[中英双语] 数学缩写列表 (List of mathematical abbreviations)

List of mathematical abbreviations

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数学缩写列表

维基百科，自由的百科全书

This article is a listing of abbreviated names of mathematical functions, function-like operators and other mathematical terminology.

这篇文章是一个数学函数，类似于函数的操作符和其他的数学术语的缩写名列表。

This list is limited to abbreviations of two or more letters. The capitalization of some of these abbreviations is not standardized – different authors use different capitalizations.

This list is incomplete; you can help by expanding it.

这个列表受限于两个或更多字母的缩略语。其中，一些缩略语字母大写并不是标准的 - 不同的作者使用不同的大写形式。

AC – Axiom of Choice.^[1] 选择公理
a.c. – absolutely continuous. 绝对连续的
acrd – inverse chord function. 逆弦函数
adj – adjugate of a matrix. 矩阵的伴随矩阵
a.e. – almost everywhere. 殆遍，几乎处处
Ai – Airy function. 艾里函数
AL – Action limit. 处置界限
Alt – alternating group (Alt(n) is also written as A_n.) 交错群
A.M. – arithmetic mean. 算数平均数
arccos – inverse cosine function. 反余弦函数
arccosec – inverse cosecant function. (Also written as arccsc.) 反余割函数
arccot – inverse cotangent function. 反余切函数
arccsc – inverse cosecant function. (Also written as arccosec.) 反余割函数
arcexc – inverse excosecant function. (Also written as arcexcsc, arcexcosec.) 反外余割函数
arcexcosec – inverse excosecant function. (Also written as arcexcsc, arcexc.) 反外余割函数
arcexcsc – inverse excosecant function. (Also written as arcexcosec, arcexc.) 反外余割函数
arcexs – inverse exsecant function. (Also written as arcexsec.) 反外正割函数
arcexsec – inverse exsecant function. (Also written as arcexs.) 反外正割函数
arcosech – inverse hyperbolic cosecant function. (Also written as arcsch.) 反双曲余割函数
arcosh – inverse hyperbolic cosine function. 反双曲余弦函数
arcoth – inverse hyperbolic cotangent function. 反双曲余切函数
arcsch – inverse hyperbolic cosecant function. (Also written as arcosech.) 反双曲余割函数
arcsec – inverse secant function. 反正割函数
arcsin – inverse sine function. 反正弦函数
arctan – inverse tangent function. 反正切函数
arctan2 – inverse tangent function with two arguments. (Also written as atan2.) 带有2个参数的反正切函数
arg – argument of a complex number.^[2] 复数的参数
arg max – argument of the maximum. 最大值时的参数
arg min – argument of the minimum. 最小值时的参数
arsech – inverse hyperbolic secant function. 反双曲正割函数
arsinh – inverse hyperbolic sine function. 反双曲正弦函数
artanh – inverse hyperbolic tangent function. 反双曲正切函数
a.s. – almost surely. 殆必，几乎必然
atan2 – inverse tangent function with two arguments. (Also written as arctan2.) 同 arctan2，带有两个参数的反正切函数
A.P. – arithmetic progression. 等差数列
Aut – automorphism group. 自同构群
bd – boundary. 边界（拓扑学）
Bi – Airy function of the second kind. 第二类艾里函数
Bias – bias of an estimator 估计器偏置
Card – cardinality of a set.^[3] (Card(X) is also written #X, ♯X or |X|.) 集合的势
cdf – cumulative distribution function. 累积分布函数
c.f. – cumulative frequency. 累积频率
char – characteristic of a ring. 环的特征
Chi – hyperbolic cosine integral function. 双曲余弦积分函数
Ci – cosine integral function. 余弦积分函数
cis – cos + i sin function. 欧拉公式函数
Cl – conjugacy class. 共轭类
cl – topological closure. 拓扑学闭包
cod, codom – codomain. 到达域
cok, coker – cokernel. 上核，余核
