Update mathematics.csv

Data/Abbr/mathematics.csv

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 ABBR,MEANING
-AC,"Axiom of Choice, or set of absolutely continuous functions."
-a.c.,absolutely continuous.
-acrd,inverse chord function.
-ad,adjoint representation (or adjoint action) of a Lie group.
-adj,adjugate of a matrix.
-a.e.,almost everywhere.
-Ai,Airy function.
-AL,Action limit.
-Alt,alternating group (Alt(n) is also written as An.)
-A.M.,arithmetic mean.
-arccos,inverse cosine function.
-arccosec,inverse cosecant function. (Also written as arccsc.)
-arccot,inverse cotangent function.
-arccsc,inverse cosecant function. (Also written as arccosec.)
-arcexc,"inverse excosecant function. (Also written as arcexcsc, arcexcosec.)"
-arcexcosec,"inverse excosecant function. (Also written as arcexcsc, arcexc.)"
-arcexcsc,"inverse excosecant function. (Also written as arcexcosec, arcexc.)"
-arcexs,inverse exsecant function. (Also written as arcexsec.)
-arcexsec,inverse exsecant function. (Also written as arcexs.)
-arcosech,inverse hyperbolic cosecant function. (Also written as arcsch.)
-arcosh,inverse hyperbolic cosine function.
-arcoth,inverse hyperbolic cotangent function.
-arcsch,inverse hyperbolic cosecant function. (Also written as arcosech.)
-arcsec,inverse secant function.
-arcsin,inverse sine function.
-arctan,inverse tangent function.
-arctan2,inverse tangent function with two arguments. (Also written as atan2.)
+AC,"Axiom of Choice, or set of absolutely continuous functions"
+a.c.,absolutely continuous
+acrd,inverse chord function
+ad,adjoint representation (or adjoint action) of a Lie group
+adj,adjugate of a matrix
+a.e.,almost everywhere
+Ai,Airy function
+AL,Action limit
+Alt,alternating group (Alt(n) is also written as An)
+A.M.,arithmetic mean
+arccos,inverse cosine function
+arccosec,inverse cosecant function (also written as arccsc)
+arccot,inverse cotangent function
+arccsc,inverse cosecant function (also written as arccosec)
+arcexc,"inverse excosecant function (also written as arcexcsc, arcexcosec)"
+arcexcosec,"inverse excosecant function (also written as arcexcsc, arcexc)"
+arcexcsc,"inverse excosecant function (also written as arcexcosec, arcexc)"
+arcexs,inverse exsecant function (also written as arcexsec)
+arcexsec,inverse exsecant function (also written as arcexs)
+arcosech,inverse hyperbolic cosecant function (also written as arcsch)
+arcosh,inverse hyperbolic cosine function
+arcoth,inverse hyperbolic cotangent function
+arcsch,inverse hyperbolic cosecant function (also written as arcosech)
+arcsec,inverse secant function
+arcsin,inverse sine function
+arctan,inverse tangent function
+arctan2,inverse tangent function with two arguments (also written as atan2)
 arg,argument of
-arg max,argument of the maximum.
-arg min,argument of the minimum.
-arsech,inverse hyperbolic secant function.
-arsinh,inverse hyperbolic sine function.
-artanh,inverse hyperbolic tangent function.
-a.s.,almost surely.
-atan2,inverse tangent function with two arguments. (Also written as arctan2.)
-A.P.,arithmetic progression.
-Aut,automorphism group.
-bd,boundary. (Also written as fr or ∂.)
-Bi,Airy function of the second kind.
-BIDMAS,"Brackets, Indices, Divide, Multiply, Add, Subtract."
+arg max,argument of the maximum
+arg min,argument of the minimum
+arsech,inverse hyperbolic secant function
+arsinh,inverse hyperbolic sine function
+artanh,inverse hyperbolic tangent function
+a.s.,almost surely
+atan2,inverse tangent function with two arguments (also written as arctan2)
+A.P.,arithmetic progression
+Aut,automorphism group
+bd,boundary (also written as fr or ∂)
+Bi,Airy function of the second kind
+BIDMAS,"Brackets, Indices, Divide, Multiply, Add, Subtract"
 Bias,bias of an estimator
 BWOC,by way of contradiction
-Card,"cardinality of a set. (Card(X) is also written #X, ♯X or |X|.)"
-cas,cos + sin function.
-cdf,cumulative distribution function.
