MATHEMATICA 教程

TraditionalForm 参考信息

TraditionalForm 与输入与输出的默认格式 StandardForm 不同. TraditionalForm 表达式不可能总给 Mathematica 提供无歧义输入,理解这一点是很重要的. 因此,尽管 StandardForm 既可作为输入格式也可作为输出格式,TraditionalForm 基本上仅用作输出格式.

一般而言,一个数学函数的 TraditionalForm 表示与它的 StandardForm 表示在两方面上不同:第一,函数的自变量放在圆括号里而不是方括号里;第二,单字符变量和函数名为斜体而不是纯文本格式.

除了这些一般意义上的不同,TraditionalForm 将很大的一组表达式变形为常规使用的数学符号. 这些表达式及其特殊的 TraditionalForm 表示将在本节教程的后面以表格形式列出.

这里显示了一个无特殊符号的数学函数;其输入和输出分别为 StandardFormTraditionalForm.
In[1]:=
Click for copyable input
Out[1]//TraditionalForm=
这是一个函数有自己特殊的 TraditionalForm 记号的例子.
In[2]:=
Click for copyable input
Out[2]//TraditionalForm=
矩阵的 TraditionalForm 表示在这里显示.
In[3]:=
Click for copyable input
Out[3]//TraditionalForm=

Mathematica 函数和命令的 TraditionalForm 表示与使用方括号(例如在 StandardForm 中)的传统数学表示不同.

这里是 Mathematica 函数 PlotTraditionalForm 表示.
In[4]:=
Click for copyable input
Out[4]//TraditionalForm=

下面各表列出了带有特定 TraditionalForm 表示的表达式. 标记有星号 () 的项包含隐藏信息(使用 TagBox 或者InterpretationBox 构建或特殊设计的字符),有可能不适合无歧义输入.

数学常数和域

数学常数和域.

数值函数

数值函数.

初等函数

StandardFormTraditionalForm
ArcCos[z]
ArcCosh[z]
ArcCot[z]
ArcCoth[z]
ArcCsc[z]
ArcCsch[z]
ArcSec[z]
ArcSech[z]
ArcSin[z]
ArcSinh[z]
ArcTan[z]
ArcTanh[z]
Cos[z]
Cos[z]p
Cosh[z]
Cosh[z]p
Cot[z]
Cot[z]p
Coth[z]
Coth[z]p
Csc[z]
Csc[z]p
Csch[z]
Csch[z]p
Log[z]
Log[z]^p
Log[b,z]
Log[b,z]^p
Sec[z]
Sec[z]p
Sech[z]
Sech[z]p
Sin[z]
Sin[z]p
Sinh[z]
Sinh[z]p
Tan[z]
Tan[z]p
Tanh[z]
Tanh[z]p

初等函数.

与阶乘相关的函数

StandardFormTraditionalForm
Beta[a,b]
Beta[z,a,b]
Beta[z0,z1,a,b]
Binomial[n,m]
Gamma[z]
Gamma[a,z]
Gamma[a,z1,z2]
GammaRegularized[a,z]
GammaRegularized[a,z0,z1]
InverseBetaRegularized[s,a,b]
InverseBetaRegularized[z0,s,a,b]
LogGamma[z]
Multinomial[n1,n2,...,nk]
Pochhammer[a,n]
PolyGamma[z]
PolyGamma[n,z]

与阶乘相关的函数.

组合函数

StandardFormTraditionalForm
BernoulliB[n]
BernoulliB[n,z]
ClebschGordan[{j1,m1},{j2,m2},{j3,m3}]
EulerE[n]
EulerE[n,z]
Fibonacci[n]
Fibonacci[n,z]
HarmonicNumber[n]
HarmonicNumber[n,r]
PartitionsP[z]
PartitionsQ[z]
Signature[e1,e2,...]
SixJSymbol[{j1,j2,j3},{j4,j5,j6}]
StirlingS1[n,m]
StirlingS2[n,m]
ThreeJSymbol[{j1,m1},{j2,m2},{j3,m3}]

组合函数.

