Mathematicaº¯Êý¼°Ê¹Ó÷½·¨

(À´Ô´£º  ±±·åÊýÄ£)

---------------------------------------------------------------------

×¢£ºÎªÁ˶ÔMathematicaÓÐÒ»¶¨Á˽âµÄͬѧϵͳÕÆÎÕMathematicaµÄÇ¿´ó

¹¦ÄÜ£¬ÎÒÃÇ°ÑËüµÄһЩ×ÊÁÏÐԵĶ«Î÷ÕûÀíÁËһϣ¬Ï£ÍûÄܶԴó¼ÒÓÐËù°ïÖú¡£

---------------------------------------------------------------------

Ò»¡¢ÔËËã·û¼°ÌØÊâ·ûºÅ

Line1; Ö´ÐÐLine£¬²»ÏÔʾ½á¹û

Line1,line2 ˳´ÎÖ´ÐÐLine1£¬2£¬²¢ÏÔʾ½á¹û

?name ¹ØÓÚϵͳ±äÁ¿nameµÄÐÅÏ¢

??name ¹ØÓÚϵͳ±äÁ¿nameµÄÈ«²¿ÐÅÏ¢

!command Ö´ÐÐDosÃüÁî

n! NµÄ½×³Ë

!!filename ÏÔʾÎļþÄÚÈÝ

< Expr>> filename ´ò¿ªÎļþд

Expr>>>filename ´ò¿ªÎļþ´ÓÎļþĩд

() ½áºÏÂÊ

[] º¯Êý

{} Ò»¸ö±í

<*Math Fun*> ÔÚcÓïÑÔÖÐʹÓÃmathµÄº¯Êý

(*Note*) ³ÌÐòµÄ×¢ÊÍ

#n µÚn¸ö²ÎÊý

## ËùÓвÎÊý

rule& °Ñrule×÷ÓÃÓÚºóÃæµÄʽ×Ó

% Ç°Ò»´ÎµÄÊä³ö

%% µ¹ÊýµÚ¶þ´ÎµÄÊä³ö

%n µÚn¸öÊä³ö

var::note ±äÁ¿varµÄ×¢ÊÍ

"Astring " ×Ö·û´®

Context ` ÉÏÏÂÎÄ

a+b ¼Ó

a-b ¼õ

a*b»òa b ³Ë

a/b ³ý

a^b ³Ë·½

base^^num ÒÔbaseΪ½øλµÄÊý

lhs&&rhs ÇÒ

lhs||rhs »ò

!lha ·Ç

++,-- ×Ô¼Ó1£¬×Ô¼õ1

+=,-=,*=,/= ͬCÓïÑÔ

>,<,>=,<=,==,!= Âß¼­Åжϣ¨Í¬c£©

lhs=rhs Á¢¼´¸³Öµ

lhs:=rhs ½¨Á¢¶¯Ì¬¸³Öµ

lhs:>rhs ½¨Á¢Ìæ»»¹æÔò

lhs->rhs ½¨Á¢Ìæ»»¹æÔò

expr//funname Ï൱ÓÚfilename[expr]

expr/.rule ½«¹æÔòruleÓ¦ÓÃÓÚexpr

expr//.rule ½«¹æÔòrule²»¶ÏÓ¦ÓÃÓÚexprÖªµÀ²»±äΪֹ

param_ ÃûΪparamµÄÒ»¸öÈÎÒâ±í´ïʽ£¨ÐÎʽ±äÁ¿£©

param__ ÃûΪparamµÄÈÎÒâ¶à¸öÈÎÒâ±í´ïʽ£¨ÐÎʽ±äÁ¿£©

¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª

¶þ¡¢ÏµÍ³³£Êý

Pi 3.1415....µÄÎÞÏÞ¾«¶ÈÊýÖµ

E 2.17828...µÄÎÞÏÞ¾«¶ÈÊýÖµ

Catalan 0.915966..¿¨ËþÀ¼³£Êý

EulerGamma 0.5772....¸ß˹³£Êý

GoldenRatio 1.61803...»Æ½ð·Ö¸îÊý

Degree Pi/180½Ç¶È»¡¶È»»Ëã

I ¸´Êýµ¥Î»

Infinity ÎÞÇî´ó

-Infinity ¸ºÎÞÇî´ó

ComplexInfinity ¸´ÎÞÇî´ó

Indeterminate ²»¶¨Ê½

¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª

Èý¡¢´úÊý¼ÆËã

Expand[expr] Õ¹¿ª±í´ïʽ

Factor[expr] Õ¹¿ª±í´ïʽ

Simplify[expr] »¯¼ò±í´ïʽ

FullSimplify[expr] ½«ÌØÊ⺯ÊýµÈÒ²½øÐл¯¼ò

PowerExpand[expr] Õ¹¿ªËùÓеÄÃÝ´ÎÐÎʽ

ComplexExpand[expr,{x1,x2...}] °´¸´Êýʵ²¿Ð鲿չ¿ª

FunctionExpand[expr] »¯¼òexprÖеÄÌØÊ⺯Êý

Collect[expr, x] ºÏ²¢Í¬´ÎÏî

Collect[expr, {x1,x2,...}] ºÏ²¢x1,x2,...µÄͬ´ÎÏî

Together[expr] ͨ·Ö

Apart[expr] ²¿·Ö·Öʽչ¿ª

Apart[expr, var] ¶ÔvarµÄ²¿·Ö·Öʽչ¿ª

Cancel[expr] Ô¼·Ö

ExpandAll[expr] Õ¹¿ª±í´ïʽ

ExpandAll[expr, patt] Õ¹¿ª±í´ïʽ

FactorTerms[poly] Ìá³ö¹²ÓеÄÊý×ÖÒò×Ó

FactorTerms[poly, x] Ìá³öÓëxÎ޹صÄÊý×ÖÒò×Ó

FactorTerms[poly, {x1,x2...}] Ìá³öÓëxiÎ޹صÄÊý×ÖÒò×Ó

Coefficient[expr, form] ¶àÏîʽexprÖÐformµÄϵÊý

Coefficient[expr, form, n] ¶àÏîʽexprÖÐform^nµÄϵÊý

Exponent[expr, form] ±í´ïʽexprÖÐformµÄ×î¸ßÖ¸Êý

Numerator[expr] ±í´ïʽexprµÄ·Ö×Ó

Denominator[expr] ±í´ïʽexprµÄ·Öĸ

ExpandNumerator[expr] Õ¹¿ªexprµÄ·Ö×Ó²¿·Ö

ExpandDenominator[expr] Õ¹¿ªexprµÄ·Öĸ²¿·Ö

TrigExpand[expr] Õ¹¿ª±í´ïʽÖеÄÈý½Çº¯Êý

TrigFactor[expr] ¸ø³ö±í´ïʽÖеÄÈý½Çº¯ÊýÒò×Ó

TrigFactorList[expr] ¸ø³ö±í´ïʽÖеÄÈý½Çº¯ÊýÒò×ӵıí

TrigReduce[expr] ¶Ô±í´ïʽÖеÄÈý½Çº¯Êý»¯¼ò

TrigToExp[expr] Èý½Çµ½Ö¸ÊýµÄת»¯

ExpToTrig[expr] Ö¸Êýµ½Èý½ÇµÄת»¯

RootReduce[expr]

