Math commands - Reference

Transcription

1 Mth commnds - Reference Unry / inry opertors Opertion Commnd Disply +sign sign 1 1 +/ sign + 1 or plusminus 1 ±1 or ±1 /+ sign +1 or minusplus 1 1 or 1 Addition Sutrction ( ) Dot product cdot Multipliction (X) times Multipliction (sterisk) * Division (s frction) over Division (s n opertor) div Division (with slsh) / / Conctention circ Division (with wide slsh) Wide ckslsh wideslsh wideslsh Boolen not neg Boolen nd nd or & or Boolen or or or or Bckslsh slsh Direct sum oplus ominus Tensoril product otimes odot odivide Customizle unry opertor uoper monop monop Customizle inry opertor oper monop monop 48 LireOffice 4.0 Mth Guide

2 Reltions Opertion Commnd Disply Is equl = = Is not equl <> or neq or Less thn < or lt < or < Less thn or equl to <= leslnt Very smll ll or << or Greter thn > or gt > or > Greter thn or equl to >= geslnt Very ig gg or >> or Approximtely pprox Similr to sim Similr to or equl simeq Congruent equiv Proportionl prop Prllel prllel Orthogonl to ortho Divides divides Does not divide ndivides Towrd towrd Arrow left dlrrow Doule rrow left nd right dlrrrow Arrow right drrrow Precedes prec Succeeds succ Precedes or equl to preccurlyeq Succeeds or equl to succcurlyeq Precedes or equl to precsim Succeeds or equl to succsim Does not precede nprec Does not succeed nsucc Definition def Imge from trnsl Origin from trnsr Mth commnds - Reference 49

3 Set opertions Opertion Commnd Disply Is in in B B Is not in notin B B Owns A owns or A ni A or A Intersection A intersection B A B Union A union B A B Difference A setminus B A B Quotient A slsh B A/ B Suset A suset B A B Suset or equl to A suseteq B A B Superset A supset B A B Superset or equl to A supseteq B A B Not suset A nsuset B A B Not suset or equl A nsuseteq B A B Not superset A nsupset B A B Not superset or equl A nsupseteq B A B Empty set emptyset Aleph leph ℵ Set of nturl numers setn N Set of integers setz Z Set of rtionl numers setq Q Set of rel numers setr R Set of complex numers setc C 50 LireOffice 4.0 Mth Guide

4 Functions Opertion Commnd Disply Asolute vlue s{} Fctoril fct{}! Squre root sqrt{} n th n root nroot{n}{} Power ^{} Exponentil func e^{} e Nturl logrithm ln() ln() Exponentil function exp() exp() Logrithm log() log() Sine sin() sin() Cosine cos() cos() Tngent tn() tn() Cotngent cot() cot() Hyperolic sine sinh() sinh() Hyperolic cosine cosh() cosh() Hyperolic tngent tnh() tnh() Hyperolic cotngent coth() coth() Arcsine rcsin() rcsin() Arccosine rccos() rccos() Arctngent rctn() rctn() Arccotngent rccot() rccot() Are hyperolic sine rsinh() rsinh() Are hyperolic cosine rcosh() rcosh() Are hyperolic tngent rtnh() rtnh() Are hyperolic cotngent rcoth() rcoth() Mth commnds - Reference 51

5 Opertors All opertors cn e used with the limit functions ( from nd to ). Opertion Commnd Disply Limit lim{} lim Lower limit liminf{} lim inf Upper limit limsup{} lim sup Sum sum{} Product prod{} Coproduc coprod{} Integrl int{} Doule integrl iint{} Triple integrl iiint{} Contour integrl lint Doule curved integrl llint Triple curved integrl lllint Lower ound shown with summtion symol Upper ound shown with product symol sum from {3} 3 prod to {3} r 3 r Upper nd lower ounds shown with integrl int from {r_0} to {r_t} r t r 0 Customized opertor oper Op from 0 to 1 1 Op 0 52 LireOffice 4.0 Mth Guide

