Update mathematics.csv

Data/Abbr/mathematics.csv

@@ -1,266 +1,266 @@
 ABBR,MEANING
-AC,"Axiom of Choice, or set of absolutely continuous functions."
+AC,"Axiom of Choice, or set of absolutely continuous functions"
-a.c.,absolutely continuous.
+a.c.,absolutely continuous
-acrd,inverse chord function.
+acrd,inverse chord function
-ad,adjoint representation (or adjoint action) of a Lie group.
+ad,adjoint representation (or adjoint action) of a Lie group
-adj,adjugate of a matrix.
+adj,adjugate of a matrix
-a.e.,almost everywhere.
+a.e.,almost everywhere
-Ai,Airy function.
+Ai,Airy function
-AL,Action limit.
+AL,Action limit
-Alt,alternating group (Alt(n) is also written as An.)
+Alt,alternating group (Alt(n) is also written as An)
-A.M.,arithmetic mean.
+A.M.,arithmetic mean
-arccos,inverse cosine function.
+arccos,inverse cosine function
-arccosec,inverse cosecant function. (Also written as arccsc.)
+arccosec,inverse cosecant function (also written as arccsc)
-arccot,inverse cotangent function.
+arccot,inverse cotangent function
-arccsc,inverse cosecant function. (Also written as arccosec.)
+arccsc,inverse cosecant function (also written as arccosec)
-arcexc,"inverse excosecant function. (Also written as arcexcsc, arcexcosec.)"
+arcexc,"inverse excosecant function (also written as arcexcsc, arcexcosec)"
-arcexcosec,"inverse excosecant function. (Also written as arcexcsc, arcexc.)"
+arcexcosec,"inverse excosecant function (also written as arcexcsc, arcexc)"
-arcexcsc,"inverse excosecant function. (Also written as arcexcosec, arcexc.)"
+arcexcsc,"inverse excosecant function (also written as arcexcosec, arcexc)"
-arcexs,inverse exsecant function. (Also written as arcexsec.)
+arcexs,inverse exsecant function (also written as arcexsec)
-arcexsec,inverse exsecant function. (Also written as arcexs.)
+arcexsec,inverse exsecant function (also written as arcexs)
-arcosech,inverse hyperbolic cosecant function. (Also written as arcsch.)
+arcosech,inverse hyperbolic cosecant function (also written as arcsch)
-arcosh,inverse hyperbolic cosine function.
+arcosh,inverse hyperbolic cosine function
-arcoth,inverse hyperbolic cotangent function.
+arcoth,inverse hyperbolic cotangent function
-arcsch,inverse hyperbolic cosecant function. (Also written as arcosech.)
+arcsch,inverse hyperbolic cosecant function (also written as arcosech)
-arcsec,inverse secant function.
+arcsec,inverse secant function
-arcsin,inverse sine function.
+arcsin,inverse sine function
-arctan,inverse tangent function.
+arctan,inverse tangent function
-arctan2,inverse tangent function with two arguments. (Also written as atan2.)
+arctan2,inverse tangent function with two arguments (also written as atan2)
 arg,argument of
-arg max,argument of the maximum.
+arg max,argument of the maximum
-arg min,argument of the minimum.
+arg min,argument of the minimum
-arsech,inverse hyperbolic secant function.
+arsech,inverse hyperbolic secant function
-arsinh,inverse hyperbolic sine function.
+arsinh,inverse hyperbolic sine function
-artanh,inverse hyperbolic tangent function.
+artanh,inverse hyperbolic tangent function
-a.s.,almost surely.
+a.s.,almost surely
-atan2,inverse tangent function with two arguments. (Also written as arctan2.)
+atan2,inverse tangent function with two arguments (also written as arctan2)
-A.P.,arithmetic progression.
+A.P.,arithmetic progression
-Aut,automorphism group.
+Aut,automorphism group
-bd,boundary. (Also written as fr or ∂.)
+bd,boundary (also written as fr or ∂)
-Bi,Airy function of the second kind.
+Bi,Airy function of the second kind
-BIDMAS,"Brackets, Indices, Divide, Multiply, Add, Subtract."
