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AsciiMath

原始链接: https://asciimath.org/

## AsciiMath 概要 AsciiMath 是一种基于文本的数学表达式符号,旨在视觉上类似于标准的数学符号。它既提供直接的文本符号(例如 `oo` 表示无穷大),也提供 TeX 替代方案(例如 `sum` 代替 `\sum`),而无需为 TeX 命令使用前导反斜杠。 该符号涵盖了广泛的元素:基本运算(+、-、*、/)、关系(=、<、>)、逻辑符号(and、or、not)、分组括号(()、[]、{}),以及用于微积分(int、del、grad)、集合(subset、union)等的各种专用符号。 AsciiMath 还支持上标、下标、分数、根式以及 sin、cos 和 log 等函数。它处理矩阵、列向量和具有定义语法规则的复杂表达式,这些规则优先考虑正确的运算顺序(下标在 superscript 之前)。字体命令允许使用粗体、黑板和其他样式变体。建议用户在 `<` 和 `>` 字符之间留出空格,以避免 HTML 解析问题。

## AsciiMath 总结 Hacker News 的讨论围绕着 AsciiMath,这是一种使用 ASCII 字符书写数学表达式的记号。它旨在实现简单和可读性,特别是通过 MathML 在网页上嵌入。但它因不一致的空格处理和不寻常的语法选择(例如使用指数符号表示求和上限)而受到批评。 一些评论员指出 AsciiMath 的解析逻辑中可能存在的缺陷,并指出细微的语法变化可能导致截然不同的输出。Typst 和 mathup 等替代方案被提及,其中 mathup 特别通过输出标准的 MathML 来解决 AsciiMath 的实现不足,而不是依赖于特定工具的集成。 对话还涉及更广泛的数学记号领域,一些人提倡更逻辑、基于 S 表达式的系统,而不是从欧拉那里继承的传统(且视觉导向)记号。最终,讨论强调了在数字环境中平衡数学排版的表达力、可读性和一致性解析的持续挑战。
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原文

Most AsciiMath symbols attempt to mimic in text what they look like rendered, like oo for `oo`. Many symbols can also be displayed using a TeX alternative, but a preceeding backslash is not required.

Operation symbols
Type TeX alt See
+ `+`
- `-`
* cdot `*`
** ast `**`
*** star `***`
// `//`
\\ backslash
setminus
`\\`
xx times `xx`
-: div `-:`
|>< ltimes `|><`
><| rtimes `><|`
|><| bowtie `|><|`
@ circ `@`
o+ oplus `o+`
ox otimes `ox`
o. odot `o.`
sum `sum`
prod `prod`
^^ wedge `^^`
^^^ bigwedge `^^^`
vv vee `vv`
vvv bigvee `vvv`
nn cap `nn`
nnn bigcap `nnn`
uu cup `uu`
uuu bigcup `uuu`
Miscellaneous symbols
Type TeX alt See
2/3 frac{2}{3} `2/3`
2^3 `2^3`
sqrt x `sqrt x`
root(3)(x) `root(3)(x)`
int `int`
oint `oint`
del partial `del`
grad nabla `grad`
+- pm `+-`
O/ emptyset `O/`
oo infty `oo`
aleph `aleph`
:. therefore `:.`
:' because `:'`
|...| |ldots| `|...|`
|cdots| `|cdots|`
vdots `vdots`
ddots `ddots`
|\ | `|\ |`
|quad| `|quad|`
/_ angle `/_`
frown `frown`
/_\ triangle `/_\\`
diamond `diamond`
square `square`
|__ lfloor `|__`
__| rfloor `__|`
|~ lceiling `|~`
~| rceiling `~|`
CC `CC`
NN `NN`
QQ `QQ`
RR `RR`
ZZ `ZZ`
"hi" text(hi) `"hi"`
Relation symbols
Type TeX alt See
= `=`
!= ne `!=`
< lt `<`
> gt `>`
<= le `<=`
>= ge `>=`
mlt ll `mlt`
mgt gg `mgt`
-< prec `-<`
-<= preceq `-<=`
>- succ `>-`
>-= succeq `>-=`
in `in`
!in notin `!in`
sub subset `sub`
sup supset `sup`
sube subseteq `sube`
supe supseteq `supe`
-= equiv `-=`
~= cong `~=`
~~ approx `~~`
prop propto `prop`
Logical symbols
Type TeX alt See
and `and`
or `or`
not neg `not`
=> implies `=>`
if `if`
<=> iff `iff`
AA forall `AA`
EE exists `EE`
_|_ bot `_|_`
TT top `TT`
|-- vdash `|--`
|== models `|==`
Grouping brackets
Type TeX alt See
( `(`
) `)`
[ `[`
] `]`
{ `{`
} `}`
(: langle `(:`
:) rangle `:)`
<< `<<`
>> `>>`
{: x ) `{: x )`
( x :} `( x :}`
abs(x) `abs(x)`
floor(x) `floor(x)`
ceil(x) `ceil(x)`
norm(vecx) `norm(vecx)`
Arrows
Type TeX alt See
uarr uparrow `uarr`
darr downarrow `darr`
rarr rightarrow `rarr`
-> to `->`
>-> rightarrowtail `>->`
->> twoheadrightarrow `->>`
>->> twoheadrightarrowtail `>->>`
|-> mapsto `|->`
larr leftarrow `larr`
harr leftrightarrow `harr`
rArr Rightarrow `rArr`
lArr Leftarrow `lArr`
hArr Leftrightarrow `hArr`
Accents
Type TeX alt See
hat x `hat x`
bar x overline x `bar x`
ul x underline x `ul x`
vec x `vec x`
tilde x `tilde x`
dot x `dot x`
ddot x `ddot x`
overset(x)(=) overset(x)(=) `overset(x)(=)`
underset(x)(=) `underset(x)(=)`
ubrace(1+2) underbrace(1+2) `ubrace(1+2)`
obrace(1+2) overbrace(1+2) `obrace(1+2)`
overarc(AB) overparen(AB) `overarc(AB)`
color(red)(x) `color(red)(x)`
cancel(x) `cancel(x)`
Greek Letters
Type See Type See
alpha `alpha`
beta `beta`
gamma `gamma` Gamma `Gamma`
delta `delta` Delta `Delta`
epsilon `epsilon`
varepsilon `varepsilon`
zeta `zeta`
eta `eta`
theta `theta` Theta `Theta`
vartheta `vartheta`
iota `iota`
kappa `kappa`
lambda `lambda` Lambda `Lambda`
mu `mu`
nu `nu`
xi `xi` Xi `Xi`
pi `pi` Pi `Pi`
rho `rho`
sigma `sigma` Sigma `Sigma`
tau `tau`
upsilon `upsilon`
phi `phi` Phi `Phi`
varphi `varphi`
chi `chi`
psi `psi` Psi `Psi`
omega `omega` Omega `Omega`
Font commands
Type TeX alt See
bb "AaBbCc" mathbf "AaBbCc" `bb "AaBbCc"`
bbb "AaBbCc" mathbb "AaBbCc" `bbb "AaBbCc"`
cc "AaBbCc" mathcal "AaBbCc" `cc "AaBbCc"`
tt "AaBbCc" mathtt "AaBbCc" `tt "AaBbCc"`
fr "AaBbCc" mathfrak "AaBbCc" `fr "AaBbCc"`
sf "AaBbCc" mathsf "AaBbCc" `sf "AaBbCc"`