ToRadicals[expr]

¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª

ËÄ¡¢½â·½³Ì

Solve[eqns, vars] ´Ó·½³Ì×éeqnsÖнâ³övars

Solve[eqns, vars, elims] ´Ó·½³Ì×éeqnsÖÐÏ÷È¥±äÁ¿elims,½â³övars

DSolve[eqn, y, x] ½â΢·Ö·½³Ì£¬ÆäÖÐyÊÇxµÄº¯Êý

DSolve[{eqn1,eqn2,...},{y1,y2...},x]½â΢·Ö·½³Ì×飬ÆäÖÐyiÊÇxµÄº¯Êý

DSolve[eqn, y, {x1,x2...}] ½âƫ΢·Ö·½³Ì

Eliminate[eqns, vars] °Ñ·½³Ì×éeqnsÖбäÁ¿varsԼȥ

SolveAlways[eqns, vars] ¸ø³öµÈʽ³ÉÁ¢µÄËùÓвÎÊýÂú×ãµÄÌõ¼þ

Reduce[eqns, vars] »¯¼ò²¢¸ø³öËùÓпÉÄܽâµÄÌõ¼þ

LogicalExpand[expr] ÓÃ&&ºÍ||½«Âß¼­±í´ïʽչ¿ª

InverseFunction[f] Çóº¯ÊýfµÄÄ溯Êý

Root[f, k] Çó¶àÏîʽº¯ÊýµÄµÚk¸ö¸ù

Roots[lhs==rhs, var] µÃµ½¶àÏîʽ·½³ÌµÄËùÓиù

¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª

Î塢΢»ý·Öº¯Êý

D[f, x] Çóf[x]µÄ΢·Ö

D[f, {x, n}] Çóf[x]µÄn½×΢·Ö

D[f,x1,x2..] Çóf[x]¶Ôx1,x2...ƫ΢·Ö

Dt[f, x] Çóf[x]µÄȫ΢·Ödf/dx

Dt[f] Çóf[x]µÄȫ΢·Ödf

Dt[f, {x, n}] n½×ȫ΢·Ödf^n/dx^n

Dt[f,x1,x2..] ¶Ôx1,x2..µÄƫ΢·Ö

Integrate[f, x] f[x]¶ÔxÔڵIJ»¶¨»ý·Ö

Integrate[f, {x, xmin, xmax}] f[x]¶ÔxÔÚÇø¼ä(xmin,xmax)µÄ¶¨»ý·Ö

Integrate[f, {x, xmin, xmax}, {y, ymin, ymax}] f[x,y]µÄ¶þÖØ»ý·Ö

Limit[expr, x->x0] xÇ÷½üÓÚx0ʱexprµÄ¼«ÏÞ

Residue[expr, {x,x0}] exprÔÚx0´¦µÄÁôÊý

Series[f, {x, x0, n}] ¸ø³öf[x]ÔÚx0´¦µÄÃݼ¶ÊýÕ¹¿ª

Series[f, {x, x0,nx}, {y, y0, ny}]ÏȶÔyÃݼ¶ÊýÕ¹¿ª£¬ÔÙ¶Ôx

Normal[expr] »¯¼ò²¢¸ø³ö×î³£¼ûµÄ±í´ïʽ

SeriesCoefficient[series, n] ¸ø³ö¼¶ÊýÖеÚn´ÎÏîµÄϵÊý

SeriesCoefficient[series, {n1,n2...}]

'»òDerivative[n1,n2...][f] Ò»½×µ¼Êý

InverseSeries[s, x] ¸ø³öÄ溯ÊýµÄ¼¶Êý

ComposeSeries[serie1,serie2...] ¸ø³öÁ½¸ö»ùÊýµÄ×éºÏ

SeriesData[x,x0,{a0,a1,..},nmin,nmax,den]±íʾһ¸öÔÚx0´¦xµÄÃݼ¶Êý£¬ÆäÖÐaiΪϵÊý

O[x]^n n½×СÁ¿x^n

O[x, x0]^n n½×СÁ¿(x-x0)^n

¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª

°Ë¡¢ÊýÖµº¯Êý

N[expr] ±í´ïʽµÄ»úÆ÷¾«¶È½üËÆÖµ

N[expr, n] ±í´ïʽµÄnλ½üËÆÖµ£¬nΪÈÎÒâÕýÕûÊý

NSolve[lhs==rhs, var] Çó·½³ÌÊýÖµ½â

NSolve[eqn, var, n] Çó·½³ÌÊýÖµ½â£¬½á¹û¾«¶Èµ½nλ

NDSolve[eqns, y, {x, xmin, xmax}]΢·Ö·½³ÌÊýÖµ½â

NDSolve[eqns, {y1,y2,...}, {x, xmin, xmax}]

΢·Ö·½³Ì×éÊýÖµ½â

FindRoot[lhs==rhs, {x,x0}] ÒÔx0Ϊ³õÖµ£¬Ñ°ÕÒ·½³ÌÊýÖµ½â

FindRoot[lhs==rhs, {x, xstart, xmin, xmax}]

NSum[f, {i,imin,imax,di}] ÊýÖµÇóºÍ£¬diΪ²½³¤

NSum[f, {i,imin,imax,di}, {j,..},..] ¶àάº¯ÊýÇóºÍ

NProduct[f, {i, imin, imax, di}]º¯ÊýÇó»ý

NIntegrate[f, {x, xmin, xmax}] º¯ÊýÊýÖµ»ý·Ö

ÓÅ»¯º¯Êý£º

FindMinimum[f, {x,x0}] ÒÔx0Ϊ³õÖµ£¬Ñ°ÕÒº¯Êý×îСֵ

FindMinimum[f, {x, xstart, xmin, xmax}]

ConstrainedMin[f,{inequ},{x,y,..}]

inequΪÏßÐÔ²»µÈʽ×飬fΪx,y..Ö®ÏßÐÔº¯Êý£¬µÃµ½×îСֵ¼°´ËʱµÄx,y..È¡Öµ

ConstrainedMax[f, {inequ}, {x, y,..}]ͬÉÏ

LinearProgramming[c,m,b] ½âÏßÐÔ×éºÏc.xÔÚm.x>=b&&x>=0Ô¼ÊøϵÄ

×îСֵ£¬x,b,cΪÏòÁ¿,mΪ¾ØÕó

LatticeReduce[{v1,v2...}] ÏòÁ¿×éviµÄ¼«Ð¡ÎÞ¹Ø×é

Êý¾Ý´¦Àí£º

Fit[data,funs,vars]ÓÃÖ¸¶¨º¯Êý×é¶ÔÊý¾Ý½øÐÐ×îС¶þ³ËÄâºÍ

data¿ÉÒÔΪ{{x1,y1,..f1},{x2,y2,..f2}..}¶àάµÄÇé¿ö

emp: Fit[{10.22,12,3.2,9.9}, {1, x, x^2,Sin[x]}, x]

Interpolation[data]¶ÔÊý¾Ý½øÐвîÖµ,

dataͬÉÏ£¬ÁíÍ⻹¿ÉÒÔΪ{{x1,{f1,df11,df12}},{x2,{f2,.}..}Ö¸¶¨¸÷½×µ¼Êý

InterpolationOrderĬÈÏΪ3´Î£¬¿ÉÐÞ¸Ä

ListInterpolation[array]¶ÔÀëÉ¢Êý¾Ý²åÖµ£¬array¿ÉΪnά

ListInterpolation[array,{{xmin,xmax},{ymin,ymax},..}]

FunctionInterpolation[expr,{x,xmin,xmax}, {y,ymin,ymax},..]