数论

数论.

与 Zeta 函数相关的函数

与 Zeta 函数相关的函数.

与超几何函数相关的函数

StandardFormTraditionalForm
AiryAi[z]
AiryAiPrime[z]
AiryBi[z]
AiryBiPrime[z]
AngerJ[,x]*
AngerJ[,,x]*
AppellF1[a,b1,b2,c,x,y]
BesselI[n,z]
BesselJ[n,z]
BesselK[n,z]
BesselY[n,z]
CosIntegral[z]
CoshIntegral[z]
DawsonF[x]*
Erf[z]
Erf[z0,z1]
Erfc[z]
Erfi[z]
ExpIntegralE[n,z]
ExpIntegralEi[z]
FresnelC[z]
FresnelS[z]
Hypergeometric0F1[a,z]
Hypergeometric0F1Regularized[a,z]
Hypergeometric1F1[a,b,z]
Hypergeometric1F1Regularized[a,b,z]
Hypergeometric2F1[a,b,c,z]
Hypergeometric2F1Regularized[a,b,c,z]
HypergeometricPFQ[{a1,...,ap},{b1,...,bq},z]
HypergeometricPFQRegularized[{a1,...,ap},{b1,...,bq},z]
HypergeometricU[a,b,z]
LegendreQ[n,x]
LegendreQ[n,m,x]
LegendreQ[n,m,a,z]
LogIntegral[z]
MeijerG[{{a1,...,an},{an+1,...,ap}},{{b1,...,bm},{bm+1,...,bq}},z]
MeijerG[{{a1,...,an},{an+1,...,ap}},{{b1,...,bm},{bm+1,...,bq}},z,r]
SinIntegral[z]
SinhIntegral[z]
StruveH[,z]
StruveL[,z]
WeberE[,x]*
WeberE[,,x]*

与超几何函数相关的函数.

正交多项式

正交多项式.

反函数

反函数.

椭圆积分

椭圆积分.

椭圆函数

椭圆函数.

Mathieu 函数

Mathieu 函数.

广义函数及相关函数

StandardFormTraditionalForm
DiracDelta[x1,x2,...]
DiscreteDelta[n1,n2,...]
HeavisideLambda[x]*
HeavisideLambda[x1,x2,...]*
HeavisidePi[x]TemplateBox[{x}, HeavisidePiSeq]*
HeavisidePi[x1,x2,...]TemplateBox[{{{x, _, 1}, ,, {x, _, 2}}}, HeavisidePiSeq]*
KroneckerDelta[n1,n2,...]
UnitBox[x]TemplateBox[{x}, UnitBoxSeq]*
UnitBox[x1,x2,...]TemplateBox[{{{x, _, 1}, ,, {x, _, 2}}}, UnitBoxSeq]*
UnitStep[x1,x2,...]
UnitTriangle[x]TemplateBox[{x}, UnitTriangleSeq]*
UnitTriangle[x1,x2,...]TemplateBox[{{{x, _, 1}, ,, {x, _, 2}, ,, ...}}, UnitTriangleSeq]*

广义函数及相关函数.

矩阵运算

矩阵运算.

逻辑运算

StandardFormTraditionalForm
And[p1,p2,...]
Implies[a,b]
Nand[p1,p2,...]
Nor[p1,p2,...]
Not[p]
Or[p1,p2,...]
Xor[p1,p2,...]

逻辑运算.

