Donald Munro donaldmunro

name

math-formatting

description

Rules for writing mathematical notation in responses using Markdown LaTeX ($...$ inline, $$...$$ display) instead of Unicode math symbols. Use this skill whenever a response will contain any mathematics at all — equations, formulas, derivations, proofs, probability, statistics, calculus, linear algebra, complexity bounds, physics, or even a single symbol like ≤, ∑ or x². Use it even when the math is incidental to a coding, data, or engineering question, and even when the user doesn't mention formatting.

Math formatting

Write all mathematical notation as Markdown LaTeX. The reason: LaTeX renders cleanly and consistently, is unambiguous, and can be copied straight into a paper, notebook, or .tex file. Unicode math characters (∑, ≤, ℝ, x², →) look

clear_vars
reset()
%display latex

u,v,w,T = SR.var('x y z t')
E_x,E_y,E_z  = function('Ex'),function('Ey'), function('Ez')
B_x,B_y,B_z  = function('Bx'),function('By'), function('Bz')
M.<t, x, y, z> = manifolds.Minkowski(positive_spacelike=False)
F = M.diff_form(2, name='F')

clear_vars
reset()
%display latex
R3 = Manifold(3, 'R^3', start_index=1)
X.<x,y,z> = R3.chart()
g = R3.metric('g')
g[1,1], g[2,2], g[3,3] = 1, 1, 1

#R2 = Manifold(2, 'R^2', ambient=R3, start_index=1)

Compiling Boost for Android

Download Boost and cd to base directory.
Create Android toolchains for desired architectures by running a script as below:
```
NDK=/opt/android-sdk/ndk-bundle/
TOOLCHAINS="$PWD/toolchains/"
```

rm -rf $TOOLCHAINS

	#ifndef _BOUNDED_MAP_H
	#define _BOUNDED_MAP_H

	#include <iostream>
	#include <map>
	#include <vector>
	#include <utility>

	/**
	* A wrapped std::multimap which limits size by removing the smallest keys first.

	# Using javah to generate .h files for Kotlin
	# Assuming JNI function calls are in MainActivity.companion
	STUDIO=/opt/android-studio
	PACKAGE=my.package
	$STUDIO/jre/bin/javah -jni -cp "$STUDIO/lib/kotlin-runtime.jar:build/tmp/kotlin-classes/debug" $PACKAGE.MainActivity.Companion

	#include <glm/gtc/type_ptr.hpp>
	..
	glm::mat4 m = glm::mat4(1.0f);
	..
	auto p = glm::value_ptr(m);
	std::cout << sizeof(p) << std::endl;
	glUniformMatrix4fv(shader_uniform_m, 1, GL_FALSE, p);

	size_t split(std::string s, std::vector<std::string>& tokens,
	std::string delim ="\t\n ")
	{
	tokens.clear();
	size_t pos = s.find_first_not_of(delim);
	while (pos != std::string::npos)
	{
	size_t next = s.find_first_of(delim, pos);
	if (pos == std::string::npos)
	tokens.emplace_back(s.substr(pos));

	#include <eigen3/Eigen/Dense>
	#include <eigen3/Eigen/Eigenvalues>
	..
	..
	using RowMatrixXf = Eigen::Matrix<float, Eigen::Dynamic, Eigen::Dynamic, Eigen::RowMajor>;
	Eigen::Map<RowMatrixXf> mapped(extended_homograpy.ptr<float>(), homography.rows, homography.cols);
	Eigen::EigenSolver<Eigen::MatrixXf> eigen_solve(mapped, true);
	auto ev = eigen_solve.eigenvectors();
	std::cout << "No of EigenVectors = " << ev.cols() << std::endl;
	for (auto i=0; i<ev.cols(); i++)

	#include <glm/gtx/string_cast.hpp>
	..
	..
	glm::mat4 mat;
	..
	..
	std::cout << glm::to_string(mat) << std::endl;