ÒÔ¶ÔÓ¦expr[xi,yi]µÄΪÊý¾Ý½øÐвåÖµ

Fourier[list] ¶Ô¸´ÊýÊý¾Ý½øÐи¶Êϱ任

InverseFourier[list] ¶Ô¸´ÊýÊý¾Ý½øÐи¶ÊÏÄæ±ä»»

Min[{x1,x2...},{y1,y2,...}]µÃµ½Ã¿¸ö±íÖеÄ×îСֵ

Max[{x1,x2...},{y1,y2,...}]µÃµ½Ã¿¸ö±íÖеÄ×î´óÖµ

Select[list, crit] ½«±íÖÐʹµÃcritΪTrueµÄÔªËØÑ¡Ôñ³öÀ´

Count[list, pattern] ½«±íÖÐÆ¥ÅäģʽpatternµÄÔªËصĸöÊý

Sort[list] ½«±íÖÐÔªËØ°´ÉýÐòÅÅÁÐ

Sort[list,p] ½«±íÖÐÔªËØ°´p[e1,e2]ΪTrueµÄ˳Ðò±È½Ïlist

µÄÈÎÁ½¸öÔªËØe1,e2,ʵ¼ÊÉÏSort[list]ÖÐĬÈÏp=Greater

¼¯ºÏÂÛ£º

Union[list1,list2..] ±ílistiµÄ²¢¼¯²¢ÅÅÐò

Intersection[list1,list2..] ±ílistiµÄ½»¼¯²¢ÅÅÐò

Complement[listall,list1,list2...]´ÓÈ«¼¯listallÖжÔlistiµÄ²î¼¯

¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª

¾Å¡¢ÐéÊýº¯Êý

Re[expr] ¸´Êý±í´ïʽµÄʵ²¿

Im[expr] ¸´Êý±í´ïʽµÄÐ鲿

Abs[expr] ¸´Êý±í´ïʽµÄÄ£

Arg[expr] ¸´Êý±í´ïʽµÄ·ø½Ç

Conjugate[expr] ¸´Êý±í´ïʽµÄ¹²éî

¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª

Ê®¡¢ÊýµÄÍ·¼°Ä£Ê½¼°ÆäËû²Ù×÷

Integer _Integer ÕûÊý

Real _Real ʵÊý

Complex _Complex ¸´Êý

Rational_Rational ÓÐÀíÊý

(*×¢£ºÄ£Ê½ÓÃÔÚº¯Êý²ÎÊý´«µÝÖУ¬ÈçMyFun[Para1_Integer,Para2_Real]

¹æ¶¨´«Èë²ÎÊýµÄÀàÐÍ£¬ÁíÍâÒ²¿ÉÓÃÀ´ÅжÏIf[Head[a]==Real,...]*)

IntegerDigits[n,b,len] Êý×ÖnÒÔb½üÖƵÄÇ°len¸öÂëÔª

RealDigits[x,b,len] ÀàÉÏ

FromDigits[list] IntegerDigitsµÄ·´º¯Êý

Rationalize[x,dx] °ÑʵÊýxÓÐÀí»¯³ÉÓÐÀíÊý£¬Îó²îСÓÚdx

Chop[expr, delta] ½«exprÖÐСÓÚdeltaµÄ²¿·ÖÈ¥µô,dxĬÈÏΪ10^-10

Accuracy[x] ¸ø³öxСÊý²¿·ÖλÊý,¶ÔÓÚPi,EµÈΪÎÞÏÞ´ó

Precision[x] ¸ø³öxÓÐЧÊý×ÖλÊý,¶ÔÓÚPi,EµÈΪÎÞÏÞ´ó

SetAccuracy[expr, n] ÉèÖÃexprÏÔʾʱµÄСÊý²¿·ÖλÊý

SetPrecision[expr, n] ÉèÖÃexprÏÔʾʱµÄÓÐЧÊý×ÖλÊý

¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª

ʮһ¡¢Çø¼äº¯Êý

Interval[{min, max}] Çø¼ä[min, max](* Solve[3 x+2==Interval[{-2,5}],x]*)

IntervalMemberQ[interval, x] xÔÚÇø¼äÄÚÂð£¿

IntervalMemberQ[interval1,interval2] Çø¼ä2ÔÚÇø¼ä1ÄÚÂð£¿

IntervalUnion[intv1,intv2...] Çø¼äµÄ²¢

IntervalIntersection[intv1,intv2...] Çø¼äµÄ½»

¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª

Ê®¶þ¡¢¾ØÕó²Ù×÷

a.b.c »ò Dot[a, b, c] ¾ØÕó¡¢ÏòÁ¿¡¢ÕÅÁ¿µÄµã»ý

Inverse[m] ¾ØÕóµÄÄæ

Transpose[list] ¾ØÕóµÄתÖÃ

Transpose[list,{n1,n2..}]½«¾ØÕólist µÚkÐÐÓëµÚnkÁн»»»

Det[m] ¾ØÕóµÄÐÐÁÐʽ

Eigenvalues[m] ÌØÕ÷Öµ

Eigenvectors[m] ÌØÕ÷ÏòÁ¿

Eigensystem[m] ÌØÕ÷ϵͳ£¬·µ»Ø{eigvalues,eigvectors}

LinearSolve[m, b] ½âÏßÐÔ·½³Ì×ém.x==b

NullSpace[m] ¾ØÕómµÄÁã¿Õ¼ä£¬¼´m.NullSpace[m]==ÁãÏòÁ¿

RowReduce[m] m»¯¼òΪ½×ÌݾØÕó

Minors[m, k] mµÄËùÓÐk*k½××Ó¾ØÕóµÄÐÐÁÐʽµÄÖµ(°éËæÕ󣬺ÃÏñÊÇ)

MatrixPower[mat, n] Õómat×Ô³Ën´Î

Outer[f,list1,list2..] listiÖи÷¸öÔªÖ®¼äÏ໥×éºÏ£¬²¢×÷ΪfµÄ²ÎÊýµÄµ½µÄ¾ØÕó

Outer[Times,list1,list2]¸ø³ö¾ØÕóµÄÍâ»ý

SingularValues[m] mµÄÆæÒìÖµ£¬½á¹ûΪ{u,w,v},

m=Conjugate[Transpose[u]].DiagonalMatrix[w].v

PseudoInverse[m] mµÄ¹ãÒåÄæ

QRDecomposition[m] QR·Ö½â

SchurDecomposition[m] Schur·Ö½â

LUDecomposition[m] LU·Ö½â

¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª

Ê®Èý¡¢±íº¯Êý

(*¡°±í¡±£¬ÎÒÈÏΪÊÇMathematicaÖÐ×îÁé»îµÄÒ»ÖÖÊý¾ÝÀàÐÍ *)