微积分

StandardFormTraditionalForm
C[n]
D[f[x]]
D[f[x],x]
D[f[x],{x,2}]
D[f[x],{x,n}]
Dt[f[x]]
Dt[f[x],x]
Dt[f[x],{x,2}]
Dt[f[x],{x,n}]
Derivative[1][f]
Derivative[2][f]
Derivative[d1,...][f]
FourierTransform[expr,t,s]
FourierTransform[expr,{t1,t2,...},{s1,s2,...}]
Integrate[expr,x]
Integrate[expr,x1,y,z]
Integrate[expr,{x,a,b}]
Integrate[expr,{x,a,b},{y,m,n},{z,p,q}]
InverseFourierTransform[expr,s,t]
InverseFourierTransform[expr,{s1,s2,...},{t1,t2,...}]
InverseLaplaceTransform[expr,s,t]
InverseLaplaceTransform[expr,{s1,s2,...},{t1,t2,...}]
LaplaceTransform[expr,t,s]
LaplaceTransform[expr,{t1,t2,...},{s1,s2,...}]
Limit[f[x],x->a]
Limit[f[x],x->a,Direction->+1]
Limit[f[x],x->a,Direction->-1]
O[x]
O[x]^n
O[x,a]
O[x,a]^n
Piecewise[{{v1,c1},{v2,c2},...}]
Residue[z]
Series[f[x],{x,a,0}]
Series[f[x],{x,a,1}]
Series[Tan[z^(2/3)],{z,0,3}]

微积分.

离散微积分

StandardFormTraditionalForm
DifferenceDelta[f,i]*
DifferenceDelta[f,{i,n}]
*
DifferenceDelta[f,{i,n,h}]*
DifferenceDelta[f,i,j,...]*
DiscreteRatio[f,i]*
DiscreteRatio[f,{i,n}]TemplateBox[{f, i, n}, DiscreteRatio3]*
DiscreteRatio[f,{i,n,h}TemplateBox[{f, i, n, h}, DiscreteRatio4]*
DiscreteRatio[f,i,j,...]*
DiscreteShift[f,i]*
DiscreteShift[f,{i,n}]TemplateBox[{f, i, n}, DiscreteShift3]*
DiscreteShift[f,{i,n,h}]TemplateBox[{f, i, n, h}, DiscreteShift4]*
DiscreteShift[f,i,j,...]*
InverseZTransform[exp,z,n]
InverseZTransform[exp,{z1,z2,...},{n1,n2,...}]
ZTransform[exp,n,z]
ZTransform[exp,{n1,n2,...},{z1,z2,...}]

离散微积分.

多项式函数

多项式函数.

q 函数

StandardFormTraditionalForm
QBinomial[n,m,q]TemplateBox[{n, m, q}, QBinomial]*
QFactorial[n,q]TemplateBox[{n, q}, QFactorial]*
QGamma[z,q]TemplateBox[{z, q}, QGamma]*
QHypergeometricPFQ[{a1,...,at},{b1,...,bs},q,z]TemplateBox[{{{a, _, 1}, ,, ..., ,, {a, _, t}}, {{b, _, 1}, ,, ..., ,, {b, _, s}}, q, z, 2, 2}, QHypergeometricPFQSeq]*
QPochhammer[a,q,n]TemplateBox[{a, q, n}, QPochhammer]*
QPochhammer[a,q]TemplateBox[{a, q}, QPochhammer2]*
QPochhammer[q]TemplateBox[{q, q}, QPochhammer2]*
QPolyGamma[z,q]TemplateBox[{0, z, q}, QPolyGamma3]*
QPolyGamma[n,z,q]TemplateBox[{n, z, q}, QPolyGamma3]*

Q 函数.