-c.f.,cumulative frequency.
-c.c.,complex conjugate.
-char,characteristic of a ring.
-Chi,hyperbolic cosine integral function.
-Ci,cosine integral function.
-cis,cos + i sin function. (Also written as expi.)
-Cl,conjugacy class.
-cl,topological closure.
-CLT,central limit theorem.
-cod,"codom,codomain."
-cok,"coker,cokernel."
-conv,convex hull of a set.
-Cor,corollary.
-corr,correlation.
-cos,cosine function.
-cosec,cosecant function. (Also written as csc.)
-cosech,hyperbolic cosecant function. (Also written as csch.)
-cosh,hyperbolic cosine function.
-cosiv,"coversine function. (Also written as cover, covers, cvs.)"
-cot,cotangent function. (Also written as ctg.)
-coth,hyperbolic cotangent function.
-cov,covariance of a pair of random variables.
-cover,"coversine function. (Also written as covers, cvs, cosiv.)"
-covercos,covercosine function. (Also written as cvc.)
-covers,"coversine function. (Also written as cover, cvs, cosiv.)"
-crd,chord function.
-csc,cosecant function. (Also written as cosec.)
-csch,hyperbolic cosecant function. (Also written as cosech.)
-ctg,cotangent function. (Also written as cot.)
-curl,curl of a vector field. (Also written as rot.)
-cvc,covercosine function. (Also written as covercos.)
-cvs,"coversine function. (Also written as cover, covers, cosiv.)"
+Card,"cardinality of a set (Card(X) is also written #X, ♯X or |X|)"
+cas,cos + sin function
+cdf,cumulative distribution function
+c.f.,cumulative frequency
+c.c.,complex conjugate
+char,characteristic of a ring
+Chi,hyperbolic cosine integral function
+Ci,cosine integral function
+cis,cos + i sin function (also written as expi)
+Cl,conjugacy class
+cl,topological closure
+CLT,central limit theorem
+cod,"codom,codomain"
+cok,"coker,cokernel"
+conv,convex hull of a set
+Cor,corollary
+corr,correlation
+cos,cosine function
+cosec,cosecant function (also written as csc)
+cosech,hyperbolic cosecant function (also written as csch)
+cosh,hyperbolic cosine function
+cosiv,"coversine function (also written as cover, covers, cvs)"
+cot,cotangent function (also written as ctg)
+coth,hyperbolic cotangent function
+cov,covariance of a pair of random variables
+cover,"coversine function (also written as covers, cvs, cosiv)"
+covercos,covercosine function (also written as cvc)
+covers,"coversine function (also written as cover, cvs, cosiv)"
+crd,chord function
+csc,cosecant function (also written as cosec)
+csch,hyperbolic cosecant function (also written as cosech)
+ctg,cotangent function (also written as cot)
+curl,curl of a vector field (also written as rot)
+cvc,covercosine function (also written as covercos)
+cvs,"coversine function (also written as cover, covers, cosiv)"
 def,define or definition.
-deg,"degree of a polynomial, or other recursively-defined objects such as well-formed formulas. (Also written as ∂.)"
-del,"del, a differential operator. (Also written as {\displaystyle \nabla }\nabla .)"
-det,determinant of a matrix or linear transformation.
-dim,dimension of a vector space.
-div,divergence of a vector field.
-DNE,"a solution for an expression does not exist, or is undefined. Generally used with limits and integrals."
-dom,"domain of a function. (Or, more generally, a relation.)"
-End,categories of endomorphisms.
-Ei,exponential integral function.
-epi,epigraph of a function.
-Eqn,equation.
-erf,error function.
-erfc,complementary error function.
-etr,exponent of the trace.
-exc,"excosecant function. (Also written as excsc, excosec.)"
-excosec,"excosecant function. (Also written as excsc, exc.)"
-excsc,"excosecant function. (Also written as excosec, exc.)"
-exs,exsecant function. (Also written as exsec.)
-exsec,exsecant function. (Also written as exs.)
-exp,exponential function. (exp x is also written as ex.)
-expi,cos + i sin function. (Also written as cis.)
-expm1,exponential minus 1 function. (Also written as exp1m.)
-exp1m,exponential minus 1 function. (Also written as expm1.)
