IMOGI

Math-Oriented Project ($Intuitive\ Mathematical\ Object\ Generation\ Interface$)

App Name Ideas:

• $Sigmath \ (\Sigma th)$

• $Mathwise$

Philosophies

• ¿Could a piece of Software be a better, more intuitive and efficient medium than pen and paper when dealing with advanced mathematical concepts?

• Interactive Manim-like software, as the ultimate teaching tool.

Must-have's

• A grid-background. This is the general working space of the software. Maybe allow various grids (workspaces) to be created.

• Matrix generation and manipulation (with Clever Notation)

• Some form of recurrence representation: ¿How do i visualize $T(n) = f(T(n-1))$?

  • Maybe have a button to replace a term using given definitions?

    $T(n) = f(T(n-1))$ Stored Definition (maybe visible from a sidebar)

    $T(n) = f(f(T(n-2)))$ After pressing the button "Apply Definition Once"

• Third-Party modules/packages are supported, so the community can further extend the software's potential, e.g:

  • Bisection Method Package (or a more general Numerical Methods Package)

  • Complex Numbers Package

  • Recursively-defined Functions Package (or a more general Non-elemental Functions Package)

  • Linear Algebra Package

  and so on...

• Some way to make $\LaTeX$ content easy to Create and Edit:

  • The User creates a Note Block (like a textbox) on a page, types in the latex code and another block right next to it displays the output in real-time. When the Note Block is de-selected, the other block disappears and the first one becomes the Rendered Output. Double-Click on the Block to edit (repeating the process)

  These Blocks can work as explanatory notes and can be moved like other objects in the software

Maybe's

• A Command Line, sort of a mix between Matlab's Command Window and Desmos's sidebar (computational requests through dynamic managing of symbols).

• Integrated Computational Engine (Wolfram|Alpha APIs accepts $\LaTeX$ source code) so the user can skip the process of doing calculations himself.

• Integrated Language Model (ChatGPT?) to help the user do something or use some tool that they're not comfortable with yet in the App

• Different grid styles, so it can look like a customized chalkboard

Backlog

¿How to make the $\LaTeX$ components editable in real time (like Desmos can)?

• Easy Fix:

  • Not actual "live" $\LaTeX$ rendering

  • Just have an "Update Render" button to do it manually

  • Save recently edited textboxes in some data structure and only re-render those

• The Hard Way:

  • All $\LaTeX$ code is saved independently

  • Current input would be rendered after pressing Space (if the commands are recognized)

  • Would require a BNF of sorts (Context-Free Grammar)