Standard Functions

sin, cos, tan, sec, csc, cot, arcsin, arccos, arctan, sinh, cosh, tanh, sech, csch, coth, exp, log, ln, det, dim, mod, gcd, lcm, lub, glb, min, max, f, g.


Special Cases

Matrices: [[a,b],[c,d]] yields to `[[a,b],[c,d]]`

Column vectors: ((a),(b)) yields to `((a),(b))`

Augmented matrices: [[a,b,|,c],[d,e,|,f]] yields to `[[a,b,|,c],[d,e,|,f]]`

Matrices can be used for layout: {(2x,+,17y,=,23),(x,-,y,=,5):} yields `{(2x,+,17y,=,23),(x,-,y,=,5):}`

Complex subscripts: lim_(N->oo) sum_(i=0)^N yields to `lim_(N->oo) sum_(i=0)^N`

Subscripts must come before superscripts: int_0^1 f(x)dx yields to `int_0^1 f(x)dx`

Derivatives: f'(x) = dy/dx yields `f'(x) = dy/dx`
For variables other than x,y,z, or t you will need grouping symbols: (dq)/(dp) for `(dq)/(dp)`

Overbraces and underbraces: ubrace(1+2+3+4)_("4 terms") yields `ubrace(1+2+3+4)_("4 terms")`.
obrace(1+2+3+4)^("4 terms") yields `obrace(1+2+3+4)^("4 terms")`.

Attention: Always try to surround the > and < characters with spaces so that the html parser does not confuse it with an opening or closing tag!


The Grammar

Here is a definition of the grammar used to parse AsciiMath expressions. In the Backus-Naur form given below, the letter on the left of the ::= represents a category of symbols that could be one of the possible sequences of symbols listed on the right. The vertical bar | separates the alternatives.

v ::= [A-Za-z] | greek letters | numbers | other constant symbols
u ::= sqrt | text | bb | other unary symbols for font commands
b ::= frac | root | stackrel | other binary symbols
l ::= ( | [ | { | (: | {: | other left brackets
r ::= ) | ] | } | :) | :} | other right brackets
S ::= v | lEr | uS | bSS             Simple expression
I ::= S_S | S^S | S_S^S | S          Intermediate expression
E ::= IE | I/I                       Expression
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