|
1 | | -# JSON LD |
2 | | - |
3 | | -A comprehensive collection of LaTeX macro definitions for mathematical notation, providing shortcuts and enhancements for mathematical typesetting in LaTeX2JS. |
4 | | - |
5 | | -## Installation |
6 | | - |
7 | | -```bash |
8 | | -npm install @latex2js/macros |
9 | | -``` |
10 | | - |
11 | | -## Features |
12 | | - |
13 | | -- **Transform Pairs**: Fourier, Z-transform, and Laplace transform notation |
14 | | -- **Mathematical Symbols**: Extended collection of mathematical operators and symbols |
15 | | -- **Set Theory**: Comprehensive set theory notation and operators |
16 | | -- **Category Theory**: Morphisms, functors, and categorical constructs |
17 | | -- **Theorem Environments**: Shortcuts for theorem, lemma, proposition, and proof environments |
18 | | -- **Typography**: Enhanced spacing and formatting for mathematical expressions |
19 | | - |
20 | | -## Usage |
21 | | - |
22 | | -### Basic Import |
23 | | - |
24 | | -```typescript |
25 | | -import macros from '@latex2js/macros'; |
26 | | - |
27 | | -// The macros are provided as a template string |
28 | | -console.log(typeof macros); // 'string' |
29 | | -``` |
30 | | - |
31 | | -### Integration with LaTeX2JS |
32 | | - |
33 | | -```typescript |
34 | | -import { LaTeX2HTML5 } from 'latex2js'; |
35 | | -import macros from '@latex2js/macros'; |
36 | | - |
37 | | -// Initialize with macros |
38 | | -const parser = new LaTeX2HTML5(); |
39 | | -parser.addMacros(macros); |
40 | | -``` |
41 | | - |
42 | | -### Integration with MathJax |
43 | | - |
44 | | -```javascript |
45 | | -import macros from '@latex2js/macros'; |
46 | | - |
47 | | -// Configure MathJax with the macros |
48 | | -window.MathJax = { |
49 | | - tex: { |
50 | | - macros: macros |
51 | | - } |
52 | | -}; |
53 | | -``` |
54 | | - |
55 | | -## Available Macros |
56 | | - |
57 | | -### Transform Pairs |
58 | | - |
59 | | -Perfect for signal processing and mathematical analysis: |
60 | | - |
61 | | -```latex |
62 | | -% Fourier Transform |
63 | | -$$\mathscr{F}\{f(t)\} = F(\omega)$$ |
64 | | -$$f(t) \FTpair F(\omega)$$ |
65 | | -
|
66 | | -% Z-Transform |
67 | | -$$\mathscr{Z}\{x[n]\} = X(z)$$ |
68 | | -$$x[n] \ZTpair X(z)$$ |
69 | | -
|
70 | | -% Laplace Transform |
71 | | -$$\mathscr{L}\{f(t)\} = F(s)$$ |
72 | | -$$f(t) \LTpair F(s)$$ |
73 | | -``` |
74 | | - |
75 | | -### Mathematical Operators |
76 | | - |
77 | | -Extended mathematical notation: |
78 | | - |
79 | | -```latex |
80 | | -% Enhanced operators |
81 | | -$$\E[X]$$ % Expectation |
82 | | -$$\Var(X)$$ % Variance |
83 | | -$$\Cov(X,Y)$$ % Covariance |
84 | | -$$\argmax_x f(x)$$ % Argument maximum |
85 | | -$$\argmin_x f(x)$$ % Argument minimum |
86 | | -``` |
87 | | - |
88 | | -### Set Theory |
89 | | - |
90 | | -Comprehensive set operations: |
91 | | - |
92 | | -```latex |
93 | | -% Set operations |
94 | | -$$A \intersection B$$ % Intersection |
95 | | -$$A \union B$$ % Union |
96 | | -$$A \setminus B$$ % Set difference |
97 | | -$$\powerset{A}$$ % Power set |
98 | | -$$A \symdiff B$$ % Symmetric difference |
99 | | -``` |
100 | | - |
101 | | -### Category Theory |
102 | | - |
103 | | -Advanced categorical constructs: |
104 | | - |
105 | | -```latex |
106 | | -% Category theory |
107 | | -$$\Hom(A, B)$$ % Hom-set |
108 | | -$$A \iso B$$ % Isomorphism |
109 | | -$$f \colon A \to B$$ % Morphism notation |
110 | | -$$\End(A)$$ % Endomorphisms |
111 | | -$$\Aut(A)$$ % Automorphisms |