(*ʵ¼ÊÉϱí¾ÍÊDZí´ïʽ£¬±í´ïʽҲ¾ÍÊÇ±í£¬ËùÒÔÏÂÃælist==expr *)

(*Ò»¸ö±íÖÐÔªËصÄλÖÿÉÒÔÓÃÓÚÒ»¸ö±íÀ´±íʾ *)

±íµÄÉú³É

{e1,e2,...} Ò»¸ö±í£¬ÔªËØ¿ÉÒÔΪÈÎÒâ±í´ïʽ£¬ÎÞÇîǶÌ×

Table[expr,{imax}] Éú³ÉÒ»¸ö±í£¬¹²imax¸öÔªËØ

Table[expr,{i, imax}] Éú³ÉÒ»¸ö±í£¬¹²imax¸öÔªËØexpr[i]

Table[expr,{i,imin,imax},{j,jmin,jmax},..] ¶àά±í

Range[imax] ¼òµ¥Êý±í{1,2,..,imax}

Range[imin, imax, di] ÒÔdiΪ²½³¤µÄÊý±í

Array[f, n] һά±í£¬ÔªËØΪf[i] (i´Ó1µ½n)

Array[f,{n1,n2..}] ¶àά±í£¬ÔªËØΪf[i,j..] (¸÷×Ô´Ó1µ½ni)

IdentityMatrix[n] n½×µ¥Î»Õó

DiagonalMatrix[list] ¶Ô½ÇÕó

ÔªËزÙ×÷

Part[expr, i]»òexpr[[i]]µÚi¸öÔª

expr[[-i]] µ¹ÊýµÚi¸öÔª

expr[[i,j,..]] ¶àά±íµÄÔª

expr[[{i1,i2,..}] ·µ»ØÓɵÚi(n)µÄÔªËØ×é³ÉµÄ×Ó±í

First[expr] µÚÒ»¸öÔª

Last[expr] ×îºóÒ»¸öÔª

Head[expr] º¯ÊýÍ·£¬µÈÓÚexpr[[0]]

Extract[expr, list] È¡³öÓɱílistÖƶ¨Î»ÖÃÉÏexprµÄÔªËØÖµ

Take[list, n] È¡³ö±ílistÇ°n¸öÔª×é³ÉµÄ±í

Take[list,{m,n}] È¡³ö±ílist´Ómµ½nµÄÔªËØ×é³ÉµÄ±í

Drop[list, n] È¥µô±ílistÇ°n¸öԪʣÏÂµÄ±í£¬ÆäËû²ÎÊýͬÉÏ

Rest[expr] È¥µô±ílistµÚÒ»¸öԪʣϵıí

Select[list, crit] °Ñcrit×÷Óõ½Ã¿Ò»¸ölistµÄÔªÉÏ£¬

ΪTrueµÄËùÓÐÔª×é³ÉµÄ±í

±íµÄÊôÐÔ

Length[expr] exprµÚÒ»ÔøÔªËصĸöÊý

Dimensions[expr] ±íµÄάÊý·µ»Ø{n1,n2..},exprΪһ¸ön1*n2...µÄÕó

TensorRank[expr] ÖÈ

Depth[expr] expr×î´óÉî¶È

Level[expr,n] ¸ø³öexprÖеÚn²ã×Ó±í´ïʽµÄÁбí

Count[list, pattern] Âú×ãģʽµÄlistÖÐÔªµÄ¸öÊý

MemberQ[list, form] listÖÐÊÇ·ñÓÐÆ¥ÅäformµÄÔª

FreeQ[expr, form] MemberQµÄ·´º¯Êý

Position[expr, pattern] ±íÖÐÆ¥ÅäģʽpatternµÄÔªËصÄλÖÃÁбí

Cases[{e1,e2...},pattern]Æ¥ÅäģʽpatternµÄËùÓÐÔªËØeiµÄ±í

±íµÄ²Ù×÷

Append[expr, elem] ·µ»Ø ÔÚ±íexprµÄ×îºó×·¼ÓelemÔªºóµÄ±í

Prepend[expr, elem] ·µ»Ø ÔÚ±íexprµÄ×îÇ°Ìí¼ÓelemÔªºóµÄ±í

Insert[list, elem, n] ÔÚµÚnԪǰ²åÈëelem

Insert[expr,elem,{i,j,..}]ÔÚÔªËØexpr[[{i,j,..}]]Ç°²åÈëelem

ª¤ Delete[expr, {i, j,..}] ɾ³ýÔªËØexpr[[{i,j,..}]]ºóʣϵıí

DeleteCases[expr,pattern]ɾ³ýÆ¥ÅäpatternµÄËùÓÐÔªºóʣϵıí

ReplacePart[expr,new,n] ½«exprµÄµÚnÔªÌ滻Ϊnew

Sort[list] ·µ»Ølist°´Ë³ÐòÅÅÁеıí

Reverse[expr] °Ñ±íexprµ¹¹ýÀ´

RotateLeft[expr, n] °Ñ±íexprÑ­»·×óÒÆn´Î

RotateRight[expr, n] °Ñ±íexprÑ­»·ÓÒÒÆn´Î

Partition[list, n] °Ñlist°´Ã¿n¸÷ԪΪһ¸ö×Ó±í·Ö¸îºóÔÙ×é³ÉµÄ´ó±í

Flatten[list] ĨƽËùÓÐ×Ó±íºóµÃµ½µÄһά´ó±í

Flatten[list,n] Ĩƽµ½µÚn²ã

Split[list] °ÑÏàͬµÄÔª×é³ÉÒ»¸ö×Ó±í£¬ÔٺϳɵĴó±í

FlattenAt[list, n] °Ñlist[[n]]´¦µÄ×Ó±íĨƽ

Permutations[list] ÓÉlistµÄÔªËØ×é³ÉµÄËùÓÐÈ«ÅÅÁеÄÁбí

Order[expr1,expr2] Èç¹ûexpr1ÔÚexpr2֮ǰ·µ»Ø1,Èç¹ûexpr1ÔÚ

expr2Ö®ºó·µ»Ø-1,Èç¹ûexpr1Óëexpr2È«µÈ·µ»Ø0

Signature[list] °Ñlistͨ¹ýÁ½Á½½»»»µÃµ½±ê׼˳ÐòËùÐèµÄ

½»»»´ÎÊý(ÅÅÁÐÊý)

ÒÔÉϺ¯Êý¾ùΪ½ö·µ»ØËùÐè±í¶ø²»¸Ä±äÔ­±í

AppendTo[list,elem] Ï൱ÓÚlist=Append[list,elem];

