MVR4
I*tciindets:6"6%%"iG%%varsG%"zGF$F$C&>8%<"?(8$"""F/9#%%trueGC%>8&&9"6#F.@$-%%ty
peG6$F4%'vectorG>F4-%(convertG6$F4%%listG>F+-%&unionG6$F+-%&minusG6$-%*intersec
tG6$-%'indetsG6#F4-FM6$F4%)monomialG-FM6$F4%)mathfuncG>F+-FG6$F+<#%*undefinedG-
%'RETURNG6#F+F$F$F$,
I'tcipwr:6$%#xxG%#nnG6,F&%"jG%"rG%"sG%"tG%"mG%"vG%"wG%"xG%"nGF$F$C->8'F/>8)F/>8
,-%%evalG6#9$>8--F^p6#9%@$-F:6$Fbp%'matrixGC$@$32F/-%'rowdimG6#Fbp2F/-%'coldimG
F`q-Fen6#""!@&/F^qF/C$>FjoFbq>8*-%$rowG6$FbpF//FbqF/C$>FjoF^q>F\r-%$colGF_r@$-F
:6$F\pFip@&/-F_q6#F\pF/C$>Fho-FcqF\s>8+-F^r6$F\pF//F_sF/C$>FhoF[s>Fas-FerFcs@$3
2F/Fho2F/FjoC%>8(-Fip6$FhoFjo?(F.F/F/FhoF1?(F+F/F/FjoF1>&F_t6$F.F+)&FasF7&F\rFf
n-Fen6#-F^p6#F_t@$3/FhoF/F\tC$@&FhqC$>F_t-Fip6$F/Fjo?(F+F/F/FjoF1>&F_t6$F/F+)F\
pFitF`rC$>F_t-Fip6$FjoF/?(F+F/F/FjoF1>&F_t6$F+F/F[vFjt@$3F[t/FjoF/C$@&FjrC$>F_t
-Fip6$F/Fho?(F+F/F/FhoF1@%/FbpFfq>FiuF/>Fiu)&FasFfnFbpFdsC$>F_t-Fip6$FhoF/?(F+F
/F/FhoF1@%F_w>FbvF/>FbvFbwFjt@$3Fgr-F:6$Fbp%(integerG@%/F[sF_sC&@%2FfqFbpC$>Fjo
Fbp>F4F\pC$>Fjo,$Fbp!"">F4-%(inverseGF\s>F_t-%&arrayG6%%)identityG;F/-F_qFN;F/-
FcqFN?(F.F/F/FjoF1>F_t-%)multiplyG6$F_tF4Fjt-Fen6#-F^p6#-%$mapG6%:6$%"yGF(F$6$%
)operatorG%&arrowGF$)F`pFepF$F$F\pFbp-Fen6#)-F^pF\sFbpF$F$F$,
I(tcimpy2:6$%"aG%"bGF$F$F$@)35-F:6$F`pFip-F:6$F`pF<5-F:6$FepFip-F:6$FepF<-F\z6$
F`pFepFg[l-%*scalarmulGFb\lF\\l-Fd\l6$FepF`p*&F`pF/FepF/F$F$F$,
I'tcimpy:F$6$F&F`oF$F$@%/F0FfqF/C%>F+F/?(F.F/F/F0F1>F+-F`[l6$F+F5-F^pFfnF$F$F$,
I(tciadd2:Fb[lF$F$F$@/3Fh[lF]\l-%'mataddGFb\l3Fj[lF_\lFh]lFj[l-Fi]l6$F`p*&FepF/
-F<6$-%(vectdimGF_pF/F/F_\l-Fi]l6$Fep*&F`pF/-F<6$-Fa^lFdpF/F/Fh[l@%/-FcqF_p-F_q
F_p-Fi]l6$F`p-Fd\l6$-Fby6%Fdy;F/F[_l;F/Fj^lFep-Fi]l6$F`p-Fd\l6$-Fip6%F[_lFj^lF/
FepF]\l@%/-FcqFdp-F_qFdp-Fi]l6$Fep-Fd\l6$-Fby6%Fdy;F/F]`l;F/F\`lF`p-Fi]l6$Fep-F
d\l6$-Fip6%F]`lF\`lF/F`p,&F`pF/FepF/F$F$F$,
I'tciadd:F$Fj\lF$F$C%>F+Ffq?(F.F/F/F0F1>F+-Fd]lFb]lFc]lF$F$F$,
I*tcifactor:F$6&F&F]oFdoFaoF$F$C'@$5F\]l2""#F0-%&ERRORG6#%:Wrong~number~of~argu
mentsG>F4&F66#F/>FhoFfq@$/F0F[bl>Fho&F66#F[bl@%5-F:6$F4FipF9-Fen6#-Fcz6%%(tcifa
