055   0
0.674059   0.674059   0
0.675654   0.675654   0
0.676265   0.676265   0
0.680479   0.680479   0
0.681907   0.681907   0
0.683428   0.683428   0
0.683768   0.683768   0
0.683976   0.683976   0
0.686717   0.686717   0
0.686937   0.686937   0
0.689851   0.689851   0
0.692568   0.692568   0
0.693317   0.693317   0
0.693473   0.693473   0
0.695056   0.695056   0
0.695635   0.695635   0
0.69622   0.69622   0
0.696341   0.696341   0
0.696588   0.696588   0
0.697542   0.697542   0
0.699389   0.699389   0
0.7015   0.7015   0
0.702506   0.702506   0
0.702806   0.702806   0
0.704234   0.704234   0
0.705034   0.705034   0
0.705681   0.705681   0
0.707831   0.707831   0
0.708386   0.708386   0
0.71022   0.71022   0
0.710364   0.710364   0
0.711852   0.711852   0
0.712794   0.712794   0
0.71302   0.71302   0
0.714228   0.714228   0
0.715932   0.715932   0
0.718053   0.718053   0
0.718308   0.718308   0
0.718866   0.718866   0
0.719517   0.719517   0
0.720511   0.720511   0
0.720864   0.720864   0
0.723148   0.723148   0
0.723723   0.723723   0
0.723763   0.723763   0
0.725242   0.725242   0
0.725589   0.725589   0
0.726341   0.726341   0
0.726466   0.726466   0
0.727901   0.727901   0
0.728289   0.728289   0
0.729464   0.729464   0
0.73029   0.73029   0
0.730375   0.730375   0
0.730392   0.730392   0
0.73123   0.73123   0
0.731738   0.731738   0
0.732803   0.732803   0
0.733553   0.733553   0
0.734275   0.734275   0
0.735824   0.735824   0
0.736842   0.736842   0
0.736859   0.736859   0
0.737336   0.737336   0
0.737706   0.737706   0
0.738314   0.738314   0
0.739886   0.739886   0
0.7402   0.7402   0
0.740594   0.740594   0
0.741131   0.741131   0
0.746841   0.746841   0
0.748019   0.748019   0
0.751963   0.751963   0
0.752717   0.752717   0
0.756089   0.756089   0
0.756362   0.756362   0
0.756671   0.756671   0
0.758211   0.758211   0
0.758433   0.758433   0
0.758503   0.758503   0
0.759328   0.759328   0
0.759582   0.759582   0
0.760086   0.760086   0
0.76107   0.76107   0
0.762261   0.762261   0
0.762469   0.762469   0
0.762706   0.762706   0
0.764155   0.764155   0
0.764748   0.764748   0
0.766069   0.766069   0
0.76843   0.76843   0
0.768547   0.768547   0
0.768946   0.768946   0
0.768983   0.768983   0
0.769194   0.769194   0
0.769319   0.769319   0
0.772875   0.772875   0
0.774539   0.774539   0
0.774882   0.774882   0
0.774886   0.774886   0
0.775285   0.775285   0
0.778147   0.778147   0
0.78024   0.78024   0
0.780922   0.780922   0
0.781325   0.781325   0
0.782776   0.782776   0
0.783052   0.783052   0
0.784532   0.784532   0
0.785192   0.785192   0
0.786001   0.786001   0
0.786035   0.786035   0
0.786041   0.786041   0
0.786264   0.786264   0
0.787118   0.787118   0
0.787196   0.787196   0
0.788034   0.788034   0
0.790835   0.790835   0
0.791464   0.791464   0
0.792164   0.792164   0
0.792291   0.792291   0
0.79276   0.79276   0
0.793302   0.793302   0
0.794259   0.794259   0
0.795897   0.795897   0
0.795974   0.795974   0
0.797024   0.797024   0
0.798212   0.798212   0
0.79951   0.79951   0
0.801092   0.801092   0
0.802292   0.802292   0
0.803692   0.803692   0
0.804489   0.804489   0
0.805338   0.805338   0
0.805667   0.805667   0
0.806967   0.806967   0
0.808235   0.808235   0
0.808278   0.808278   0
0.808655   0.808655   0
0.808875   0.808875   0
0.811185   0.811185   0
0.811705   0.811705   0
0.811992   0.811992   0
0.812138   0.812138   0
0.81288   0.81288   0
0.81412   0.81412   0
0.815071   0.815071   0
0.815298   0.815298   0
0.815705   0.815705   0
0.815967   0.815967   0
0.816505   0.816505   0
0.819036   0.819036   0
0.820938   0.820938   0
0.821544   0.821544   0
0.822587   0.822587   0
0.823302   0.823302   0
0.823327   0.823327   0
0.82404   0.82404   0
0.824891   0.824891   0
0.826272   0.826272   0
0.826656   0.826656   0
0.828555   0.828555   0
0.828923   0.828923   0
0.829393   0.829393   0
0.833245   0.833245   0
0.834491   0.834491   0
0.835269   0.835269   0
0.836107   0.836107   0
0.838705   0.838705   0
0.838942   0.838942   0
0.84127   0.84127   0
0.8425   0.8425   0
0.8431   0.8431   0
0.843919   0.843919   0
0.846719   0.846719   0
0.848627   0.848627   0
0.848683   0.848683   0
0.851209   0.851209   0
0.85191   0.85191   0
0.85342   0.85342   0
0.856801   0.856801   0
0.857146   0.857146   0
0.86092   0.86092   0
0.861175   0.861175   0
0.861595   0.861595   0
0.864275   0.864275   0
0.86507   0.86507   0
0.865099   0.865099   0
0.865198   0.865198   0
0.865396   0.865396   0
0.866546   0.866546   0
0.868396   0.868396   0
0.868769   0.868769   0
0.869814   0.869814   0
0.870019   0.870019   0
0.870422   0.870422   0
0.870502   0.870502   0