112 | | -``` |
113 | | - |
114 | | -### Theorem Environments |
115 | | - |
116 | | -Shortcuts for mathematical writing: |
117 | | - |
118 | | -```latex |
119 | | -\begin{thm}[Fundamental Theorem] |
120 | | -Every continuous function on a closed interval is uniformly continuous. |
121 | | -\end{thm} |
122 | | -
|
123 | | -\begin{lem} |
124 | | -This is a supporting lemma. |
125 | | -\end{lem} |
126 | | -
|
127 | | -\begin{prop} |
128 | | -This is a proposition. |
129 | | -\end{prop} |
130 | | -
|
131 | | -\begin{proof} |
132 | | -The proof follows from the definition. |
133 | | -\end{proof} |
134 | | -``` |
135 | | - |
136 | | -### Typography Enhancements |
137 | | - |
138 | | -Improved spacing and formatting: |
139 | | - |
140 | | -```latex |
141 | | -% Enhanced spacing |
142 | | -$$a \,+\, b$$ % Thin spaces around operators |
143 | | -$$\int_a^b f(x) \dd x$$ % Proper differential notation |
144 | | -$$\vec{v} \cdot \vec{u}$$ % Vector notation |
145 | | -``` |
146 | | - |
147 | | -## Complete Macro List |
148 | | - |
149 | | -The package includes over 140 macro definitions covering: |
150 | | - |
151 | | -- **Analysis**: Real and complex analysis notation |
152 | | -- **Algebra**: Group theory, ring theory, field theory |
153 | | -- **Topology**: Topological spaces and continuous maps |
154 | | -- **Probability**: Probability theory and statistics |
155 | | -- **Logic**: Logical operators and quantifiers |
156 | | -- **Geometry**: Geometric constructions and notation |
157 | | -- **Computer Science**: Algorithms and complexity theory |
158 | | - |
159 | | -## Integration Examples |
160 | | - |
161 | | -### With React Components |
162 | | - |
163 | | -```jsx |
164 | | -import { LaTeX } from 'latex2react'; |
165 | | -import macros from '@latex2js/macros'; |
166 | | - |
167 | | -function MathDocument() { |
168 | | - const content = ` |
169 | | - \\begin{thm}[Fourier Transform] |
170 | | - For any function $f \\in L^1(\\mathbb{R})$: |
171 | | - $$f(t) \\FTpair F(\\omega) = \\int_{-\\infty}^{\\infty} f(t) e^{-i\\omega t} \\dd t$$ |
172 | | - \\end{thm} |
173 | | - `; |
174 | | - |
175 | | - return <LaTeX content={content} macros={macros} />; |
176 | | -} |
177 | | -``` |
178 | | - |
179 | | -### With Vue Components |
180 | | - |
181 | | -```vue |
182 | | -<template> |
183 | | - <latex :content="mathContent" :macros="macros" /> |
184 | | -</template> |
185 | | -
|
186 | | -<script> |
187 | | -import macros from '@latex2js/macros'; |
188 | | -
|
189 | | -export default { |
190 | | - data() { |
191 | | - return { |
192 | | - macros, |
193 | | - mathContent: ` |
194 | | - $$\\E[X] = \\int_{-\\infty}^{\\infty} x f_X(x) \\dd x$$ |
195 | | - ` |
196 | | - }; |
197 | | - } |
198 | | -}; |
199 | | -</script> |
200 | | -``` |
201 | | - |
202 | | -### With HTML5 Integration |
203 | | - |
204 | | -```html |
205 | | -<!DOCTYPE html> |
206 | | -<html> |
207 | | -<head> |
208 | | - <script src="path/to/latex2html5.bundle.js"></script> |
209 | | -</head> |
210 | | -<body> |
211 | | - <script type="text/latex"> |
212 | | - \begin{thm} |
213 | | - The Pythagorean theorem: $a^2 + b^2 = c^2$ |
214 | | - \end{thm} |
215 | | - </script> |
216 | | - |
217 | | - <script> |
218 | | - // Macros are automatically included in the HTML5 bundle |
219 | | - LaTeX2HTML5.init(); |
220 | | - </script> |
221 | | -</body> |
222 | | -</html> |
223 | | -``` |
| 1 | +# jsonldjs |
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