+deg,"degree of a polynomial, or other recursively-defined objects such as well-formed formulas (also written as ∂)"
+del,"del, a differential operator (also written as {\displaystyle \nabla }\nabla )"
+det,determinant of a matrix or linear transformation
+dim,dimension of a vector space
+div,divergence of a vector field
+DNE,"a solution for an expression does not exist, or is undefined. Generally used with limits and integrals"
+dom,"domain of a function (Or, more generally, a relation)"
+End,categories of endomorphisms
+Ei,exponential integral function
+epi,epigraph of a function
+Eqn,equation
+erf,error function
+erfc,complementary error function
+etr,exponent of the trace
+exc,"excosecant function (also written as excsc, excosec)"
+excosec,"excosecant function (also written as excsc, exc)"
+excsc,"excosecant function (also written as excosec, exc)"
+exs,exsecant function (also written as exsec)
+exsec,exsecant function (also written as exs)
+exp,exponential function (exp x is also written as ex)
+expi,cos + i sin function (also written as cis)
+expm1,exponential minus 1 function (also written as exp1m)
+exp1m,exponential minus 1 function (also written as expm1)
 Ext,Ext functor.
 ext,exterior.
 extr,a set of extreme points of a set.
 FIP,finite intersection property.
 FOC,first order condition.
 FOL,first-order logic.
-fr,boundary. (Also written as bd or ∂.)
+fr,boundary (also written as bd or ∂)
 Frob,Frobenius endomorphism.
-Gal,Galois group. (Also written as Γ.)
-gcd,greatest common divisor of two numbers. (Also written as hcf.)
-gd,Gudermannian function.
-GF,Galois field.
-GF,generating function.
-GL,general linear group.
-GM,geometric mean.
-glb,greatest lower bound. (Also written as inf.)
-GP,geometric progression.
-grad,gradient of a function.
-hacover,"hacoversine function. (Also written as hacovers, hcv.)"
-hacovercos,hacovercosine function. (Also written as hcc.)
-hacovers,"hacoversine function. (Also written as hacover, hcv.)"
-hav,haversine function. (Also written as sem.)
-havercos,havercosine function. (Also written as hvc.)
-hcc,hacovercosine function. (Also written as hacovercos.)
-hcv,"hacoversine function. (Also written as hacover, hacovers.)"
-hcf,highest common factor of two numbers. (Also written as gcd.)
-H.M.,harmonic mean.
-HOL,higher-order logic.
-Hom,Hom functor.
-hom,hom-class.
+Gal,Galois group (also written as Γ)
+gcd,greatest common divisor of two numbers (also written as hcf)
+gd,Gudermannian function
+GF,Galois field
+GF,generating function
+GL,general linear group
+GM,geometric mean
+glb,greatest lower bound (also written as inf)
+GP,geometric progression
+grad,gradient of a function
+hacover,"hacoversine function (also written as hacovers, hcv)"
+hacovercos,hacovercosine function (also written as hcc)
+hacovers,"hacoversine function (also written as hacover, hcv)"
+hav,haversine function (also written as sem)
+havercos,havercosine function (also written as hvc)
+hcc,hacovercosine function (also written as hacovercos)
+hcv,"hacoversine function (also written as hacover, hacovers)"
+hcf,highest common factor of two numbers (also written as gcd)
+H.M.,harmonic mean
+HOL,higher-order logic
+Hom,Hom functor
+hom,hom-class
 hot,higher order term
 HOTPO,half or triple plus one
-hvc,havercosine function. (Also written as havercos.)
-hyp,hypograph of a function.
-iff,if and only if.
-IH,induction hypothesis.
-iid,independent and identically distributed random variables.
-Im,imaginary part of a complex number (Also written as {\displaystyle \Im }\Im ).
+hvc,havercosine function (also written as havercos)
+hyp,hypograph of a function
+iff,if and only if
+IH,induction hypothesis
+iid,independent and identically distributed random variables
+Im,imaginary part of a complex number (also written as {\displaystyle \Im }\Im )
 im,image
-inf,infimum of a set. (Also written as glb.)
-int,interior.
-I.o.,Infinitely often.
-ker,kernel.
-lb,binary logarithm (log2). (Also written as ld.)
-lcm,lowest common multiple (a.k.a. least common multiple) of two numbers.
-LCHS,locally compact Hausdorff second countable.
-ld,binary logarithm (log2). (Also written as lb.)
-lerp,linear interpolation.[5]
-lg,common logarithm (log10) or binary logarithm (log2).
-LHS,left-hand side of an equation.