6 Attriutes Opertion Commnd Disply Acute ccent cute á Grve ccent grve à Reverse circumflex check ǎ Breve reve ă Circle circle å Dot dot ȧ Doule dot ddot ä Triple dot dddot Line ove r ā Vector rrow vec Tilde tilde ã Circumflex ht â Wide vector rrow widevec c c Wide tilde widetilde c ãc Wide circumflex wideht c âc Line over overline c c Line under underline c c Line through overstrike c c Trnsprent (useful to get plceholder of given size) phntom Bold font old Not old font nold Itlic font9 itl "" or itlic "" or Not itlic font nitlic Font size size 16 qv qv Font size size +12 qv qv Font size size *1.5 qv qv Following item in sns serif font10 font sns qv qv Following item in serif font font serif qv qv 9 Unquoted text tht is not commnd is considered to e vrile. Vriles re, y defult, itlicized. 10 There re three custom fonts: sns serif (without kicks), serifs (with kicks), nd fixed (non-proportionl). To chnge the ctul fonts used for custom fonts nd the fonts used for vriles (unquoted text), numers nd functions, use Formt > Fonts (see pge 25). Mth commnds - Reference 53

7 Opertion Commnd Disply Following item in fixed font font fixed qv qv Mke color of following text cyn11 color cyn qv qv Mke color of following text yellow color yellow qv qv Mke color of following text white color white qv qv Mke color of following text green color green qv qv Mke color of following text lue color lue qv qv Mke color of following text red color red qv qv Mke color of following text lck color lck qv qv Mke color of following text mgent color mgent qv qv Mke color green returns to defult color lck Brce items to chnge color of more thn one item Brckets color green X qv color green {X qv} Opertion Commnd Disply Group rckets (used for progrm control) {} Round Brckets () () Squre Brckets [] [] Doule Squre Brckets ldrcket c rdrcket c Brces lrce w rrce {w } Angle Brckets lngle d rngle d Opertor Brckets lngle mline rngle Upper hlf squre rckets lceil rceil Lower hlf squre rckets lfloor rfloor Single line lline rline Doule line ldline rdline Sclle round rckets (dd the word left efore left rcket nd right efore right rcket) Squre rckets sclle (s ove) left ( stck{ # # z} right ) ( left [ over right ] [ ] z) X qv X qv 11 For ll coloring, the color will pply only to the text immeditely following the commnd until the next spce is encountered. In order to hve the color pply to more chrcters, plce the text you wnt in color in curly rckets. 54 LireOffice 4.0 Mth Guide

8 Opertion Commnd Disply Doule squre rckets sclle Brce sclle Angle rcket sclle Opertor rckets sclle Upper hlf squre rckets sclle Lower hlf squre rckets sclle Line sclle Doule line sclle Unpired rckets (dd left efore left rcket nd right efore right rcket) Isolted rcket Over rce sclle Under rce sclle left ldrcket over right rdrcket left lrce over right rrce { } left lngle over right rngle left lngle over mline c right rngle c left lceil over right rceil left lfloor over right rfloor left lline over right rline left ldline over right rdline left lngle over right rfloor left lrce stck {=2#=3} right none { =2 =3 {the rce is ove} overrce {the rce is elow} underrce {f} the rce is ove therce is elow f Mth commnds - Reference 55