PrependTo[list,elem] Ï൱ÓÚlist=Prepend[list,elem];

--¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª

Ê®ËÄ¡¢»æͼº¯Êý

¶þά×÷ͼ

Plot[f,{x,xmin,xmax}] һάº¯Êýf[x]ÔÚÇø¼ä[xmin,xmax]Éϵĺ¯ÊýÇúÏß

Plot[{f1,f2..},{x,xmin,xmax}] ÔÚÒ»ÕÅͼÉÏ»­¼¸ÌõÇúÏß

ListPlot[{y1,y2,..}] »æ³öÓÉÀëÉ¢µã¶Ô(n,yn)×é³ÉµÄͼ

ListPlot[{{x1,y1},{x2,y2},..}] »æ³öÓÉÀëÉ¢µã¶Ô(xn,yn)×é³ÉµÄͼ

ParametricPlot[{fx,fy},{t,tmin,tmax}] ÓɲÎÊý·½³ÌÔÚ²ÎÊý±ä»¯·¶Î§ÄÚµÄÇúÏß

ParametricPlot[{{fx,fy},{gx,gy},...},{t,tmin,tmax}]

ÔÚÒ»ÕÅͼÉÏ»­¶àÌõ²ÎÊýÇúÏß

Ñ¡Ï

PlotRange->{0,1} ×÷ͼÏÔʾµÄÖµÓò·¶Î§

AspectRatio->1/GoldenRatioÉú³ÉͼÐεÄ×ݺá±È

PlotLabel ->label ±êÌâÎÄ×Ö

Axes ->{False,True} ·Ö±ðÖƶ¨ÊÇ·ñ»­x,yÖá

AxesLabel->{xlabel,ylabel}x,yÖáÉϵÄ˵Ã÷ÎÄ×Ö

Ticks->None,Automatic,funÓÃʲô·½Ê½»­ÖáµÄ¿Ì¶È

AxesOrigin ->{x,y} ×ø±êÖáÔ­µãλÖÃ

AxesStyle->{{xstyle}, {ystyle}}ÉèÖÃÖáÏßµÄÏßÐÔÑÕÉ«µÈÊôÐÔ

Frame ->True,False ÊÇ·ñ»­±ß¿ò

FrameLabel ->{xmlabel,ymlabel,xplabel,yplabel}

±ß¿òËıßÉϵÄÎÄ×Ö

FrameTicksͬTicks ±ß¿òÉÏÊÇ·ñ»­¿Ì¶È

GridLines ͬTicks ͼÉÏÊÇ·ñ»­Õ¤¸ñÏß

FrameStyle ->{{xmstyle},{ymstyle}ÉèÖñ߿òÏßµÄÏßÐÔÑÕÉ«µÈÊôÐÔ

ListPlot[data,PlotJoined->True] °ÑÀëÉ¢µã°´Ë³ÐòÁ¬Ïß

PlotSytle->{{style1},{style2},..}ÇúÏßµÄÏßÐÔÑÕÉ«µÈÊôÐÔ

PlotPoints->15 ÇúÏßÈ¡Ñùµã£¬Ô½´óԽϸÖÂ

Èýά×÷ͼ

Plot3D[f,{x,xmin,xmax}, {y,ymin,ymax}]

¶þάº¯Êýf[x,y]µÄ¿Õ¼äÇúÃæ

Plot3D[{f,s}, {x,xmin,xmax}, {y,ymin,ymax}]

ͬÉÏ£¬ÇúÃæµÄȾɫÓÉs[x,y]Öµ¾ö¶¨

ListPlot3D[array] ¶þάÊý¾ÝÕóarrayµÄÁ¢Ìå¸ß¶Èͼ

ListPlot3D[array,shades]ͬÉÏ£¬ÇúÃæµÄȾɫÓÉshades[Êý¾Ý]Öµ¾ö¶¨

ParametricPlot3D[{fx,fy,fz},{t,tmin,tmax}]

¶þÔªÊý·½³ÌÔÚ²ÎÊý±ä»¯·¶Î§ÄÚµÄÇúÏß

ParametricPlot3D[{{fx,fy,fz},{gx,gy,gz},...},{t,tmin,tmax}]

¶àÌõ¿Õ¼ä²ÎÊýÇúÏß

Ñ¡Ï

ViewPoint ->{x,y,z} ÈýάÊӵ㣬ĬÈÏΪ{1.3,-2.4,2}

Boxed -> True,False ÊÇ·ñ»­Èýά³¤·½Ìå±ß¿ò

BoxRatios->{sx,sy,sz} ÈýÖá±ÈÀý

BoxStyle Èýά³¤·½Ìå±ß¿òÏßÐÔÑÕÉ«µÈÊôÐÔ

Lighting ->True ÊÇ·ñȾɫ

LightSources->{s1,s2..} siΪijһ¸ö¹âÔ´si={{dx,dy,dz},color}

colorΪµÆÉ«£¬Ïòdx,dy,dz·½ÏòÕÕÉä

AmbientLight->ÑÕÉ«º¯Êý ÂýÉ¢Éä¹âµÄ¹âÔ´

Mesh->True,False ÊÇ·ñ»­ÇúÃæÉÏÓëx,yÖáƽÐеĽØÃæµÄ½ØÏß

MeshStyle ½ØÏßÏßÐÔÑÕÉ«µÈÊôÐÔ

MeshRange->{{xmin,xmax}, {ymin,ymax}}Íø¸ñ·¶Î§

ClipFill->Automatic,None,color,{bottom,top}

Ö¸¶¨Í¼Ðζ¥²¿¡¢µ×²¿³¬½çºóËù»­µÄÑÕÉ«

Shading ->False,True ÊÇ·ñȾɫ

HiddenSurface->True,False ÂÔÈ¥±»ÕÚס²»ÏÔʾ²¿·ÖµÄÐÅÏ¢

µÈ¸ßÏß

ContourPlot[f,{x,xmin,xmax},{y,ymin,ymax}]

¶þάº¯Êýf[x,y]ÔÚÖ¸¶¨Çø¼äÉϵĵȸßÏßͼ

ListContourPlot[array] ¸ù¾Ý¶þάÊý×éarrayÊýÖµ»­µÈ¸ßÏß

Ñ¡Ï

Contours->n »­nÌõµÈ¸ßÏß

Contours->{z1,z2,..} ÔÚzi´¦»­µÈ¸ßÏß

ContourShading -> False ÊÇ·ñÓÃÉîdzȾɫ

ContourLines -> True ÊÇ·ñ»­µÈ¸ßÏß

ContourStyle -> {{style1},{style2},..}µÈ¸ßÏßÏßÐÔÑÕÉ«µÈÊôÐÔ

FrameTicks ͬÉÏ

ÃܶÈͼ

DensityPlot[f,{x,xmin,xmax},{y,ymin,ymax}]