Cor – corollary. 推论，余定理
corr – correlation. 相关
cos – cosine function. 余弦函数
cosec – cosecant function. (Also written as csc.) 余割函数
cosech – hyperbolic cosecant function. (Also written as csch.) 双曲余割函数
cosh – hyperbolic cosine function. 双曲余弦函数
cosiv – coversine function. (Also written as cover, covers, cvs.) 余矢函数
cot – cotangent function. (Also written as ctg.) 余切函数
coth – hyperbolic cotangent function. 双曲余切函数
cov – covariance of a pair of random variables. 协方差
cover – coversine function. (Also written as covers, cvs, cosiv.) 余矢函数
covercos – covercosine function. (Also written as cvc.) 正矢函数
covers – coversine function. (Also written as cover, cvs, cosiv.) 余矢函数
crd – chord function. 弦（几何）函数
csc – cosecant function. (Also written as cosec.) 余割函数
csch – hyperbolic cosecant function. (Also written as cosech.) 双曲余割函数
ctg – cotangent function. (Also written as cot.) 余切函数
curl – curl of a vector field. (Also written as rot.) 向量场的旋度
cvc – covercosine function. (Also written as covercos.) 余余矢函数
cvs – coversine function. (Also written as cover, covers, cosiv.) 正余矢函数
def – define or definition. 定义
deg – degree of a polynomial. (Also written as ∂.) 多项式的次数
del – del, a differential operator. (Also written as .) 微分运算符
det – determinant of a matrix or linear transformation. 矩阵或线性变换的行列式
dim – dimension of a vector space. 向量空间的维度
div – divergence of a vector field. 向量场的散度
dkl – decalitre 公斗。公斗是一个容积单位，符号是daL。公斗本身不是国际单位制(SI)单位，而是接受与SI合并使用的非SI单位。1 公斗等于10 公升。
DNE – a solution for an expression does not exist, or is undefined. Generally used with limits and integrals. 不存在，或未定义，通常用于极限和积分。
dom – domain of a function.^[1] (Or, more generally, a relation.) 函数的定义域
End – categories of endomorphisms. 自同态范畴
Ei – exponential integral function. 指数积分函数
Eqn – equation. 方程
erf – error function. 误差函数
erfc – complementary error function. 余误差函数（互补误差函数）
etr — exponent of the trace. 迹指数
exc — excosecant function. (Also written as excsc, excosec.) 外余割函数
excosec — excosecant function. (Also written as excsc, exc.) 外余割函数
excsc — excosecant function. (Also written as excosec, exc.) 外余割函数
exs — exsecant function. (Also written as exsec.) 外正割函数
exsec — exsecant function. (Also written as exs.) 外正割函数
exp – exponential function. (exp x is also written as e^x.) 指数函数
expm1 – exponential minus 1 function. (Also written as exp1m.) 指数减1函数
exp1m – exponential minus 1 function. (Also written as expm1.) 指数减1函数
Ext – Ext functor. Ext 函子
ext – exterior. 外部（拓扑学）
FIP – finite intersection property. 有限交集性质
FOL – first-order logic. 一阶逻辑
Frob – Frobenius endomorphism. 弗罗贝尼乌斯自同态
Gal – Galois group. (Also written as Γ.) 伽罗瓦群
gcd – greatest common divisor of two numbers. (Also written as hcf.) 两个数的最大公因数
gd – Gudermannian function. 古德曼函数
GF – Galois field. 伽罗瓦，即有限域（Finite field）
GL – general linear group. 一般线性群
G.M. – geometric mean. 几何平均数
glb – greatest lower bound. (Also written as inf.) 最大下界
G.P. – geometric progression. 等比数列
grad – gradient of a function. 函数梯度
hacover – hacoversine function. (Also written as hacovers, hcv.) 正半余矢函数
hacovercos – hacovercosine function. (Also written as hcc.) 余半余矢函数