-Li,offset logarithmic integral function.
-li,logarithmic integral function or linearly independent.
-lim,"limit of a sequence, or of a function."
-lim inf,limit inferior.
-lim sup,limit superior.
-LLN,law of large numbers.
-ln,"natural logarithm, loge."
-lnp1,natural logarithm plus 1 function.
-ln1p,natural logarithm plus 1 function.
-log,"logarithm. (If without a subscript, this may mean either log10 or loge.)"
-logh,"natural logarithm, loge."
-LST,language of set theory.
-lub,least upper bound. (Also written sup.)
-max,maximum of a set.
-MGF,moment-generating function.
-M.I.,mathematical induction.
-min,minimum of a set.
-mod,modulo.
-Mp,metaplectic group.
-mtanh,modified hyperbolic tangent function. (Also written as mth.)
-mth,modified hyperbolic tangent function. (Also written as mtanh.)
-mx,matrix.
-NAND,not-and in logic.
-No.,number.
-NOR,not-or in logic.
-NTS,need to show.
-OBGF,ordinary bivariate generating function.
-ob,object class.
-ord,ordinal number of a well-ordered set.[4]
-pdf,probability density function.
-pf,proof.
-PGL,projective general linear group.
+inf,infimum of a set (also written as glb)
+int,interior
+I.o.,Infinitely often
+ker,kernel
+lb,binary logarithm (log2) (also written as ld)
+lcm,lowest common multiple (a.k.a. least common multiple) of two numbers
+LCHS,locally compact Hausdorff second countable
+ld,binary logarithm (log2) (also written as lb)
+lerp,linear interpolation
+lg,common logarithm (log10) or binary logarithm (log2)
+LHS,left-hand side of an equation
+Li,offset logarithmic integral function
+li,logarithmic integral function or linearly independent
+lim,"limit of a sequence, or of a function"
+lim inf,limit inferior
+lim sup,limit superior
+LLN,law of large numbers
+ln,"natural logarithm, loge"
+lnp1,natural logarithm plus 1 function
+ln1p,natural logarithm plus 1 function
+log,"logarithm (If without a subscript, this may mean either log10 or loge)"
+logh,"natural logarithm, loge"
+LST,language of set theory
+lub,least upper bound (also written sup)
+max,maximum of a set
+MGF,moment-generating function
+M.I.,mathematical induction
+min,minimum of a set
+mod,modulo
+Mp,metaplectic group
+mtanh,modified hyperbolic tangent function (also written as mth)
+mth,modified hyperbolic tangent function (also written as mtanh)
+mx,matrix
+NAND,not-and in logic
+No.,number
+NOR,not-or in logic
+NTS,need to show
+OBGF,ordinary bivariate generating function
+ob,object class
+ord,ordinal number of a well-ordered set
+pdf,probability density function
+pf,proof
+PGL,projective general linear group
 PI,the constant 3.14159265359
 Pin,pin group.
-pmf,probability mass function.
-Pn,previous number.
+pmf,probability mass function
+Pn,previous number
 Pr,probability of an event
-PSL,projective special linear group.
+PSL,projective special linear group
 PSO,projective orthogonal group.
-PSU,projective special unitary group.
-PU,projective unitary group.
-QED,"Quod erat demonstrandum, a Latin phrase used at the end of a definitive proof."
-QEF,"quod erat faciendum, a Latin phrase sometimes used at the end of a geometrical construction."
-ran,range of a function.
-rank,rank of a matrix. (Also written as rk.)
+PSU,projective special unitary group
+PU,projective unitary group
+QED,"Quod erat demonstrandum, a Latin phrase used at the end of a definitive proof"
+QEF,"quod erat faciendum, a Latin phrase sometimes used at the end of a geometrical construction"
+ran,range of a function
+rank,rank of a matrix (also written as rk)
 Re,real part of a complex number
-resp,respectively.
-RHS,right-hand side of an equation.
-rk,rank. (Also written as rank.)
-RMS,"rms,root mean square."
-rng,non-unital ring.
-rot,rotor of a vector field. (Also written as curl.)
-RTP,required to prove.
-RV,random variable. (or as R.V.)
+resp,respectively
+RHS,right-hand side of an equation
+rk,rank (also written as rank)
+RMS,"rms,root mean square"
+rng,non-unital ring
+rot,rotor of a vector field (also written as curl)
+RTP,required to prove
+RV,random variable (or as R.V)
 R,Real numbers
 SD,standard deviation
 SE,standard error
-sec,secant function.