¶þάº¯Êýf[x,y]ÔÚÖ¸¶¨Çø¼äÉϵÄÃܶÈͼ

ListDensityPlot[array] ͬÉÏ

ͼÐÎÏÔʾ

Show[graphics,options] ÏÔʾһ×éͼÐζÔÏó£¬optionsΪѡÏîÉèÖÃ

Show[g1,g2...] ÔÚÒ»¸öͼÉϵþ¼ÓÏÔʾһ×éͼÐζÔÏó

GraphicsArray[{g1,g2,...}]ÔÚÒ»¸öͼÉÏ·Ö¿éÏÔʾһ×éͼÐζÔÏó

SelectionAnimate[notebook,t]°ÑÑ¡ÖеÄnotebookÖеÄͼ»­Ñ­»··ÅÓ³

Ñ¡Ï(´Ë´¦Ñ¡ÏîÊÊÓÃÓÚÈ«²¿Í¼Ðκ¯Êý)

Background->ÑÕÉ«º¯Êý Ö¸¶¨»æͼµÄ±³¾°ÑÕÉ«

RotateLabel -> True Êú×ÅдÎÄ×Ö

TextStyle ´ËºóÊä³öÎÄ×ÖµÄ×ÖÌ壬ÑÕÉ«´óСµÈ

ColorFunction->HueµÈ °ÑÆä×÷ÓÃÓÚijµãµÄº¯ÊýÖµÉϾö¶¨Ä³µãµÄÑÕÉ«

RenderAll->False ÊÇ·ñ¶ÔÕÚµ²²¿·ÖҲȾɫ

MaxBend ÇúÏß¡¢ÇúÃæ×î´óÍäÇú¶È

»æͼº¯Êý£¨Ðø£©

ͼԪº¯Êý

Graphics[prim, options]

primΪÏÂÃæ¸÷ÖÖº¯Êý×é³ÉµÄ±í£¬±íʾһ¸ö¶þάͼÐζÔÏó

Graphics3D[prim, options]

primΪÏÂÃæ¸÷ÖÖº¯Êý×é³ÉµÄ±í£¬±íʾһ¸öÈýάͼÐζÔÏó

SurfaceGraphics[array, shades]±íʾһ¸öÓÉarrayºÍshade¾ö¶¨µÄÇúÃæ¶ÔÏó

ContourGraphics[array]±íʾһ¸öÓÉarray¾ö¶¨µÄµÈ¸ßÏßͼ¶ÔÏó

DensityGraphics[array]±íʾһ¸öÓÉarray¾ö¶¨µÄÃܶÈͼ¶ÔÏó

ÒÔÉ϶¨ÒåͼÐζÔÏ󣬿ÉÒÔ½øÐжԱäÁ¿¸³Öµ£¬ºÏ²¢ÏÔʾµÈ²Ù×÷£¬Ò²¿ÉÒÔ´æÅÌ

Point[p] p={x,y}»ò{x,y,z}£¬ÔÚÖ¸¶¨Î»Öû­µã

Line[{p1,p2,..}]¾­ÓÉpiµãÁ¬Ïß

Rectangle[{xmin, ymin}, {xmax, ymax}] »­¾ØÐÎ

Cuboid[{xmin,ymin,zmin},{xmax,ymax,zmax}]ÓɶԽÇÏßÖ¸¶¨µÄ³¤·½Ìå

Polygon[{p1,p2,..}] ·â±Õ¶à±ßÐÎ

Circle[{x,y},r] »­Ô²

Circle[{x,y},{rx,ry}] »­ÍÖÔ²£¬rx,ryΪ°ë³¤¶ÌÖá

Circle[{x,y},r,{a1,a2}] ´Ó½Ç¶Èa1¡«a2µÄÔ²»¡

Disk[{x, y}, r] Ìî³äµÄÔ°¡¢ÍÖÔ²¡¢Ô²»¡µÈ²ÎÊýͬÉÏ

Raster[array,ColorFunction->f] ÑÕÉ«Õ¤¸ñ

Text[expr,coords] ÔÚ×ø±êcoordsÉÏÊä³ö±í´ïʽ

PostScript["string"] Ö±½ÓÓÃPostScriptͼԪÓïÑÔд

Scaled[{x,y,..}] ·µ»ØµãµÄ×ø±ê£¬ÇÒ¾ù´óÓÚ0СÓÚ1

ÑÕÉ«º¯Êý(Ö¸¶¨Æäºó»æͼµÄÑÕÉ«)

GrayLevel[level] »Ò¶ÈlevelΪ0~1¼äµÄʵÊý

RGBColor[red, green, blue] RGBÑÕÉ«£¬¾ùΪ0~1¼äµÄʵÊý

Hue[h, s, b] ÁÁ¶È£¬±¥ºÍ¶ÈµÈ£¬¾ùΪ0~1¼äµÄʵÊý

CMYKColor[cyan, magenta, yellow, black] CMYKÑÕÉ«

ÆäËûº¯Êý(Ö¸¶¨Æäºó»æͼµÄ·½Ê½)

Thickness[r] ÉèÖÃÏß¿íΪr

PointSize[d] ÉèÖûæµãµÄ´óС

Dashing[{r1,r2,..}] ÐéÏßÒ»¸öµ¥ÔªµÄ¼ä¸ô³¤¶È

ImageSize->{x, y} ÏÔʾͼÐδóС(ÏñËØΪµ¥Î»)

ImageResolution->r ͼÐνâÎö¶Èr¸ödpi

ImageMargins->{{left,right},{bottom,top}}ËıߵĿհ×

ImageRotated->False ÊÇ·ñÐýת90¶ÈÏÔʾ

¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª

Ê®Îå¡¢Á÷³Ì¿ØÖÆ

·ÖÖ§

If[condition, t, f] Èç¹ûconditionΪTrue,Ö´ÐÐt¶Î£¬·ñÔòf¶Î

If[condition, t, f, u] ͬÉÏ£¬¼´·ÇTrueÓÖ·ÇFalse£¬ÔòÖ´ÐÐu¶Î

Which[test1,block1,test2,block2..] Ö´ÐеÚһΪTrueµÄtesti¶ÔÓ¦µÄblocki

Switch[expr,form1,block1,form2,block2..]

Ö´ÐеÚÒ»¸öexprËùÆ¥ÅäµÄformiËù¶ÔÓ¦µÄblocki¶Î

Ñ­»·

Do[expr,{imax}] Öظ´Ö´ÐÐexpr imax´Î

Do[expr,{i,imin,imax}, {j,jmin,jmax},...]¶àÖØÑ­»·

While[test, body] Ñ­»·Ö´ÐÐbodyÖ±µ½testΪFalse

For[start,test,incr,body]ÀàËÆÓÚCÓïÑÔÖеÄfor£¬×¢Òâ"£¬"Óë";"µÄÓ÷¨Ïà·´

examp: For[i=1;t =x,i^2<10,i++,t =t+i;Print[t]]