+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|.)"
+Card,"cardinality of a set (Card(X) is also written #X, ♯X or |X|)"
-cas,cos + sin function.
+cas,cos + sin function
-cdf,cumulative distribution function.
+cdf,cumulative distribution function
-c.f.,cumulative frequency.
+c.f.,cumulative frequency
-c.c.,complex conjugate.
+c.c.,complex conjugate
-char,characteristic of a ring.
+char,characteristic of a ring
-Chi,hyperbolic cosine integral function.
+Chi,hyperbolic cosine integral function
-Ci,cosine integral function.
+Ci,cosine integral function
-cis,cos + i sin function. (Also written as expi.)
+cis,cos + i sin function (also written as expi)
-Cl,conjugacy class.
+Cl,conjugacy class
-cl,topological closure.
+cl,topological closure
-CLT,central limit theorem.
+CLT,central limit theorem
-cod,"codom,codomain."
+cod,"codom,codomain"
-cok,"coker,cokernel."
+cok,"coker,cokernel"
-conv,convex hull of a set.
+conv,convex hull of a set
-Cor,corollary.
+Cor,corollary
-corr,correlation.
+corr,correlation
-cos,cosine function.
+cos,cosine function
-cosec,cosecant function. (Also written as csc.)
+cosec,cosecant function (also written as csc)
-cosech,hyperbolic cosecant function. (Also written as csch.)
+cosech,hyperbolic cosecant function (also written as csch)
-cosh,hyperbolic cosine function.
+cosh,hyperbolic cosine function
-cosiv,"coversine function. (Also written as cover, covers, cvs.)"
+cosiv,"coversine function (also written as cover, covers, cvs)"
-cot,cotangent function. (Also written as ctg.)
+cot,cotangent function (also written as ctg)
-coth,hyperbolic cotangent function.
+coth,hyperbolic cotangent function
-cov,covariance of a pair of random variables.
+cov,covariance of a pair of random variables
-cover,"coversine function. (Also written as covers, cvs, cosiv.)"
+cover,"coversine function (also written as covers, cvs, cosiv)"
-covercos,covercosine function. (Also written as cvc.)
+covercos,covercosine function (also written as cvc)
-covers,"coversine function. (Also written as cover, cvs, cosiv.)"
+covers,"coversine function (also written as cover, cvs, cosiv)"
-crd,chord function.
+crd,chord function
-csc,cosecant function. (Also written as cosec.)
+csc,cosecant function (also written as cosec)
-csch,hyperbolic cosecant function. (Also written as cosech.)
+csch,hyperbolic cosecant function (also written as cosech)
-ctg,cotangent function. (Also written as cot.)
+ctg,cotangent function (also written as cot)
-curl,curl of a vector field. (Also written as rot.)
+curl,curl of a vector field (also written as rot)
-cvc,covercosine function. (Also written as covercos.)
+cvc,covercosine function (also written as covercos)
-cvs,"coversine function. (Also written as cover, covers, cosiv.)"
+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 ∂.)"
+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 .)"
+del,"del, a differential operator (also written as {\displaystyle \nabla }\nabla )"
-det,determinant of a matrix or linear transformation.
+det,determinant of a matrix or linear transformation
-dim,dimension of a vector space.
+dim,dimension of a vector space
-div,divergence of a vector field.
+div,divergence of a vector field
-DNE,"a solution for an expression does not exist, or is undefined. Generally used with limits and integrals."
+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.)"
+dom,"domain of a function (Or, more generally, a relation)"
-End,categories of endomorphisms.
+End,categories of endomorphisms
-Ei,exponential integral function.
+Ei,exponential integral function
-epi,epigraph of a function.
+epi,epigraph of a function
-Eqn,equation.
+Eqn,equation
-erf,error function.
+erf,error function
-erfc,complementary error function.
+erfc,complementary error function
-etr,exponent of the trace.
+etr,exponent of the trace
-exc,"excosecant function. (Also written as excsc, excosec.)"
