Difference between revisions of "User:Johnxyz1"
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− | Below are some stuff I am doing to practice <math>\LaTeX</math> | + | Favorite topic: <cmath>\text{Counting \& Probability}</cmath>for which I am reading AOPS intermediate book on |
+ | |||
+ | Favorite color: <cmath>\text{\textcolor{green}{Green}}</cmath> | ||
+ | |||
+ | Favorite software: <cmath>MS\ \text{Excel}</cmath> | ||
+ | |||
+ | Favorite Typesetting Software: <cmath>\text{\LaTeX}</cmath> | ||
+ | |||
+ | Favorite Operating System: Linux (although I am rarely on one) | ||
+ | |||
+ | Below are some stuff I am doing to practice <math>\text{\LaTeX}</math>. That does not mean I know all of it (actually the only ones I do not know yet is the cubic one and the <math>e^{i\pi}</math> one) | ||
<cmath>\text{If }ax^2+bx+c=0\text{, then }x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</cmath> | <cmath>\text{If }ax^2+bx+c=0\text{, then }x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</cmath> | ||
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<cmath>\begin{align*} | <cmath>\begin{align*} | ||
x &= \sqrt[3]{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right) + \sqrt{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right)^2 + \left(\frac{c}{3a} - \frac{b^2}{9a^2}\right)^3}} \\ | x &= \sqrt[3]{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right) + \sqrt{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right)^2 + \left(\frac{c}{3a} - \frac{b^2}{9a^2}\right)^3}} \\ | ||
− | &+ \sqrt[3]{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right) - \sqrt{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right)^2 + \left(\frac{c}{3a} - \frac{b^2}{9a^2}\right)^3}} - \frac{b}{3a} \\ | + | & + \sqrt[3]{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right) - \sqrt{\left(\frac{-b^3}{27a^3} + \frac{bc}{6a^2} - \frac{d}{2a}\right)^2 + \left(\frac{c}{3a} - \frac{b^2}{9a^2}\right)^3}} - \frac{b}{3a} \\ |
− | &\text{(I copied it from another website but I typeset it myself; I am pretty sure those are not copyrightable. I still need \textit{years} to understand this.)} | + | &\text{(I copied it from another website but I typeset it myself;}\\ |
+ | &\text{I am pretty sure those are not copyrightable. I still need \textit{years} to even understand this.)}\\ | ||
+ | &\text{This is the cubic formula, although it is \textit{rarely} actually used and memorized a lot. The equation is}\\ | ||
+ | &ax^3+bx^2+cx+d=0 | ||
\end{align*} | \end{align*} | ||
</cmath> | </cmath> | ||
+ | |||
+ | |||
+ | Source code for equations: | ||
+ | |||
+ | https://1drv.ms/t/c/c49430eefdbfaa19/EQw12iwklslElg9_nCMh0f0BVthxSSl-BOJAwsXtGbbhPg?e=1LfZJm | ||
+ | |||
+ | |||
+ | |||
+ | |||
+ | Asymptote test (with autoGraph): | ||
+ | |||
+ | <asy>/* AUTO-GRAPH V-4 beta by PythonNut*/ | ||
+ | |||
+ | /* Customizations: feel free to edit */ | ||
+ | import math; | ||
+ | import graph; | ||
+ | /* x maximum and minimum */ | ||
+ | int X_max = 10; | ||
+ | int X_min =-10; | ||
+ | /* y maximum and minimum */ | ||
+ | int Y_max = 10; | ||
+ | int Y_min = -10; | ||
+ | /* linewidth */ | ||
+ | real line_width = 0.75; | ||
+ | /* graph color */ | ||
+ | pen graph_color = magenta; | ||
+ | /* special */ | ||
+ | bool mark_lattice = false; | ||
+ | bool show_grid = true; | ||
+ | real X_tick_density = 1; | ||
+ | real Y_tick_density = 1; | ||
+ | real ratio = 1; | ||
+ | real resolution = 0.0001; | ||
+ | int size = 300; | ||
+ | /* graph function */ | ||
+ | real f(real x) | ||
+ | { | ||
+ | return sin(x)*sin(x); /* type function to be graphed here */ | ||
+ | } | ||
+ | |||
+ | /* The Code. Do not disturb unless you know what you are doing */ | ||
+ | bool ib(real t){ return (Y_min <= f(t) && f(t) <= Y_max); } | ||
+ | |||
+ | size(size);unitsize(size*ratio,size);Label l;l.p=fontsize(6); | ||
+ | xaxis("$x$",X_min,X_max,Ticks(l,X_tick_density,(X_tick_density/2),NoZero),Arrows); | ||
+ | yaxis("$y$",Y_min,Y_max,Ticks(l,Y_tick_density,(Y_tick_density/2),NoZero),Arrows);// | ||
+ | if (show_grid){add(shift(X_min,Y_min)*grid(X_max-X_min,Y_max-Y_min));} | ||
+ | |||
+ | real t, T1, T2; | ||
+ | |||
+ | for (T1 = X_min ; T1 <= X_max ; T1 += resolution){ | ||
+ | while (! ib(T1) && T1 <= X_max){T1 += resolution;} | ||
+ | if(T1 > X_max){break;} | ||
+ | T2 = T1; | ||
+ | while ( ib(T1) && T1 <= X_max){T1 += resolution;} | ||
+ | T1 -= resolution; | ||
+ | draw(graph(f,T2,T1,n=2400),graph_color+linewidth(line_width),Arrows); | ||
+ | } | ||
+ | |||
+ | if (mark_lattice){ | ||
+ | for (t = X_min; t <= X_max; ++t){ | ||
+ | if (f(t)%1==0 && ib(t)){ | ||
+ | dot((t,f(t)),graph_color+linewidth(line_width*4)); | ||
+ | } | ||
+ | } | ||
+ | } | ||
+ | dot((0,0));</asy> | ||
+ | |||
+ | |||
+ | If you want to typeset your own LaTeX equation in a STANDALONE PDF like AOPS does (although they do images), use the standalone documentclass. |
Revision as of 21:35, 4 July 2024
Favorite topic: for which I am reading AOPS intermediate book on
Favorite color:
Favorite software:
Favorite Typesetting Software:
Favorite Operating System: Linux (although I am rarely on one)
Below are some stuff I am doing to practice . That does not mean I know all of it (actually the only ones I do not know yet is the cubic one and the one)
Source code for equations:
https://1drv.ms/t/c/c49430eefdbfaa19/EQw12iwklslElg9_nCMh0f0BVthxSSl-BOJAwsXtGbbhPg?e=1LfZJm
Asymptote test (with autoGraph):
If you want to typeset your own LaTeX equation in a STANDALONE PDF like AOPS does (although they do images), use the standalone documentclass.