c2GF4Fho-Fen6#-Facl6$F4FhoF$F$F$,
I(tcigcd2:Fb[lF$F$F$@%3-F:6$F`pF`x-F:6$FepF`x-%%igcdGFb\l-%$gcdGFb\lF$F$F$,
I'tcigcd:F$Fj\lF$F$@%F\]lFfqC%>F+Ffq?(F.F/F/F0F1>F+-FfclFb]lFc]lF$F$F$,
I)tcismith:F$F$F$F$@&Febl-%&smithG6$FablFgbl/F0F/-%'ismithG6#FablF$F$F$,
I)tcixprod:6$%"AG%"BGFb[lF$F$C%>F.-%'tciargGF_p>F+-F\flFdp@%3-%)tciisvecGF7-Fbf
lFfn-%*crossprodGFft-F`[lFftF$F$F$,
I)tcidprod:FfelFb[lF$F$C%>F.F[fl>F+F^fl@%F`fl-%(dotprodGFftFfflF$F$F$,
I'tciarg:6#Fc[l6#F&F$F$@'Fh[l@'/F[_lF/-Fen6#-F^r6$F`pF//Fj^lF/-Fen6#-FerFigl-Fe
nF_p-F:6$F`pFA-Fen6#-F?F[\lF^hlF$F$F$,
I'tcidiv:F$6'FdoFc[lFd[l%"cGF_oF$F$C$@'/F0""$>F.&F66#F[ilFeblC%>F+-FMFcel>F4-FM
6#Fgbl@'/-%%nopsGFfnF/>F.-%#opGFju/-FhilFNF/>F.-F[jl6$F/F4C$>Fho-FJ6$F+F4@%/-Fh
il6#FhoF/>F.-F[jlF\w-Fen6#.%)needvarsG-F]bl6#%Opolynomial~divide~needs~two~or~t
hree~argumentsG@'2-%'degreeG6$FablF.-Fe[m6$FgblF.-Fen6#*&FablF/FgblF\y-%'divide
G6%FablFgbl.F_tFjt-Fen6#,&-%$quoG6%FablFgblF.F/*&-%$remGFe\mF/FgblF\yF/F$F$F$,
I(tciroot:F$6%%$varG%%vsetG%"pGF$F$C&>F4Fabl>F+FL@'Febl>F.FgblF`el@%Ffil>F.Fjil
F[[m-F]bl6#%Rpolynomial~root~finder~needs~one~or~two~argumentsG@%2-Fe[m6$F4F.""
&C$>%-_EnvExplicitGF1-%&solveGF\^m-%'fsolveG6%F4F.%(complexGF$F$F$,
I(tcifac2:6$FdoFao6$F`o%$ansGF$F$C%>F.F]p@'0FepFfq>F+-%%modpG6$-%'FactorGF7Fep-
F:6$F.F`x>F+-%(ifactorGF7>F+-%'factorGF7@%/F+.F.-F]bl6#%?Maple~only~factors~exp
ressionsG-Fen6#Fc]lF$F$F$,
I+tcicombine:6$FdoFgz6$F&F]oF$F$@%Fg[l-Fen6#-Fcz6%%)tcicomb2GF`pFep-Fen6#-F_amF
b\lF$F$F$,
I)tcicomb2:Fh`m6#F`oF$F$@-/FepFfq-%(combineG6%F`p%%trigG%)symbolicG/FepF/-Fiam6
%F`p%$expGF\bm/FepF[bl-Fiam6%F`p%&powerGF\bm/FepF[il-Fiam6%F`p%#lnGF\bm/Fep""%-
Fiam6%F`p%$PsiGF\bm-Fiam6$F`pF\bmF$F$F$,
I)tcisolve:F$6(%#iiGF'Fd[lFc[lFeoFboF$F$C$@$2F0F/Fdq@)F`elC'>F+-F"6#-F[jl6$F/Fa
bl?(F.F[blF/-FhilFcelF1>F+-FD6$F+-F"6#-F[jl6$F.Fabl>FjoF+?(F.F/F/-Fhil6#FjoF1C%
>Fho-F[jl6$F.Fjo>F_t-%'lengthGFhjl@$32F[blF_t-%'testeqG6$%#QUG-%*substringG6$Fh
o;,&F_tF/F\yF/F_t>F+-FG6$F+<#Fho@%/FgilF_dm-Fb^m6$FablF+F[[m3-F:6$FablFip-F:6$F