+exc,"excosecant function (also written as excsc, excosec)"
-excosec,"excosecant function. (Also written as excsc, exc.)"
+excosec,"excosecant function (also written as excsc, exc)"
-excsc,"excosecant function. (Also written as excosec, exc.)"
+excsc,"excosecant function (also written as excosec, exc)"
-exs,exsecant function. (Also written as exsec.)
+exs,exsecant function (also written as exsec)
-exsec,exsecant function. (Also written as exs.)
+exsec,exsecant function (also written as exs)
-exp,exponential function. (exp x is also written as ex.)
+exp,exponential function (exp x is also written as ex)
-expi,cos + i sin function. (Also written as cis.)
+expi,cos + i sin function (also written as cis)
-expm1,exponential minus 1 function. (Also written as exp1m.)
+expm1,exponential minus 1 function (also written as exp1m)
-exp1m,exponential minus 1 function. (Also written as expm1.)
+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.)
+Gal,Galois group (also written as Γ)
-gcd,greatest common divisor of two numbers. (Also written as hcf.)
+gcd,greatest common divisor of two numbers (also written as hcf)
-gd,Gudermannian function.
+gd,Gudermannian function
-GF,Galois field.
+GF,Galois field
-GF,generating function.
+GF,generating function
-GL,general linear group.
+GL,general linear group
-GM,geometric mean.
+GM,geometric mean
-glb,greatest lower bound. (Also written as inf.)
+glb,greatest lower bound (also written as inf)
-GP,geometric progression.
+GP,geometric progression
-grad,gradient of a function.
+grad,gradient of a function
-hacover,"hacoversine function. (Also written as hacovers, hcv.)"
+hacover,"hacoversine function (also written as hacovers, hcv)"
-hacovercos,hacovercosine function. (Also written as hcc.)
+hacovercos,hacovercosine function (also written as hcc)
-hacovers,"hacoversine function. (Also written as hacover, hcv.)"
+hacovers,"hacoversine function (also written as hacover, hcv)"
-hav,haversine function. (Also written as sem.)
+hav,haversine function (also written as sem)
-havercos,havercosine function. (Also written as hvc.)
+havercos,havercosine function (also written as hvc)
-hcc,hacovercosine function. (Also written as hacovercos.)
+hcc,hacovercosine function (also written as hacovercos)
-hcv,"hacoversine function. (Also written as hacover, hacovers.)"
+hcv,"hacoversine function (also written as hacover, hacovers)"
-hcf,highest common factor of two numbers. (Also written as gcd.)
+hcf,highest common factor of two numbers (also written as gcd)
-H.M.,harmonic mean.
+H.M.,harmonic mean
-HOL,higher-order logic.
+HOL,higher-order logic
-Hom,Hom functor.
+Hom,Hom functor
-hom,hom-class.
+hom,hom-class
 hot,higher order term
 HOTPO,half or triple plus one
-hvc,havercosine function. (Also written as havercos.)
+hvc,havercosine function (also written as havercos)
-hyp,hypograph of a function.
+hyp,hypograph of a function
-iff,if and only if.
+iff,if and only if
-IH,induction hypothesis.
+IH,induction hypothesis
-iid,independent and identically distributed random variables.
+iid,independent and identically distributed random variables
-Im,imaginary part of a complex number (Also written as {\displaystyle \Im }\Im ).
+Im,imaginary part of a complex number (also written as {\displaystyle \Im }\Im )
 im,image
-inf,infimum of a set. (Also written as glb.)
+inf,infimum of a set (also written as glb)
-int,interior.
+int,interior
-I.o.,Infinitely often.
+I.o.,Infinitely often
-ker,kernel.
+ker,kernel
-lb,binary logarithm (log2). (Also written as ld.)
+lb,binary logarithm (log2) (also written as ld)
-lcm,lowest common multiple (a.k.a. least common multiple) of two numbers.
+lcm,lowest common multiple (a.k.a. least common multiple) of two numbers
-LCHS,locally compact Hausdorff second countable.
+LCHS,locally compact Hausdorff second countable
-ld,binary logarithm (log2). (Also written as lb.)