完整的字母序列表

StandardFormTraditionalForm
Abs[z]
AiryAi[z]
AiryAiPrime[z]
AiryBi[z]
AiryBiPrime[z]
Algebraics
And[p1,p2,...]
AngerJ[,x]*
AngerJ[,,x]*
AppellF1[a,b1,b2,c,x,y]
ArcCos[z]
ArcCosh[z]
ArcCot[z]
ArcCoth[z]
ArcCsc[z]
ArcCsch[z]
ArcSec[z]
ArcSech[z]
ArcSin[z]
ArcSinh[z]
ArcTan[z]
ArcTanh[z]
Arg[z]
ArithmeticGeometricMean[a,b]
BernoulliB[n]
BernoulliB[n,z]
BesselI[n,z]
BesselJ[n,z]
BesselK[n,z]
BesselY[n,z]
Beta[a,b]
Beta[z,a,b]
Beta[z0,z1,a,b]
BetaRegularized[z,a,b]
BetaRegularized[z0,z1,a,b]
Binomial[n,m]
Booleans
C[n]
CarmichaelLambda[n]
Catalan
Ceiling[z]
ChampernowneNumber[b]*
ChebyshevT[n,x]
ChebyshevU[n,x]
ClebschGordan[{j1,m1},{j2,m2},{j3,m3}]
Complexes
Conjugate[z]TemplateBox[{z}, Conjugate]*
Cos[z]
Cos[z]p
Cosh[z]
Cosh[z]p
CosIntegral[z]
CoshIntegral[z]
Cot[z]
Cot[z]p
Coth[z]
Coth[z]p
Csc[z]
Csc[z]p
Csch[z]
Csch[z]p
Cyclotomic[n,z]
D[f[x]]
D[f[x],x]
D[f[x],{x,2}]
D[f[x],{x,n}]
Dt[f[x]]
Dt[f[x],x]
Dt[f[x],{x,2}]
Dt[f[x],{x,n}]
DawsonF[x]*
DedekindEta[t]
Derivative[1][f]
Derivative[2][f]
Derivative[d1,...][f]
Det[A]
DifferenceDelta[f,i]*
DifferenceDelta[f,{i,n}]
*
DifferenceDelta[f,{i,n,h}]*
DifferenceDelta[f,i,j,...]*
DiracDelta[x1,x2,...]
DiscreteDelta[n1,n2,...]
DiscreteRatio[f,i]*
DiscreteRatio[f,{i,n}]TemplateBox[{f, i, n}, DiscreteRatio3]*
DiscreteRatio[f,{i,n,h}TemplateBox[{f, i, n, h}, DiscreteRatio4]*
DiscreteRatio[f,i,j,...]*
DiscreteShift[f,i]*
DiscreteShift[f,{i,n}]TemplateBox[{f, i, n}, DiscreteShift3]*
DiscreteShift[f,{i,n,h}]TemplateBox[{f, i, n, h}, DiscreteShift4]*
DiscreteShift[f,i,j,...]*
DivisorSigma[k,n]
EllipticE[m]
EllipticE[,m]
EllipticF[,m]
EllipticK[m]
EllipticNomeQ[m]
EllipticPi[n,m]
EllipticPi[n,,m]
EllipticTheta[a,u,q]
EllipticThetaPrime[a,u,q]
Erf[z]
Erf[z0,z1]
Erfc[z]
Erfi[z]
EulerE[n]
EulerE[n,z]
EulerGamma
EulerPhi[n]
ExpIntegralE[n,z]
ExpIntegralEi[z]
Fibonacci[n]
Fibonacci[n,z]
Floor[z]
FourierTransform[expr,t,s]
FourierTransform[expr,{t1,t2,...},{s1,s2,...}]
FractionalPart[x]
FresnelC[z]
FresnelS[z]
Gamma[z]
Gamma[a,z]
Gamma[a,z1,z2]
GammaRegularized[a,z]
GammaRegularized[a,z0,z1]
GCD[n1,n2,...]
GegenbauerC[n,x]
GegenbauerC[n,m,x]
Glaisher
GoldenRatio
HarmonicNumber[n]
HarmonicNumber[n,r]
HeavisideLambda[x]*
HeavisideLambda[x1,x2,...]*