0.873842   0.873842   0
0.873924   0.873924   0
0.874378   0.874378   0
0.874869   0.874869   0
0.875509   0.875509   0
0.876558   0.876558   0
0.876877   0.876877   0
0.877067   0.877067   0
0.878393   0.878393   0
0.879207   0.879207   0
0.879594   0.879594   0
0.880858   0.880858   0
0.881861   0.881861   0
0.882336   0.882336   0
0.883328   0.883328   0
0.885861   0.885861   0
0.885921   0.885921   0
0.887148   0.887148   0
0.88875   0.88875   0
0.889836   0.889836   0
0.890378   0.890378   0
0.891767   0.891767   0
0.891815   0.891815   0
0.892657   0.892657   0
0.894519   0.894519   0
0.89598   0.89598   0
0.896731   0.896731   0
0.898076   0.898076   0
0.898616   0.898616   0
0.899193   0.899193   0
0.89981   0.89981   0
0.900337   0.900337   0
0.901849   0.901849   0
0.902355   0.902355   0
0.902722   0.902722   0
0.902743   0.902743   0
0.903554   0.903554   0
0.905362   0.905362   0
0.906098   0.906098   0
0.907824   0.907824   0
0.908673   0.908673   0
0.909072   0.909072   0
0.910487   0.910487   0
0.912438   0.912438   0
0.914483   0.914483   0
0.914566   0.914566   0
0.916082   0.916082   0
0.916431   0.916431   0
0.916523   0.916523   0
0.91689   0.91689   0
0.918483   0.918483   0
0.919221   0.919221   0
0.920066   0.920066   0
0.92008   0.92008   0
0.920837   0.920837   0
0.920892   0.920892   0
0.921995   0.921995   0
0.925065   0.925065   0
0.925159   0.925159   0
0.92527   0.92527   0
0.925796   0.925796   0
0.926482   0.926482   0
0.927156   0.927156   0
0.92743   0.92743   0
0.927886   0.927886   0
0.92815   0.92815   0
0.928265   0.928265   0
0.928351   0.928351   0
0.929532   0.929532   0
0.929717   0.929717   0
0.929939   0.929939   0
0.930107   0.930107   0
0.930636   0.930636   0
0.931172   0.931172   0
0.931369   0.931369   0
0.932445   0.932445   0
0.932582   0.932582   0
0.934632   0.934632   0
0.936018   0.936018   0
0.93683   0.93683   0
0.937641   0.937641   0
0.9394   0.9394   0
0.939947   0.939947   0
0.940393   0.940393   0
0.942321   0.942321   0
0.942633   0.942633   0
0.943088   0.943088   0
0.943175   0.943175   0
0.943383   0.943383   0
0.943844   0.943844   0
0.944388   0.944388   0
0.945649   0.945649   0
0.950975   0.950975   0
0.951389   0.951389   0
0.951501   0.951501   0
0.953888   0.953888   0
0.954536   0.954536   0
0.957716   0.957716   0
0.958159   0.958159   0
0.958439   0.958439   0
0.958482   0.958482   0
0.960815   0.960815   0
0.963257   0.963257   0
0.9654   0.9654   0
0.967701   0.967701   0
0.968789   0.968789   0
0.971323   0.971323   0
0.971474   0.971474   0
0.972577   0.972577   0
0.972853   0.972853   0
0.972892   0.972892   0
0.973039   0.973039   0
0.973333   0.973333   0
0.974006   0.974006   0
0.975541   0.975541   0
0.975695   0.975695   0
0.976913   0.976913   0
0.977425   0.977425   0
0.978029   0.978029   0
0.979022   0.979022   0
0.97946   0.97946   0
0.98096   0.98096   0
0.981241   0.981241   0
0.981523   0.981523   0
0.98343   0.98343   0
0.984216   0.984216   0
0.984582   0.984582   0
0.985972   0.985972   0
0.986924   0.986924   0
0.987257   0.987257   0
0.988469   0.988469   0
0.991214   0.991214   0
0.992372   0.992372   0
0.99716   0.99716   0
0.997619   0.997619   0


You can see that the difference is zero for every trial.
.

[gill1109]

Where did I promise that? Don't make things up.
.

I asked you. You said you would code it. I suppose you didn't understand my question.

But there is progress, now you do understand my question! You can simply say "no" if you don't want to do it / don't know how to do it.

It is obvious that there is no sense for me to continue with this since you are going to refuse to understand it anyways. You saw the sample output. That will have to do it. The product calculation is validated via computer program.
.

Nobody is interested in the product calculation. I know that you reproduce the singlet correlations exactly. I know exactly how you do it, *after* you have evaluated those two limits.

We have been asking about the limit concept which you use. Joy's mathematical derivations involve using some calculus theorems about limits. But he starts with writing down some formulas which use "illegal" notation. Or to be more kind, undefined notation.

[Joy Christian]

Joy's mathematical derivations involve using some calculus theorems about limits. But he starts with writing down some formulas which use "illegal" notation. Or to be more kind, undefined notation.

There is nothing illegal or undefined about the notation I have used. Anyone who understands GA knows that the limit operations are equivalent to the divisions by bivectors Fred has used.

***