9 Formts Opertion Commnd Disply Right superscript ^{} Right suscript _{} Left superscript lsup{} Left suscript lsu{} Center superscript csup{} Center suscript csu{} New line sldkfjo newline sdkfj sldkfjo sdkfj Smll gp (grve) stuff `stuff stuff stuff Lrge gp (tilde) stuff~stuff stuff stuff No gp nospce { x + y } x + y Norml x+y x+ y Verticl stck of 2 inom{}{} Verticl stck, more thn 2 stck{ # # z} Mtrix Align chrcter to left (text is ligned center y defult) Align chrcter to center Align chrcter to right Equtions ligned t '=' (using 'mtrix') Equtions ligned t '=' (using 'phntom') mtrix{ # ## c # d } stck{hello world # lignl()} stck{ Hello world # lignc()} stck{ Hello world # lignr()} mtrix{ # "=" # lignl{} ## {} # "=" # lignl{c+1} } stck{ lignl{} = # lignl{phntom{} = c+1} } z c d Hello world () Hello world () Hello world () = =c+1 = =c+1 56 LireOffice 4.0 Mth Guide

10 Others Opertion Commnd Disply Infinity infinity or infty or Prtil prtil Nl nl There exists exists There does not exist notexists For ll forll H r hr ħ Lmd r lmdr ƛ Rel prt re R Imginry prt im I Weierstrss p wp Reversed epsilon ckepsilon Left rrow leftrrow Right rrow rightrrow Up rrow uprrow Down rrow downrrow Dots t ottom dotslow Dots t middle dotsxis Dots verticl dotsvert Dots digonl upwrd dotsup or dotsdig or Dots digonl downwrd dotsdown Mth commnds - Reference 57

11 Cution In loclized versions of Writer, the mrkup nmes of Greek nd specil chrcters re loclized. If this document is not loclized to the sme lnguge, then the nmes elow my not work for input. You my still use the Symol ctlog (Figure 9) to select the desired chrcter y its glyph. This will lso disply the chrcter's loclized mrkup nme. Once entered, the chrcters will disply properly in ny lnguge. Contrry to commnds, specil chrcters re cse sensitive. Chrcters Greek Itlic chrcters cn e otined y dding n i fter the per cent chrcter. For instnce, %ipi Π insted of %PI Π. %ALPHA Α %BETA Β %GAMMA Γ %DELTA Δ %EPSILON Ε %ZETA Ζ %ETA Η %THETA Θ %IOTA Ι %KAPPA Κ %LAMBDA Λ %MU Μ %NU Ν %XI Ξ %OMICRON Ο %PI Π %RHO Ρ %SIGMA Σ %TAU Τ %UPSILON Υ %PHI Φ %CHI Χ %PSI Ψ %OMEGA Ω %lph α %et β %gmm γ %delt δ %epsilon ϵ %vrepsilon ε %zet ζ %et η %thet θ %vrthet ϑ %iot ι %kpp κ %lmd λ %mu μ %nu ν %xi ξ %omicron ο %pi π %vrpi ϖ %rho ρ %vrrho ϱ %sigm σ %vrsigm ς %tu τ %upsilon υ %phi ϕ %vrphi φ %chi χ %psi ψ %omeg ω Chrcters Specil Some specil chrcters correspond to the sme symol s n opertor ut there is no syntx verifiction (presence of left or right elements). %perthousnd %tendto %element %noelement %infinite %ngle %nd %or %notequl %identicl %strictlygreterthn %strictlylessthn 58 LireOffice 4.0 Mth Guide