HeavisidePi[x]TemplateBox[{x}, HeavisidePiSeq]*
HeavisidePi[x1,x2,...]TemplateBox[{{{x, _, 1}, ,, {x, _, 2}}}, HeavisidePiSeq]*
HermiteH[n,x]
Hypergeometric0F1[a,z]
Hypergeometric0F1Regularized[a,z]
Hypergeometric1F1[a,b,z]
Hypergeometric1F1Regularized[a,b,z]
Hypergeometric2F1[a,b,c,z]
Hypergeometric2F1Regularized[a,b,c,z]
HypergeometricPFQ[{a1,...,ap},{b1,...,bq},z]
HypergeometricPFQRegularized[{a1,...,ap},{b1,...,bq},z]
HypergeometricU[a,b,z]
Implies[a,b]
Integers
Integrate[expr,x]
Integrate[expr,x1,y,z]
Integrate[expr,{x,a,b}]
Integrate[expr,{x,a,b},{y,m,n},{z,p,q}]
Inverse[A]
InverseBetaRegularized[s,a,b]
InverseBetaRegularized[z0,s,a,b]
InverseEllipticNomeQ[q]
InverseErf[z0,s]
InverseFourierTransform[expr,s,t]
InverseFourierTransform[expr,{s1,s2,...},{t1,t2,...}]
InverseFunction[f]
InverseJacobiCD[u,m]
InverseJacobiCN[u,m]
InverseJacobiCS[u,m]
InverseJacobiDC[u,m]
InverseJacobiDN[u,m]
InverseJacobiDS[u,m]
InverseJacobiNC[u,m]
InverseJacobiND[u,m]
InverseJacobiNS[u,m]
InverseJacobiSC[u,m]
InverseJacobiSD[u,m]
InverseJacobiSN[u,m]
InverseLaplaceTransform[expr,s,t]
InverseLaplaceTransform[expr,{s1,s2,...},{t1,t2,...}]
InverseWeierstrassP[p,{g2,g3}]
InverseZTransform[exp,z,n]
InverseZTransform[exp,{z1,z2,...},{n1,n2,...}]
JacobiAmplitude[u,m]
JacobiCD[u,m]
JacobiCN[u,m]
JacobiCS[u,m]
JacobiDC[u,m]
JacobiDN[u,m]
JacobiDS[u,m]
JacobiNC[u,m]
JacobiND[u,m]
JacobiNS[u,m]
JacobiSC[u,m]
JacobiSD[u,m]
JacobiSN[u,m]
JacobiP[n,a,b,x]
JacobiSymbol[n,m]
JacobiZeta[,m]
Khinchin*
KleinInvariantJ[]
KroneckerDelta[n1,n2,...]
LaguerreL[n,x]
LaguerreL[n,a,x]
LegendreP[n,x]
LegendreP[n,m,x]
LegendreP[n,m,a,z]
LaplaceTransform[expr,t,s]
LaplaceTransform[expr,s,t]
LCM[n1,n2,...]
LegendreQ[n,x]
LegendreQ[n,m,x]
LegendreQ[n,m,a,z]
LerchPhi[z,s,a]
Limit[f[x],x->a]
Limit[f[x],x->a,Direction->+1]
Limit[f[x],x->a,Direction->-1]
LiouvilleLambda[n]TemplateBox[{n}, LiouvilleLambda]*
Log[z]
Log[b,z]
Log[z]^p
Log[b,z]^p
LogGamma[z]
LogIntegral[z]
MangoldtLambda[n]TemplateBox[{n}, MangoldtLambda]*
MathieuCharacteristicA[r,q]
MathieuCharacteristicB[r,q]
Max[z]
MeijerG[{{a1,...,an},{an+1,...,ap}},{{b1,...,bm},{bm+1,...,bq}},z]
MeijerG[{{a1,...,an},{an+1,...,ap}},{{b1,...,bm},{bm+1,...,bq}},z,r]
Min[z]
Mod[m,n]
ModularLambda[]