+ld,binary logarithm (log2) (also written as lb)
-lerp,linear interpolation.[5]
+lerp,linear interpolation
-lg,common logarithm (log10) or binary logarithm (log2).
+lg,common logarithm (log10) or binary logarithm (log2)
-LHS,left-hand side of an equation.
+LHS,left-hand side of an equation
-Li,offset logarithmic integral function.
+Li,offset logarithmic integral function
-li,logarithmic integral function or linearly independent.
+li,logarithmic integral function or linearly independent
-lim,"limit of a sequence, or of a function."
+lim,"limit of a sequence, or of a function"
-lim inf,limit inferior.
+lim inf,limit inferior
-lim sup,limit superior.
+lim sup,limit superior
-LLN,law of large numbers.
+LLN,law of large numbers
-ln,"natural logarithm, loge."
+ln,"natural logarithm, loge"
-lnp1,natural logarithm plus 1 function.
+lnp1,natural logarithm plus 1 function
-ln1p,natural logarithm plus 1 function.
+ln1p,natural logarithm plus 1 function
-log,"logarithm. (If without a subscript, this may mean either log10 or loge.)"
+log,"logarithm (If without a subscript, this may mean either log10 or loge)"
-logh,"natural logarithm, loge."
+logh,"natural logarithm, loge"
-LST,language of set theory.
+LST,language of set theory
-lub,least upper bound. (Also written sup.)
+lub,least upper bound (also written sup)
-max,maximum of a set.
+max,maximum of a set
-MGF,moment-generating function.
+MGF,moment-generating function
-M.I.,mathematical induction.
+M.I.,mathematical induction
-min,minimum of a set.
+min,minimum of a set
-mod,modulo.
+mod,modulo
-Mp,metaplectic group.
+Mp,metaplectic group
-mtanh,modified hyperbolic tangent function. (Also written as mth.)
+mtanh,modified hyperbolic tangent function (also written as mth)
-mth,modified hyperbolic tangent function. (Also written as mtanh.)
+mth,modified hyperbolic tangent function (also written as mtanh)
-mx,matrix.
+mx,matrix
-NAND,not-and in logic.
+NAND,not-and in logic
-No.,number.
+No.,number
-NOR,not-or in logic.
+NOR,not-or in logic
-NTS,need to show.
+NTS,need to show
-OBGF,ordinary bivariate generating function.
+OBGF,ordinary bivariate generating function
-ob,object class.
+ob,object class
-ord,ordinal number of a well-ordered set.[4]
+ord,ordinal number of a well-ordered set
-pdf,probability density function.
+pdf,probability density function
-pf,proof.
+pf,proof
-PGL,projective general linear group.
+PGL,projective general linear group
 PI,the constant 3.14159265359
 Pin,pin group.
-pmf,probability mass function.
+pmf,probability mass function
-Pn,previous number.
+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.
+PSU,projective special unitary group
-PU,projective unitary group.
+PU,projective unitary group
-QED,"Quod erat demonstrandum, a Latin phrase used at the end of a definitive proof."
+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."
+QEF,"quod erat faciendum, a Latin phrase sometimes used at the end of a geometrical construction"
-ran,range of a function.
+ran,range of a function
-rank,rank of a matrix. (Also written as rk.)
+rank,rank of a matrix (also written as rk)
 Re,real part of a complex number
-resp,respectively.
+resp,respectively
-RHS,right-hand side of an equation.
+RHS,right-hand side of an equation
-rk,rank. (Also written as rank.)
+rk,rank (also written as rank)
-RMS,"rms,root mean square."
+RMS,"rms,root mean square"
-rng,non-unital ring.
+rng,non-unital ring
-rot,rotor of a vector field. (Also written as curl.)
+rot,rotor of a vector field (also written as curl)
-RTP,required to prove.
+RTP,required to prove
-RV,random variable. (or as R.V.)
+RV,random variable (or as R.V)
 R,Real numbers
 SD,standard deviation
 SE,standard error
-sec,secant function.
+sec,secant function
-sech,hyperbolic secant function.