12 Reserved words in lphetic order A reserved word is n expression with prticulr use nd is controlled y LireOffice. You cnnot use it s vrile nme. To e le to use these words without interference from Mth, you need to plce them etween ". The commented list follows. ` : smll spce. See grve opertor. ^ : superscript. See ht nd wideht opertors. _ : suscript - : sutrction -+ : '-+' sign with '-' over '+'. : point; need chrcter efore ( : opening prenthesis ) : closing prenthesis [ : opening squre rcket ] : closing squre rcket { : opening rcket for grouping chrcters } : closing rcket for grouping chrcters * : product / : division on one line \ : efore rcket (squre rcket, prenthesis or rce), tret it s norml chrcter. See slsh nd setminus opertors. & : Boolen opertor 'nd' # : seprtion etween elements in tle ## : seprtion etween lines in mtrix % : indicte specil nme (displyed if nme not recognized) %% : comment + : ddition +- : '+-' sign with '+' over '-' < : opertor less thn <?> : indicte plceholder round opertors uilt with models. Displyed s smll squre in the formul. F4 nd Mj+F4 keys to nvigte through them. << : opertor much less thn <= : opertor less or equl <> : opertor different = : opertor equlity > : opertor greter thn >= : opertor greter or equl >> : opertor much greter thn : logicl opertor or ~ : lrge spce. See opertor tilde. s : function solute vlue cute : cute ccent for one chrcter leph : 1 st letter of Herew lphet (crdinl numer). lign : (ottom verticl lignment) 12 lignc : centered horizontl lignment 12 These osolete shortcuts re for lignottom, lign-mid nd lign-top, (verticl lignments). Mth recognizes them, ut nothing is chnged. lignl : left lignment lignm : (centered verticl lignment) 12 lignr : right lignment lignt : (top verticl lignment) 12 nd : logicl opertor nd pprox : sign pproximtely, two ~ one over ech rccos : function rc cosine rccot : function rc cotngent rcosh : re hyperolic cosine rcoth : re hyperolic cotngent rcsin : function rc sine rctn : function rc tngent rsinh : function re hyperolic sinus rtnh : function re hyperolic tngent ckepsilon : upside down epsilon. r : dd r to next chrcter. inom : put 2 elements one over ech lck : lck color for 'color' lue : lue color for 'color' old : old font oper : next chrcter is treted s inry opertor (unchnged size) reve : hlf circle turned up slsh : opertor \, s difference cdot : opertor '.' for multipliction check : upside down circumflex ccent circ : 'round' opertor for composition of functions circle : dd circle over next chrcter color : set color: lck, lue, cyn, green, mgent, red, white, yellow coprod : coproduct (upside down Π) or direct sum cos : function cosine cosh : hyperolic cosine cot : cotngent coth : hyperolic cotngent csu : centered suscript csup : centered superscript cyn : cyn color for 'color' dddot : dd three points over: triple derivtive in physics ddot : dd two points over: doule derivtive in physics def : equl sign with DEF overwritten div : divide sign ':' with '-' in the middle divides : opertor (Sheffer r), sme s logicl sign or dlrrow : left doule rrow dlrrrow : left nd right doule rrow (equivlent) Mth commnds - Reference 59

