-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathumath2latex.html
216 lines (144 loc) · 6.13 KB
/
umath2latex.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/strict.dtd">
<html>
<head>
<meta charset="utf-8">
<title>UMath2LaTeX: Parsing UnicodeMath and converting to it LaTeX</title>
<meta charset="utf-8">
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/katex.min.css" integrity="sha384-9eLZqc9ds8eNjO3TmqPeYcDj8n+Qfa4nuSiGYa6DjLNcv9BtN69ZIulL9+8CqC9Y" crossorigin="anonymous">
<script defer src="https://cdn.jsdelivr.net/npm/[email protected]/dist/katex.min.js" integrity="sha384-K3vbOmF2BtaVai+Qk37uypf7VrgBubhQreNQe9aGsz9lB63dIFiQVlJbr92dw2Lx" crossorigin="anonymous"></script>
<script defer src="https://cdn.jsdelivr.net/npm/[email protected]/dist/contrib/auto-render.min.js" integrity="sha384-kmZOZB5ObwgQnS/DuDg6TScgOiWWBiVt0plIRkZCmE6rDZGrEOQeHM5PcHi+nyqe" crossorigin="anonymous"
onload="renderMathInElement(document.body,{delimiters: [{left: '$$', right: '$$', display: true},{left: '$', right: '$', display: false},]});"></script>
<script src="umath2latex.js"></script>
<script src="mathinput.js"></script>
<script>window.onload = function () {new MathInput("INPUT");}</script>
<style> .katex { font-size: 1.1em; } body { margin: 100px; }</style>
</head>
<body>
<h1>UMath2LaTeX: Parsing UnicodeMath and converting to LaTeX</h1>
<p>All UnicodeMath expressions in the box below are converted when you click the "Parse" button.
Feel free to edit the expressions. <br>
Typing Unicode in a browser is a bit of an issue, but you can try LaTeX commands followed by [space].</p>
<textarea id="INPUT" style="height: 5in; width: 100%; font-family: 'STIXGeneral'; font-size: 24pt;">
∀x>0 x^a x^b = x^(a+b)
a∣b ⟺ ∃c ∈ ℤ(ac=b)
A ∪ B = \{x ∣ x ∈ A or x ∈ B\}
d/dx(f(x)) = lim_{h→0}(f(x+h)-f(x))/h
d/dx(f(x)g(x)) = d/dx(f(x))g(x) + f(x)d/dx(g(x))
(fg)' = f'g+fg'
x+⋅y
∫_a^b f(x) dx = lim_{n→∞} ∑_{i=1}^n f(x_i^*)(b-a)/n
∫ f(x) dx = F(x)+C
∫_C f(x) dx = 0
∏_(i=1)^(n+1) a_i = (∏_(i=1)^n a_i)a_(n+1)
δ + 1
lim_{x→a} f(x) = L ⟺ ∀ɛ>0 ∃δ>0 ∀x(0 < |x-a| < δ ⟹ |f(x)-L| < ɛ)
sin xy
sin x+y
sinx
f(x) y
a:A×A→A
A ⊨ φ
1/2x
1/2⋅x
f(x,y,z,u,v,w)
xRy and yRz ⟹ xRz
f(x)^2
f^2(x) = f(x)^2
sin^2 x
n:ℕ
f'(x) = (f(x))' = d/dx(f(x))
ℕ ⊂ ℤ ⊂ ℚ ⊂ ℝ ⊂ ℂ
lim f(x)
2(1+1) = -21.0
f[X] = \{f(x) ∣ x ∈ X\}
A×A×A×A→A→A→A→A
h : ℝ^m → ℝ^n
(f+g)(x)
(f,…,g)
f
asso(⋅) = ((x⋅y)⋅z = x⋅(y⋅z))
comm(⋅) = (x⋅y = y⋅x)
idem(⋅) = (x⋅x = x)
SemilatticeAx(⋅) = asso(⋅) and comm(⋅) and idem(⋅)
abso(∨,∧) = ((x∨y)∧x = x)
LatticeAx(∨,∧) = (SemilatticeAx(∨) and SemilatticeAx(∧) and abso(∨,∧) and abso(∧,∨))
∀x>0x^ax^b=x^(a+b)
∀x,y>0((xy)^a = x^ay^a)
|x+y| ≤ |x|+|y|
|xy| = (|x||y|)
|xy| = |x||y|
x+y = y+x
(x+y)+z = x+(y+z)
x+0 = x
x+-x = 0
-x+x = 0
(xy)z = x(yz)
x(y+z) = xy+xz
(x+y)⋅z = x⋅z+y⋅z
a|b ⟺ ∃c ∈ ℤ(ac=b)
</textarea>
<input id="PARSE" value=Parse type=button
onclick="var out = convert(document.getElementById('INPUT').value);
document.getElementById('OUTPUT').innerHTML = out[0];
document.getElementById('MathOutput').innerHTML = out[1];