hacovers – hacoversine function. (Also written as hacover, hcv.) 正半余矢函数
hav – haversine function. (Also written as sem.) 正半正矢函数
havercos – havercosine function. (Also written as hvc.) 余半正矢函数
hcc – hacovercosine function. (Also written as hacovercos.) 余半余矢函数
hcv – hacoversine function. (Also written as hacover, hacovers.) 正半余矢函数
hcf – highest common factor of two numbers. (Also written as gcd.) 最大公因数
H.M. – harmonic mean. 调和平均数
HOL – higher-order logic. 高阶逻辑
Hom – Hom functor. Hom 函子
hom – hom-class hom类
hvc – havercosine function. (Also written as havercos.) 余半正矢函数
iff – if and only if. 当且仅当
iid – independent and identically distributed random variables. 独立同分布随机变量
Im – imaginary part of a complex number^[2] (Also written as ).复数的虚部
im – image 像（数学）
inf – infimum of a set. (Also written as glb.) 集合的下确界
int – interior. 内部（拓扑学）
ker – kernel. 核（范畴论 Category theory）
lb – binary logarithm (log₂). (Also written as ld.) 以2为底的对数
lcm – lowest common multiple or least common multiple of two numbers. 两个数的最小公倍数
ld – binary logarithm (log₂). (Also written as lb.) 以2为底的对数
lerp – linear interpolation.^[4] 线性插值
lg – common logarithm (log₁₀) or binary logarithm (log₂). 常用对数或以2为底的对数
LHS – left-hand side of an equation. 方程的左侧
Li – offset logarithmic integral function. 偏移对数积分函数
li – logarithmic integral function or linearly independent. 对数积分函数或线性无关
lim – limit of a sequence, or of a function. 数列极限或函数极限
lim inf – limit inferior. 下极限
lim sup – limit superior. 上极限
ln – natural logarithm, log_e. 自然对数
lnp1 – natural logarithm plus 1 function. 自然对数加1极限
ln1p – natural logarithm plus 1 function. 自然对数加1极限
log – logarithm. (If without a subscript, this may mean either log₁₀ or log_e.) 对数
logh – natural logarithm, log_e.^[5] 自然对数
LST – language of set theory. 集合论语言
lub – least upper bound.^[1] (Also written sup.) 最小上界
max – maximum of a set. 集合的最大值
M.I. – mathematical induction. 数学归纳法
min – minimum of a set. 集合的最小值
mod – modulo. 模数运算
mtanh – modified hyperbolic tangent function. (Also written as mth.) 修改后的双曲正切函数
mth – modified hyperbolic tangent function. (Also written as mtanh.) 修改后的双曲正切函数
mx – matrix. 矩阵
NAND – not-and in logic. 与非逻辑
No. – number. 数
NOR – not-or in logic. 或非逻辑
NTS – need to show. 需要展示，需要展现
ob – object class. 对象类
ord – ordinal number of a well-ordered set.^[3] 良序集的序数
pdf – probability density function. 概率密度函数
pf – proof. 证明
PGL – projective general linear group. 射影一般线性群
pmf – probability mass function. 概率质量函数
Pr – probability of an event. (See Probability theory. Also written as P or .) 事件概率
PSL – projective special linear group. 射影特殊线性群
QED – "Quod erat demonstrandum", a Latin phrase used at the end of a definitive proof. 证明完毕，拉丁语，用在明确证明的结束处。
QEF – "quod erat faciendum", a Latin phrase sometimes used at the end of a construction. 拉丁语，meaning "which had to be done"，有时用在一次作图的结尾，意思是这就是要做的。
ran – range of a function. 函数的值域
rank – rank. (Also written as rk.) 秩（线性代数）
Re – real part of a complex number.^[2] (Also written .) 复数的实数部分
resp – respectively. 分别地，各自地
RHS – right-hand side of an equation. 方程的右侧