Òì³£¿ØÖÆ

Throw[value] Í£Ö¹¼ÆË㣬°Ñvalue·µ»Ø¸ø×î½üÒ»¸öCatch´¦Àí

Throw[value, tag] ͬÉÏ£¬

Catch[expr] ¼ÆËãexpr,Óöµ½Throw·µ»ØµÄÖµÔòÍ£Ö¹

Catch[expr, form] µ±Throw[value, tag]ÖÐTagÆ¥Åäformʱֹͣ

ª¤ ÆäËû¿ØÖÆ

Return[expr] ´Óº¯Êý·µ»Ø£¬·µ»ØֵΪexpr

Return[ ] ·µ»ØÖµNull

Break[ ] ½áÊø×î½üµÄÒ»ÖØÑ­»·

Continue[ ] Í£Ö¹±¾´ÎÑ­»·£¬½øÐÐÏÂÒ»´ÎÑ­»·

Goto[tag] ÎÞÌõ¼þתÏòLabel[Tag]´¦

Label[tag] ÉèÖÃÒ»¸ö¶Ïµã

Check[expr,failexpr] ¼ÆËãexpr,Èç¹ûÓгö´íÐÅÏ¢²úÉú£¬Ôò·µ»ØfailexprµÄÖµ

Check[expr,failexpr,s1::t1,s2::t2,...]µ±Ìض¨ÐÅÏ¢²úÉúʱÔò·µ»Øfailexpr

CheckAbort[expr,failexpr]µ±²úÉúabortÐÅϢʱ·Å»Øfailexpr

Interrupt[ ] ÖжÏÔËÐÐ

Abort[ ] ÖжÏÔËÐÐ

TimeConstrained[expr,t] ¼ÆËãexpr£¬µ±ºÄʱ³¬¹ýtÃëʱÖÕÖ¹

MemoryConstrained[expr,b]¼ÆËãexpr£¬µ±ºÄÓÃÄڴ泬¹ýb×Ö½ÚʱÖÕÖ¹ÔËËã

½»»¥Ê½¿ØÖÆ

Print[expr1,expr2,...] ˳´ÎÊä³öexpriµÄÖµ

examp: Print[ "X=" , X//N , " " ,f[x+1]];

Input[ ] ²úÉúÒ»¸öÊäÈë¶Ô»°¿ò£¬·µ»ØËùÊäÈëÈÎÒâ±í´ïʽ

Input["prompt"] ͬÉÏ£¬promptΪ¶Ô»°¿òµÄÌáʾ

Pause[n] ÔËÐÐÔÝÍ£nÃë

¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª

Ê®Áù¡¢º¯Êý±à³Ì

(*º¯Êý±à³ÌÊÇMathematicaÖкÜÓÐÌØÉ«Ò²ÊÇ×îÁé»îµÄÒ»²¿·Ö£¬Ëü³ä·ÖÌåÏÖÁË *)

(*MathematicaµÄ¡°Ò»Çж¼ÊDZí´ïʽ¡±µÄÌص㣬Èç¹ûÄãÏëʹÄãµÄMathematica³Ì *)

(*Ðò¿ìÓڸ߼¶ÓïÑÔ,½¨ÒéÄã°Ñ±¾²¿·Ö¸ãͨ*)

´¿º¯Êý

Function[body]»òbody& Ò»¸ö´¿º¯Êý£¬½¨Á¢ÁËÒ»×é¶ÔÓ¦·¨Ôò£¬×÷Óõ½ºóÃæµÄ±í´ïʽÉÏ

Function[x, body] µ¥×Ô±äÁ¿´¿º¯Êý

Function[{x1,x2,...},body]¶à×Ô±äÁ¿´¿º¯Êý

#£¬#n ´¿º¯ÊýµÄµÚÒ»¡¢µÚn¸ö×Ô±äÁ¿

## ´¿º¯ÊýµÄËùÓÐ×Ô±äÁ¿µÄÐòÁÐ

examp: ^& [2,3] ·µ»ØµÚÒ»¸ö²ÎÊýµÄµÚ¶þ¸ö²ÎÊý´Î·½

Ó³Éä

Map[f,expr]»òf/@expr ½«f·Ö±ð×÷Óõ½exprµÚÒ»²ãµÄÿһ¸öÔªÉϵõ½µÄÁбí

Map[f,expr,level] ½«f·Ö±ð×÷Óõ½exprµÚlevel²ãµÄÿһ¸öÔªÉÏ

Apply[f,expr]»òf@@expr ½«exprµÄ¡°Í·¡±»»Îªf

Apply[f,expr,level] ½«exprµÚlevel²ãµÄ¡°Í·¡±»»Îªf

MapAll[f,expr]»òf//@expr°Ñf×÷Óõ½exprµÄÿһ²ãµÄÿһ¸öÔªÉÏ

MapAt[f,expr,n] °Ñf×÷Óõ½exprµÄµÚn¸öÔªÉÏ

MapAt[f,expr,{i,j,...}] °Ñf×÷Óõ½expr[[{i,j,...}]]ÔªÉÏ

MapIndexed[f,expr] ÀàËÆMapAll,µ«¶¼¸½¼ÓÆäÓ³ÉäÔªËصÄλÖÃÁбí

Scan[f, expr] °´Ë³Ðò·Ö±ð½«f×÷ÓÃÓÚexprµÄÿһ¸öÔª

Scan[f,expr,levelspec] ͬÉÏ£¬½ö×÷ÓõÚlevel²ãµÄÔªËØ

¸´ºÏÓ³Éä

Nest[f,expr,n] ·µ»ØnÖظ´ºÏº¯Êýf[f[...f[expr]...]]

NestList[f,expr,n] ·µ»Ø0Öص½nÖظ´ºÏº¯ÊýµÄÁбí{expr,f[expr],f[f[expr]]..}

FixedPoint[f, expr] ½«f¸´ºÏ×÷ÓÃÓÚexprÖ±µ½½á¹û²»Ôٸıä,¼´ÕÒµ½Æä²»¶¨µã

FixedPoint[f, expr, n] ×î¶à¸´ºÏn´Î£¬Èç¹û²»ÊÕÁ²ÔòÍ£Ö¹

FixedPointList[f, expr] ·µ»Ø¸÷´Î¸´ºÏµÄ½á¹ûÁбí

FoldList[f,x,{a,b,..}] ·µ»Ø{x,f[x,a],f[f[x,a],b],..}

Fold[f, x, list] ·µ»ØFoldList[f,x,{a,b,..}]µÄ×îºóÒ»¸öÔª

ComposeList[{f1,f2,..},x]·µ»Ø{x,f1[x],f2[f1[x]],..}µÄ¸´ºÏº¯ÊýÁбí

Distribute[f[x1,x2,..]] f¶Ô¼Ó·¨µÄ·ÖÅäÂÊ

Distribute[expr, g] ¶ÔgµÄ·ÖÅäÂÊ

Identity[expr] exprµÄÈ«µÈ±ä»»

Composition[f1,f2,..] ×é³É¸´ºÏ´¿º¯Êýf1[f2[..fn[ ]..]