-sech,hyperbolic secant function.
-seg,initial segment of.[1]
-sem,haversine function. (Also written as hav.)
-SFIP,strong finite intersection property.
-sgn,sign function.
-Shi,hyperbolic sine integral function.
-Si,sine integral function.
-sin,sine function.
-sinc,sinc function.
-sinh,hyperbolic sine function.
-siv,"versine function. (Also written as ver, vers.)"
-SL,special linear group.
-SO,special orthogonal group.
-SOC,second order condition.
-Soln,solution.
-Sp,symplectic group.
-Sp,"trace of a matrix, from the German 'spur' used for the trace."
-sp,"linear span of a set of vectors. (Also written as span or written with angle brackets.)"
-Spec,spectrum of a ring.
-Spin,spin group.
-s.t.,such that or so that or subject to.
-st,standard part function.
-STP,[it is] sufficient to prove.
-SU,special unitary group.
-sup,"supremum of a set. (Also written as lub, which stands for least upper bound.)"
-supp,support of a function.
-swish,"swish function, an activation function in data analysis."
-Sym,"symmetric group (Sym(n) is also written as Sn) or symmetric algebra."
-tan,"tangent function. (Also written as tgn, tg.)"
-tanh,hyperbolic tangent function.
+sec,secant function
+sech,hyperbolic secant function
+seg,initial segment of
+sem,haversine function (also written as hav)
+SFIP,strong finite intersection property
+sgn,sign function
+Shi,hyperbolic sine integral function
+Si,sine integral function
+sin,sine function
+sinc,sinc function
+sinh,hyperbolic sine function
+siv,"versine function (also written as ver, vers)"
+SL,special linear group
+SO,special orthogonal group
+SOC,second order condition
+Soln,solution
+Sp,symplectic group
+Sp,"trace of a matrix, from the German 'spur' used for the trace"
+sp,"linear span of a set of vectors (also written as span or written with angle brackets)"
+Spec,spectrum of a ring
+Spin,spin group
+s.t.,such that or so that or subject to
+st,standard part function
+STP,[it is] sufficient to prove
+SU,special unitary group
+sup,"supremum of a set (also written as lub, which stands for least upper bound)"
+supp,support of a function
+swish,"swish function, an activation function in data analysis"
+Sym,"symmetric group (Sym(n) is also written as Sn) or symmetric algebra"
+tan,"tangent function (also written as tgn, tg)"
+tanh,hyperbolic tangent function
 TAU,"the constant 6.283185307179586476925286766559"
-TFAE,the following are equivalent.
-tg,"tangent function. (Also written as tan, tgn.)"
-tgn,"tangent function. (Also written as tan, tg.)"
-Thm,theorem.
-Tor,Tor functor.
-Tr,"trace, either the field trace, or the trace of a matrix or linear transformation."
+TFAE,the following are equivalent
+tg,"tangent function (also written as tan, tgn)"
+tgn,"tangent function (also written as tan, tg)"
+Thm,theorem
+Tor,Tor functor
+Tr,"trace, either the field trace, or the trace of a matrix or linear transformation"
 undef,a function or expression is undefined
-V,volume.
-var,variance of a random variable.
-vcs,vercosine function. (Also written as vercos.)
-ver,"versine function. (Also written as vers, siv.)"
-vercos,vercosine function. (Also written as vcs.)
-vers,"versine function. (Also written as ver, siv.)"
-W^5,"which was what we wanted. Synonym of Q.E.D."
-walog,without any loss of generality.
-wff,well-formed formula.
-whp,with high probability.
-wlog,without loss of generality.
+V,volume
+var,variance of a random variable
+vcs,vercosine function (also written as vercos)
+ver,"versine function (also written as vers, siv)"
+vercos,vercosine function (also written as vcs)
+vers,"versine function (also written as ver, siv)"
+W^5,"which was what we wanted. Synonym of Q.E.D"
+walog,without any loss of generality
+wff,well-formed formula
+whp,with high probability
+wlog,without loss of generality
 WMA,we may assume.
 WO,well-ordered set
-wp1,with probability 1.
-wrt,with respect to or with regard to.
+wp1,with probability 1
+wrt,with respect to or with regard to
 WTP,want to prove
 WTS,want to show
 XOR,exclusive or in logic