rk – rank. (Also written as rank.) 秩（线性代数）
RMS, rms – root mean square. 均方根
rng – non-unital ring. 伪环pseudo-ring
rot – rotor of a vector field. (Also written as curl.) 向量场的旋度
RTP – required to prove. 需要证明
RV – Random Variable. (or as R.V.) 随机变量
sec – secant function. 正割函数
sech – hyperbolic secant function. 双曲正割函数
seg – initial segment of.^[1] 初始线段，起始线段
sem – haversine function. (Also written as hav.) 正半正矢函数
SFIP – strong finite intersection property. 强有限交集性质
sgn – signum function. 符号函数
Shi – hyperbolic sine integral function. 双曲正弦积分函数
Si – sine integral function. 正弦积分函数
sin – sine function. 正弦函数
sinc – sinc function. sinc函数
sinh – hyperbolic sine function. 双曲正弦函数
siv – versine function. (Also written as ver, vers.) 正矢函数
SL – special linear group. 特殊线性组
Soln – solution. 解答
sp – linear span of a set of vectors. (Also written with angle brackets.) 一组向量的线性范围
Spec – spectrum of a ring. 环的谱
s.t. – such that or so that. 以便
st – standard part function. 标准局部函数
STP – [it is] sufficient to prove. 足以证明
sup – supremum of a set.^[1] (Also written lub.) 上确界，最小上界
supp – support of a function. 函数的支撑集
Sym – symmetric group (Sym(n) is also written as S_n.) 对称群（n次对称群）
tan – tangent function. (Also written as tgn, tg.) 正切函数
tanh – hyperbolic tangent function. 双曲正切函数
TFAE – the following are equivalent. 以下是等价的
tg – tangent function. (Also written as tan, tgn.) 正切函数
tgn – tangent function. (Also written as tan, tg.) 正切函数
Thm – theorem. 定理
Tor – Tor functor. Tor 函子
Tr – trace, either the field trace, or the trace of a matrix or linear transformation. 迹，或场迹，或矩阵或线性变换的迹
undef – a function or expression is undefined 函数或表达式未定义
var – variance of a random variable. 随机变量的方差
vcs – vercosine function. (Also written as vercos.) 余矢函数
ver – versine function. (Also written as vers, siv.) 正矢函数
vercos – vercosine function. (Also written as vcs.) 余矢函数
vers – versine function. (Also written as ver, siv.) 正矢函数
W^5 – which was what we wanted. Synonym of Q.E.D. 这就是我们想要的，Q.E.D.的同义词
walog – without any loss of generality. 不失一般性
wff – well-formed formula. 合式公式
whp – with high probability. 很大概率地
wlog – without loss of generality. 不失一般性
WMA – we may assume. 我们可能假设
WO – well-ordered set.^[1] 良序集
wp1 - with probability 1. 以概率1
wrt – with respect to or with regard to. 对
WTP – want to prove. 想要证明
WTS – want to show. 想要展示，想要展现
XOR – exclusive or in logic. 异或逻辑
ZF – Zermelo–Fraenkel axioms of set theory.^[3] 集合论的策梅洛-弗兰克尔公理
ZFC – Zermelo–Fraenkel axioms (with the Axiom of Choice) of set theory.^[3] 集合论的（含有选择公理）策梅洛-弗兰克尔公理

References

Goldrei, Derek (1996). Classic Set Theory. London, UK: Chapman and Hall. pp. 283–287 (Index). ISBN 0-412-60610-0.
Priestley, H. A. (2003). Introduction to Complex Analysis (2 ed.). Oxford University Press. p. 321 (Notation index) ISBN 978-0-19-852562-2.
Hamilton, A. G. (1982). Numbers, sets and axioms. Cambridge University Press. pp. 249–251 (Index of symbols). ISBN 0-521-24509-5. Raymond, Eric S. (2003), "LERP", Jargon File, 4.4.7
Jolley, L.B.W. (1961). Summation of Series (2 (revised) ed.). New York, USA: Dover Publications, Inc.LCCN 61-65274.