Operate[p,f[x,y]] ·µ»Øp[f][x, y]

Through[p[f1,f2][x]] ·µ»Øp[f1[x],f2[x]]

Compile[{x1,x2,..},expr]±àÒëÒ»¸öº¯Êý£¬±àÒëºóÔËÐÐËٶȿÉÒÔ´ó´ó¼Ó¿ì

Compile[{{x1,t1},{x2,t2}..},expr] ͬÉÏ£¬¿ÉÒÔÖƶ¨º¯Êý²ÎÊýÀàÐÍ

¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª¡ª

Ê®Æß¡¢Ìæ»»¹æÔò

lhs->rhs ½¨Á¢ÁËÒ»¸ö¹æÔò£¬°Ñlhs»»Îªrhs,²¢ÇórhsµÄÖµ

lhs:>rhs ͬÉÏ£¬Ö»ÊDz»Á¢¼´ÇórhsµÄÖµ£¬ÖªµÀʹÓøùæÔòʱ²ÅÇóÖµ

Replace[expr,rules] °ÑÒ»×é¹æÔòÓ¦Óõ½exprÉÏ£¬Ö»×÷ÓÃÒ»´Î

expr /. rules ͬÉÏ

expr //.rules ½«¹æÔòrules²»¶Ï×÷Óõ½exprÉÏ£¬Ö±µ½ÎÞ·¨×÷ÓÃΪֹ

Dispatch[{lhs1->rhs1,lhs2->rhs2,...}]×ۺϸ÷¸ö¹æÔò£¬²úÉúÒ»×éÓÅ»¯µÄ¹æÔò×é

>************************************************************************<

MathematicaµÄ³£¼ûÎÊÌâ

>************************************************************************<

===================================

1).Mathematica ¿ÉÒÔ¶¨Òå±äÁ¿ÎªÊµÊýô£¿

1. ÔÚSimplify/FullSimplify¿ÉÒÔʹÓÃ\[Element]£¬Èç

Simplify[Re[a+b*I],a\[Element]Reals]

2. ¿ÉÒÔʹÓÃComplexExpand[]À´Õ¹¿ª±í´ïʽ£¬Ä¬ÈÏ£º·ûºÅ¾ùΪʵÊý£º

Unprotect[Abs];

Abs[x_] := Sqrt[Re[x]^2 + Im[x]^2];

ComplexExpand[Abs[a + b*I], a]

3. ʹÓÃ/:£¬¶Ô·ûºÅ¹ØÁªÏàÓ¦µÄת»»¹æÔò

x /: Im[x] = 0;

x /: Re[x] = x;

y /: Im[y] = 0;

y /: Re[y] = y;

Re[x+y*I]

===================================

2).MathematicaÖÐÈçºÎÖжÏÔËË㣿

Alt+. Ö±½ÓÖÕÖ¹µ±Ç°Ö´ÐеÄÔËËã

Alt+, ѯÎÊÊÇ·ñÖÕÖ¹»òÕß¼ÌÐø

Èç¹û²»ÄÜÖÕÖ¹£¬Óò˵¥Kernel\Quit Kernal\LocalÀ´Í˳öµ±Ç°ÔËËã

===================================

3).Çë¸ßÊÖÍƼöMathematica²Î¿¼Êé

ÎÒÆù½ñΪֹ¿´µ½µÄ×îºÃµÄÒ»±¾¾ÍÊÇMathematica×Ô¼º´øµÄ°ïÖúÀïÃæµÄThe Mathematica Book£¬ÄÚÈÝÈ«Ã棬ѭÐò½¥½ü£¬·Ç³£ÈÝÒ×ѧϰʹÓá£ÆäËûËù¼ûµ½µÄһЩÖÐÎÄÊé¼®»ù±¾É϶¼ÊÇÖ±½Ó·­Òë°ïÖúµÄÄÚÈÝ£¬Ã»ÓÐʲô

ÐÂÒâ¡£

===================================

4).ÇëÎÊÔÚMathematicaÖÐÈçºÎ»­¼«×ø±êͼ?

<< Graphics`Graphics`

PolarPlot[]

PolarListPlot[]

===================================

5).MathematicaÖÐÈçºÎ¶ÔÀëÉ¢µã×÷»ý·Ö£¿

ÀëÉ¢µÄµãͨ¹ý²åÖµ»òÕßÄâºÏ¾Í¿ÉÒԵõ½Á¬ÐøµÄº¯Êý£¬È»ºó¿ÉÒԶԸú¯ÊýÇó»ý·ÖºÍ΢·Ö¡£ÏÂÃæÊÇÒ»¸öÀý×Ó£º

f[x_] := NIntegrate[Sin[Cos[x]], {x, 0, a}];

data = Table[{a, f[x]}, {a, 0, 10}];

expr = Interpolation[data];

Plot[expr[a], {a, 0, 10}];

Plot[Evaluate[D[expr[a], a]], {a, 0, 10}]

Èç¹ûÏëʵÏÖMatlabÖеÄcumsumµÄ¹¦ÄÜ£º

Drop[FoldList[Plus, 0, {a1,a2,¡­,an}], 1]

===================================

6).ÔÚMathematicaÖд´Á¢palette£¿

ÔÚ°ïÖúÖвéÕÒ"Creating Palettes (Windows)"

===================================

7).Mathematica¿ÉÒÔ×÷Óû§½çÃæÂð?

MathematicaµÄGUIÉè¼ÆÊÇͨ¹ýËüµÄ½»»¥Ê½µÄNoteBookʵÏֵģ¬¿ÉÒԲο¼Mathematica°ïÖúÎļþÖеÄdemoÀý×Ó£¬»ò²Î¿¼°ïÖú2.10.6

===================================

8).MathematicaÖÐÈçºÎʹÓÃÖÐÎÄ?

Mathematica3/4/4.1ÖÐÈç¹ûʹÓÃÖÐÎÄ£¬ÐèÒªÏÈÑ¡ÖÐËùÔÚµÄcell£¬»òÕßÑ¡ÖÐÊäÈëµÄÖÐÎÄÂÒÂ룬Ôڲ˵¥format fontÖÐÑ¡ÖжÔÓ¦µÄÖÐÎÄ×ÖÌåºó²ÅÄÜÕýÈ·ÏÔʾ¡£

×îеÄ4.2ÔÚ¹ú¼Ê»¯ÓнϴóµÄ¸Ä½ø£¬¿ÉÒÔÖ±½ÓÊäÈëÖÐÎÄ£¬²Î¼û

http://www.wolfram.com/products/mathematica/newin42/publishing.html

===================================

9).MathematicaÖÐÈçºÎʹÓÃSolve[]Çó½âµÄ½á¹û£¿

Solve[]Çó½âµÄ½á¹ûÊÇÒÔÒ»¸ö"±í"»òÕß"Ìæ»»¹æÔò"µÄÐÎʽ¸ø³öÀ´µÄ£¬²¢Ã»Óаѽá¹ûÕæÕýÌæ»»¸øδ֪Á¿¡£Èç¹û

sol = Solve[a*x^2 + b*x + c == 0, x];

x=x /. sol[[1]]

Ò²¿ÉÒÔʹÓöԱíÔªËصIJÙ×÷°Ñ½á¹ûÈ¡³öÀ´£¬±ÈÈçÔÚÉÏÃæµÄÀý×ÓÖУº

x1=sol[[1,1,2]]

x2=sol[[2,1,2]]