MoebiusMu[n]
Multinomial[n1,n2,...,nk]
MultiplicativeOrder[k,n]
Nand[p1,p2,...]
NevilleThetaC[u,m]
NevilleThetaD[u,m]
NevilleThetaN[u,m]
NevilleThetaS[u,m]
Nor[p1,p2,...]
Not[p]
O[x]
O[x]^n
O[x,a]
O[x,a]^n
Or[p1,p2,...]
PartitionsP[z]
PartitionsQ[z]
Piecewise[{{v1,c1},{v2,c2},...}]
Pochhammer[a,n]
PolyGamma[z]
PolyGamma[n,z]
PolyLog[,z]
PolyLog[,p,z]
PolynomialMod[poly,m]
PowerMod[a,b,n]
Prime[n]
PrimeNu[n]TemplateBox[{x}, PrimeNu]*
PrimeOmega[n]TemplateBox[{n}, PrimeOmega]*
PrimePi[z]
PrimeZetaP[x]*
Primes
ProductLog[z]
ProductLog[k,z]
QBinomial[n,m,q]TemplateBox[{n, m, q}, QBinomial]*
QFactorial[n,q]TemplateBox[{n, q}, QFactorial]*
QGamma[z,q]TemplateBox[{z, q}, QGamma]*
QHypergeometricPFQ[{a1,...,at},{b1,...,bs},q,z]TemplateBox[{{{a, _, 1}, ,, ..., ,, {a, _, t}}, {{b, _, 1}, ,, ..., ,, {b, _, s}}, q, z, 2, 2}, QHypergeometricPFQSeq]*
QPochhammer[a,q,n]TemplateBox[{a, q, n}, QPochhammer]*
QPochhammer[a,q]TemplateBox[{a, q}, QPochhammer2]*
QPochhammer[q]TemplateBox[{q, q}, QPochhammer2]*
QPolyGamma[z,q]TemplateBox[{0, z, q}, QPolyGamma3]*
QPolyGamma[n,z,q]TemplateBox[{n, z, q}, QPolyGamma3]*
RamanujanTau[n]
Rationals
Reals
Residue[z]
RiemannR[x]*
RiemannSiegelTheta[t]
RiemannSiegelZ[t]
Sec[z]
Sec[z]p
Sech[z]
Sech[z]p
Series[f[x],{x,a,0}]
Series[f[x],{x,a,1}]
Series[Tan[z^(2/3)],{z,0,3}]
Sign[z]
Signature[e1,e2,...]
Sin[z]
Sin[z]p
Sinh[z]
Sinh[z]p
SinIntegral[z]
SinhIntegral[z]
SixJSymbol[{j1,j2,j3},{j4,j5,j6}]
SphericalHarmonicY[l,m,,]
SquaresR[d,n]*
StieltjesGamma[n]
StieltjesGamma[n,a]*
StirlingS1[n,m]
StirlingS2[n,m]
StruveH[,z]
StruveL[,z]
Tan[z]
Tan[z]p
Tanh[z]
Tanh[z]p
ThreeJSymbol[{j1,m1},{j2,m2},{j3,m3}]
Transpose[A]
UnitBox[x]TemplateBox[{x}, UnitBoxSeq]*
UnitBox[x1,x2,...]TemplateBox[{{{x, _, 1}, ,, {x, _, 2}}}, UnitBoxSeq]*
UnitStep[x1,x2,...]
UnitTriangle[x]TemplateBox[{x}, UnitTriangleSeq]*
UnitTriangle[x1,x2,...]TemplateBox[{{{x, _, 1}, ,, {x, _, 2}, ,, ...}}, UnitTriangleSeq]*
WeberE[,x]*
WeberE[,,x]*
WeierstrassP[u,{g2,g3}]
WeierstrassPPrime[u,{g2,g3}]
WeierstrassSigma[u,{g2,g3}]
WeierstrassZeta[u,{g2,g3}]
Xor[p1,p2,...]
Zeta[s]
Zeta[s,a]
ZTransform[exp,n,z]
ZTransform[exp,{n1,n2,...},{z1,z2,...}]

完整的字母序列表.

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