+sech,hyperbolic secant function
-seg,initial segment of.[1]
+seg,initial segment of
-sem,haversine function. (Also written as hav.)
+sem,haversine function (also written as hav)
-SFIP,strong finite intersection property.
+SFIP,strong finite intersection property
-sgn,sign function.
+sgn,sign function
-Shi,hyperbolic sine integral function.
+Shi,hyperbolic sine integral function
-Si,sine integral function.
+Si,sine integral function
-sin,sine function.
+sin,sine function
-sinc,sinc function.
+sinc,sinc function
-sinh,hyperbolic sine function.
+sinh,hyperbolic sine function
-siv,"versine function. (Also written as ver, vers.)"
+siv,"versine function (also written as ver, vers)"
-SL,special linear group.
+SL,special linear group
-SO,special orthogonal group.
+SO,special orthogonal group
-SOC,second order condition.
+SOC,second order condition
-Soln,solution.
+Soln,solution
-Sp,symplectic group.
+Sp,symplectic group
-Sp,"trace of a matrix, from the German 'spur' used for the trace."
+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.)"
+sp,"linear span of a set of vectors (also written as span or written with angle brackets)"
-Spec,spectrum of a ring.
+Spec,spectrum of a ring
-Spin,spin group.
+Spin,spin group
-s.t.,such that or so that or subject to.
+s.t.,such that or so that or subject to
-st,standard part function.
+st,standard part function
-STP,[it is] sufficient to prove.
+STP,[it is] sufficient to prove
-SU,special unitary group.
+SU,special unitary group
-sup,"supremum of a set. (Also written as lub, which stands for least upper bound.)"
+sup,"supremum of a set (also written as lub, which stands for least upper bound)"
-supp,support of a function.
+supp,support of a function
-swish,"swish function, an activation function in data analysis."
+swish,"swish function, an activation function in data analysis"
-Sym,"symmetric group (Sym(n) is also written as Sn) or symmetric algebra."
+Sym,"symmetric group (Sym(n) is also written as Sn) or symmetric algebra"
-tan,"tangent function. (Also written as tgn, tg.)"
+tan,"tangent function (also written as tgn, tg)"
-tanh,hyperbolic tangent function.
+tanh,hyperbolic tangent function
 TAU,"the constant 6.283185307179586476925286766559"
-TFAE,the following are equivalent.
+TFAE,the following are equivalent
-tg,"tangent function. (Also written as tan, tgn.)"
+tg,"tangent function (also written as tan, tgn)"
-tgn,"tangent function. (Also written as tan, tg.)"
+tgn,"tangent function (also written as tan, tg)"
-Thm,theorem.
+Thm,theorem
-Tor,Tor functor.
+Tor,Tor functor
-Tr,"trace, either the field trace, or the trace of a matrix or linear transformation."
+Tr,"trace, either the field trace, or the trace of a matrix or linear transformation"
 undef,a function or expression is undefined
-V,volume.
+V,volume
-var,variance of a random variable.
+var,variance of a random variable
-vcs,vercosine function. (Also written as vercos.)
+vcs,vercosine function (also written as vercos)
-ver,"versine function. (Also written as vers, siv.)"
+ver,"versine function (also written as vers, siv)"
-vercos,vercosine function. (Also written as vcs.)
+vercos,vercosine function (also written as vcs)
-vers,"versine function. (Also written as ver, siv.)"
+vers,"versine function (also written as ver, siv)"
-W^5,"which was what we wanted. Synonym of Q.E.D."
+W^5,"which was what we wanted. Synonym of Q.E.D"
-walog,without any loss of generality.
+walog,without any loss of generality
-wff,well-formed formula.
+wff,well-formed formula
-whp,with high probability.
+whp,with high probability
-wlog,without loss of generality.
+wlog,without loss of generality
 WMA,we may assume.
 WO,well-ordered set
-wp1,with probability 1.
+wp1,with probability 1
-wrt,with respect to or with regard to.
+wrt,with respect to or with regard to
 WTP,want to prove
 WTS,want to show
 XOR,exclusive or in logic