renderMathInElement(document.getElementById('MathOutput'),{delimiters: [{left: '$$', right: '$$', display: true},{left: '$', right: '$', display: false},]});">
<noscript><p>You may not see any output if you have JavaScript turned off</p></noscript>
<p></p>
<h3>Typeset output:</h3>
<span id="MathOutput"></span>
<p></p>
<hr>
<p></p>
<h3>Raw input / LaTeX / Prefix form (to check term-tree)</h3>
<pre id=OUTPUT></pre>
Some remarks about the parser:
<ul>
<li> The top-down parsing algorithm is due to Vaughan Pratt (1973).
The implementation is based on Douglas Crockford's
article <a href="http://javascript.crockford.com/tdop/tdop.html">Top
Down Operator Precedence</a> where he uses the algorithm to parse
Simplified JavaScript.
<li> The current input language is UnicodeMath,
based on standard conventions for mathematical symbols and
operations. The types for symbols and expressions are
<ul>
<li> <b>variable symbols</b> single latin letters ($u,v,w,x,y,z$)
with possible subscripts ($u_0,u_1,\dots,z_0,z_1,\dots$)
<li> <b>constant symbols</b>, the default type for all symbols not assigned to other types
($a,b,\dots,\alpha,\beta,\dots,\emptyset,\infty,0,1,\dots$)
<li> prefix/infix/postfix/aroundfix <b>function symbols</b> with
standard precedence ($+,-,\cdot,/,\cup,\cap,\sqrt{\phantom{x}},\ln,\sin,| |, \dots$)
<li> <b>terms</b> built from function symbols applied to constants and terms
<li> prefix/infix <b>relation symbols</b> with lower
precedence than function symbols ($∈,=,≤,<,≥,>,…$)
<li> <b>atomic formulas</b> built from relation symbols applied
to terms
<li> prefix/infix <b>logical symbols</b> with lower precedence
than relation symbols
($\neg$, or, and, $\implies,\iff,\exists,\forall,\dots$)
<li> <b>formulas</b> built from logical symbols applied to
atomic formulas and formulas
<li> <b>metalogical symbols</b> and <b>large operator
symbols</b> (osym) that combine mathematical expressions from several
of the above types ($\vdash,\models,\bigvee,\bigwedge,\bigcup,\bigcap,\sum,\prod,\lim,\int,\dots$)
</ul>
<li> Standard mathematical notation makes liberal use of <b>invisible
times</b> and <b>function application</b> by juxtaposition (i.e., when two
symbols are adjacent with the symbol on the left neither prefix nor infix and
the symbols on the right neither infix nor postfix). The parser
treats this situation as a binary operation called <b>\,</b> (LaTeX thin space).
<li> Infix symbols that are usually considered associative
($+,\cdot,=$) have variable arity and chain over a list of arguments
(rather than having left or right associated parse trees).
<li> Many symbols are overloaded, but context is used to disambigute
these situations. Each symbol has a default type, but its type can be
changed dynamically.
<li> The abstract syntax tree contains the symbol (sym:string), and
arguments (arg, arg2, arg3), where the latter three are either a tree or a list of trees.
</ul>
<hr>
<p align="center">
<small>Peter Jipsen --- January 2019 --- Chapman University</small>
</p>
</body>
</html>