13 dot : dd point over: derivtive in physics dotsxis : lign... horizontlly in the middle dotsdig : lign three points with +45 slop dotsdown : lign three points with -45 slop dotslow : lign... on the ottom dotsup : lign three points with +45 slop dotsvert : lign verticlly 3 points downrrow : down rrow drrrow : right doule rrow (imply) emptyset : empty set equiv : equivlent (equl sign with three strikes) exists : there exist (reversed E) exp : exponentil function fct : fctoril function (dd '!' fter) fixed : font ttriute font : select font forll : whtever (upside down A) from : goes with 'to' for limits of integrls, sums, etc. func : trnsforms vrile in function ge : greter or equl, horizontl = sign geslnt : greter or equl, olique = sign gg : much greter then '>>' grve : dd grve ccent green : green color for 'color' gt : opertor plus grnd que ht : dd circumflex ccent hr : strik h (h), reduced Plnck s constnt (divided y π) iiint : triple integrl, three times integrl sign iint : doule integrl, twice integrl sign im : function imginry prt in : is element of infinity : infinity symol infty : infinity symol int : simple integrl intersection : intersection opertor itl : itlicized font itlic : itlicized font lmdr : strike lmd lngle : < to open '<...>' (ngulr rcket opertor: lngle... mline... rngle) lrce : visile left rce '{' lceil : left squre rcket without ottom ldrcket : doule left squre rcket ldline : left doule line (norm) ' ' le : less or equl, horizontl = sign left : next chrcter is treted s n opening rcket leftrrow : left rrow leslnt : less or equl, olique = sign lfloor : left squre rcket without top lim : limit opertor liminf : inferior limit opertor limsup : superior limit opertor lint : line integrl (with circle) ll : much lower thn opertor lline : left r to open solute vlue ' ' llint : doule line integrl (with circle) lllint : triple line integrl (with circle) ln : function nturl logrithm log : function deciml logrithm lsu : left suscript lsup : left superscript lt : opertor less thn '<' mgent : mgent color for 'color' mtrix : defines mtrix minusplus : ' +' sign, plus under '-' mline : verticl line ' ' (ngulr rcket opertor: lngle... mline... rngle) nl : nl opertor, upside down Δ. nold : not old font. ndivides : does not divide opertor, / verticlly stroked neg : opertor no neq : opertor different newline : new line ni : inverted sign is element of nitlic : not itlic font none : comined with 'left' or 'right' to indicte invisile left or right rcket notin : is not element of opertor nroot : n th root nsuset : is not strictly include in opertor nsuseteq : is not include or equl in opertor nsupset : reversed is not strictly include in opertor nsupseteq : reversed is not include or equl in opertor odivide : opertor / in circle odot : opertor '.' in circle ominus : opertor ' ' in circle oper : trnsforms next vrile in lrge opertor with limits (like Σ) oplus : direct sum opertor, + in circle or : logicl opertor or, upside down ^ ortho : orthogonl opertor, perpendiculr symol otimes : tensor product opertor, x in circle over : division opertor, to write division with horizontl frction r overrce : put next element over previous one with n horizontl rce overline : dd n horizontl r over next element overstrike : strike-through chrcters owns : reversed is element of prllel : prllel opertor ' ' prtil : round d for prtil derivtive phntom : invisile element, to let empty spce 60 LireOffice 4.0 Mth Guide

14 plusminus : opertor '+-' with '+' over prod : product opertor, Π prop : proportionl opertor rngle : '>' to close '<...>' (ngulr rcket opertor: lngle... mline... rngle) rrce : visile right rce rceil : right squre rcket without ottom rdrcket : doule right squre rcket rdline : right doule line (norm) ' ' re : rel prt function red : red color for 'color' rfloor : right squre rcket without top right : next chrcter is treted s closing rcket rightrrow : right rrow rline : right r to close solute vlue ' ' rsu : suscript rsup : superscript sns : font option serif : font option setc : set of complex numers setminus : opertor \, sutrction of sets setn : set of nturl numers setq : set of rtionl numers setr : set of rel numers setz : set of integers sim : opertor equivlent, write one ~ simeq : opertor similrly equl, write doule ~ sin : function sine sinh : function hyperolic sine size : chnge font size slsh : opertor slsh '/' sqrt : opertor squre root stck : define stck of elements seprted with '#' su : suscript suset : strictly include opertor suseteq : include or equl opertor sum : sum opertor, Σ sup : superscript supset : reversed strictly include opertor supseteq : reversed include or equl opertor tn : tngent function tnh : hyperolic tngent function tilde : dd tilde '~' over next chrcter times : multipliction opertor, 'X' to : goes with 'from' for limits of integrls, sums, etc. towrd : rrow to the right trnsl : 2 smll joined circles, the one of the left is filled (sign of correspondence Imge from) trnsr : 2 smll joined circles, the one of the right is filled (sign of correspondence Origin of) underrce : put next element under previous one with n horizontl rce underline : dd n horizontl r under next element union : union opertor, U uoper : next chrcter is treted s unry opertor (unchnged size) uprrow : up rrow vec : dd smll rrow over next chrcter white : white color for 'color' wideslsh : opertor with ig '\' wideht : dd n ht over next element wideslsh : division opertor with ig '/' widetilde : dd tilde on next element widevec : dd n rrow over next element wp : Weierstrss p function yellow : yellow color for 'color' Mth commnds - Reference 61