#mathematica

[shonk]

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[wikipediagrams]

[painfuldischarge]

MacRenderMan

Some historical floppy disk fun from old Pixar days. When Pixar decided to sell RenderMan to the public we had to come up with a good name (It was REYES, Renders Everything You’ve Ever Saw / Seen). You could already buy a version that a ran on the Pixar Image Computer CHAP (Channel Processor) called CHAPREYES. I don’t know if we ever sold any, but we did render Red’s Dream on it, in part. The…

[jadagul]

Working out how to do that polar video nicely helped me figure out how to do something I'd been working on for a while a couple years ago and never got where I wanted with: visualizations of elliptic curves as complex surfaces.

I went to see if I've talked about elliptic curves before, and I actually talked about this exact issue here. But now I've leveled up in Mathematica so I can do the visuals better.

Oversimplified, an elliptic curve is an equation that looks like y^2 = x^3+ax+b for some integers a and b. And they have lots of interesting number theoretic properties if you look for solutions that are rational numbers, none of which I want to talk about right now.

If you graph these equations over the real numbers you get pictures like one of these two (left: y^2=x^3+7x+1; right: y^2=x^3-7x+1):

And we like to imagine points at infinity in each direction, so the picture on the left looks like one giant circle (going through infinity at the top/bottom), and the picture on the right looks like two disconnected circles. And the difference is basically whether we get one or three solutions to the cubic when we set y equal to zero.

But over the complex numbers they should all look the same. The problem is, graphs of complex functions are four-dimensional and that's hard to display. But in that four-dimensional space, we should get a torus: a circle moved through a circular path (which still includes the point at infinity).

But we can make three-dimensional graphs, and then we can let them vary over time. So here is an animation of y^2=x^3+7x+1, with time controlling the imaginary coordinate of the output:

And here is y^2=x^3-7x+1:

You can see the moment in the middle where they "snap" into the real-plane-only version.

But now that I have these movies looking good, I want to go back and figure out better ways to slice them; here we're not getting "just" the "real solutions" plane ever, which I think makes them a little harder to interpret.

[nothoward]

Because.

- Newton's Fourth Law

[transmanray]

calculator for suicidal people

[mathart]

Vertex normals in a Mathematica Manipulate[]

This is not obvious or easy in Mathematica, because Import[... , "OBJ"] does not preserve Winged-Edge mesh topology. So, you have to go through considerable effort to associate doubly-connected mesh edges back to polygons to compute the equivalent normal vector to the surface located at the vertices.

[allisongreenlee]

Ancient Civilizations: Euclid and the Legacy of Ancient Alexandrian Mathematics

The knowledge contained in Elements remained unmatched for centuries...

[dark-white1]

Hello friends. I uploaded my first application to the Google Play store. Can you download it to help me even if it is an amateur game.

[wikipediagrams]

[dd3ah]

Mit dem Raspberry Pi arbeiten viele Funkamateure. Hier wird beschrieben wie man das mitgelieferte Wolfram Mathematica nutzen kann um ein besseres Verständnis zu erhalten, was bei Frequenzmodulation geschieht.

[bar-apps]

Matlab o Mathematica

¡Descubre las diferencias entre Matlab y Mathematica de Wolfram en el ámbito técnico y científico! En esta página, explorarás las distintas aplicaciones de estas potentes herramientas en áreas como matemáticas, procesamiento de señales e imágenes

[albeo]

Matlab o Mathematica

¡Descubre las diferencias entre Matlab y Mathematica de Wolfram en el ámbito técnico y científico! En esta página, explorarás las distintas aplicaciones de estas potentes herramientas en áreas como matemáticas, procesamiento de señales e imágenes

[usaq22]

LargeLanguageModelProgramming

(1) While Learning the "WolfRamAlpha" Programming Language, The iMPORTANCE of Customization Occurred to Me.

(2) The Following iS an E-Mail That Will Be Sent to All Major Programming Facilities, with Changes Expected by the Year 2100.

(3)

iN Copying Your Documentation, iT Has Occurred to Me that "Language Customization" iS the Best Teacher for New Learners.

Mathematica Has a Good Base, However, i Suggest You Allow the "Text Formatting" of GOOGLE DOCS & MiCROSOFT WORD (To Start), as an Aid to Those Switching from Different Platforms (FORMAT > GOOGLE DOCS or MiCROSOFT WORD or EXCEL or ...).

Add a "Code" Tab to NoteBooks: (File, Edit, Format, iNSERT, CODE, Evaluation, View, Help | Share, Publish)

(3.1) File, Edit, Format, iNSERT, "CODE" > (Command iNDEX, KeyBoard ShortCuts, User's iNDEX), Evaluation, View, Help ...

(3.2) Command iNDEX = All of Wolfram Alpha's (or Other Programming Languages) "Functions", Sortable by (Alphabetical, Categories[Math, Chemistry, Electrical, Plumbing, ...], Most Used[AllTime, Current User, iN a Specific Category], Changed By User [Words that Have Been Replaced with Syntax and Capitalization the User Has Chosen {Show Conflicts when Users Change Commands, for Proper Resolution}], Newly Added... 

(3.3) KeyBoard ShortCuts = All Default KeyBoard ShortCuts (Sorted Similarly to [3.2]), Allowing Users to Customize the KeyBoard ShortCuts {Show Conflicts for Resolution}.

(3.5) Users iNDEX = A List of the WolframAlpha Command's That Have Been Changed by the User {Sorted Similarly to [3.2]}. 

When Users Write the Code Using Their "Custom Commands", All Custom Commands Will Be Converted to "Default WolframAlpha Commands" When "Exported", So Code Documentation and Readability Will Translate Across Users and Platforms.

 What iS the Need for [1 -> 4]? 

(5.1) We Are Already Programmed to Read English, or Other Native Language.

(5.2) iF "Natural Language" iS Not Enough, Customization of "Default Commands" Should Be Standard (Not Just on WolfRam, but iN Every Language).

(5.3) iF i'M Used to Typing "deletealloutput" i Should be Able to Customize the Command "Delete All Output", So i Can Type "deletealloutput" to Perform the Same Action.

New Learners Can Enjoy CopyWriteLearning While Maximizing Their Time Use by Using iNPUT'S They Will Remember (iF They Forget, the "Command iNDEX" Will Show them What iNPUTS they Have Replaced, and Can Reset 1 or All Commands iN the "Users iNDEX"[3.5]).

(6.1) Additionally, The LargeLanguageDataModelsThat Can Be Harvested by Analyzing "What Commands Were Replaced with What" Will Reveal Universal Programming on an EarthWide Scale. 

[painfuldischarge]

Plotting some roots.