A tool to display **mathematical proofs** as **structured** objects, see https://francoisschwarzentruber.github.io/prooffold/
+# FFT -![prooffoldsqrt2](https://user-images.githubusercontent.com/43071857/154649245-5c78c7a0-0562-4232-a087-5590c193cb94.gif) +This tool shows the circuit of the Fast Fourier Transform for an input of 8 complex numbers (i.e. a polynomial of degree 7). The user can modify with the mouse the input, and see in real-time the output of the FFT algorithm. -Video: [https://www.youtube.com/watch?v=FPZiGevIyR8] - - -## Screenshots - -![prooffold_inequalitiesastabs](https://user-images.githubusercontent.com/43071857/194746547-cec69dd2-3cb4-41b3-9ede-9149066afcac.gif) -![image](https://user-images.githubusercontent.com/43071857/194717214-e9785336-711f-4bdb-b455-dfcfd2293ac1.png) -![prooffoldrrt](https://user-images.githubusercontent.com/43071857/154652110-b4573d44-1de9-4af3-9a58-bb295e5888d2.gif) -![prooffoldeuclideanTSP](https://user-images.githubusercontent.com/43071857/154651408-12462e46-c220-47e8-b43c-ad0ca2848d8e.gif) -![prooffoldkonig](https://user-images.githubusercontent.com/43071857/154651369-334d3700-ffc0-4713-9c12-61ca5f6bcf00.gif) -![prooffoldcook](https://user-images.githubusercontent.com/43071857/154651387-e604c450-f15e-4834-a3fa-d950024dec7f.gif) - - -## Raison d'être - -It tries to solve two main issues of traditional proofs written in a book: -- the global organization of a proof in a textbook is often not very clear. This is due to the linearity of a textual proof. Here, the proof is displayed in panels, making an emphasis on the structure of the proof -- In a textbook, justifications of a statement often ends up "by Theorem 1.2.3, Lemma 42.4 and Corollary 8.8.4 and Equation 1". Here, by clicking on a statement, the arguments used to deduced that fact are highlighted. - - - - - - - -# Features - - - [X] Structured proofs - - [X] LaTEX for writing formulas - - [X] Labels [(1) (2)] and references [by (1,2)] - - [X] inline graphs via graphviz - - [X] interactive canvas described in Processing (P5JS) - - [X] Automatic aligned equations and inequations - - [ ] Asciiart, it partially works but soon via https://github.com/francoisschwarzentruber/asciidraw we will be able to write nice pictures - - [ ] Arrows of implications - - [ ] Include Tikz pictures - - - -# Documentation - -## Overview - -Proofs are easy to be written. - - Fact - Theorem. $a^2 = b^2 + c^2$. - { - explain sth of the proof of the theorem - an amazing fact (1) - { - proof of that amazing fact - } - we have that $x = 0$ (2) - Thus we have bling by (1,2) - } - Another Fact - - -Each line is a fact, or simple text. Blocks (panels) are delimited by `{` and `}` and corresponds to a detailed proof of the fact written just before the block. ` (1)`, ` (2)` etc. and ` by (1,2)` enable to highlight some facts used to prove another fact. In the example below, `Thus we have bling` is deduced from `an amazing fact` and `we have that $x = 0$`. - - - - -Graphs in graphviz are described by: - - graph { - <