gblF<@%2-FcqFcel-F_qFcel-%*leastsqrsGF_el-%)linsolveGF_el3Fgfm-F:6$FgblFipC$>F4
-F?Fjfm@%F\gm-F`gm6$FablF4-FbgmF[hm-Fb^mF_elF$F$F$,
I'getvar:6#%"eG6%F&F]oF^oF$F$C%@$/-FhilF_pF/C&@$-F:6$F`p%)functionG-Fen6#-F^hm6
#-F[jl6$F/F`p@$Fh[lC$?(F.F/F/F[_lF1?(F+F/F/Fj^lF1C$>F4-F^hm6#&F`pFft@$0F4Ffq-Fe
nFNFdq@$-F:6$F`p%'stringGF^hlFdq?(F.FfhmF\yF/F1C%@$-F:6$-F[jl6$F.F`pFajm-Fen6#F
gjm>F4-F^hmFjjm@$F\jmF]jmFdqF$F$F$,
I'tciint:F$6&F\]m%$xQxG%%funcGF[_mF$F$C(@$Febl-Fen6#-%$intGF_el@$/F0FjbmC%>F4-F
^p6#-%%subsG6$/FgblF+Fabl>Fho-Fh[n6$F4/F+;F]il&F66#Fjbm-Fen6#-%)simplifyG6#-F^p
6#-F`\n6$/F+FgblFho>F.-F^hmFcel@$3F`el0F.Ffq-Fen6#-Fh[nFf[m@$FjhlC%>F4-F^p6#-F`
\n6$/F.F+Fabl>Fho-Fh[n6$F4/F+;FgblF]il-Fen6#-F]]n6#-F^p6#-F`\n6$/F+F.Fho-F]bl6#
%Dwrong~number~of~arguments~in~tciintGF$F$F$,
I(tcikill:F$6#FccmF$F$C$-%(readlibG6#%)unassignG?(F.F/F/F0F1-F\`n6#F5F$F$F$,
I(tceigen:6$Fc[lFeo6$%$vexGF[_mF$F$C%>F+-%&evalfG6#-%*EigenvalsG6$F`pF.@$Fgam-F
en6#-F^p6#-F?6$F+FA-Fen6#-F^pF7F$F$F$,
I*tcidsolve:6&%%eqnsGF'%&namesG%(procnumGFg_nF$F$C(Fi_n?(F.F/F/-Fhil6#9&F1-F\`n
6#-F[jl6$F.Fabn>(%$ftpG9'-%'dsolveG6%F`p-F?6$Fep%$setG/F:%(numericG?(F.F/F/F_bn
F1-%(tciasgnG6%Fdbn-F[jl6$F.FepFgbn>(%(ftprefsGFibn-FhilFdp-Fen6#.FabnF$F$F$,
I+tcideftest:FaglF$F$F$C&@$4Fh[l-F]bl6#%:argument~must~be~a~matrixG@$2Ffq-%%nor
mG6$,&F`pF/-%*conjugateGF_pF\yF/-F]bl6#%4matrix~must~be~realG@$2Ffq-Fjdn6$,&F`p
F/-%*transposeGF_pF\yF/-F]bl6#%9matrix~must~be~symmetricG@+/-%)definiteG6$F`p.%
-negative_defGF1-Fen6#%'negdefG/-F_fn6$F`p.%-positive_defGF1-Fen6#%'posdefG/-F_
fn6$F`p.%1positive_semidefGF1-Fen6#%&psdefG/-F_fn6$F`p.%1negative_semidefGF1-Fe
n6#%&nsdefG-Fen6#%&indefGF$F$F$,
I+tciextrema:F$6&F'%$locGF[_mF&F$F$C$@'5FeblF`elC%>F.F,?(FhoF/F/F0F1>F.-FD6$F.-
F"6#&F6Fhjl@%/-FhilF7F/@%F`el>F4-F^p6#-%(extremaG6&FablF,F..F+>F4-F^p6#-Fiin6&F
ablFgblF.F[jn@%F`el-Fen6#.%*needvars0G-Fen6#.%*needvars1GFjhl>F4-F^p6#-Fiin6&Fa
blFgblF]ilF[jn-F]bl6#%EWrong~number~of~arguments~in~ExtremaG-Fen6%F4.%#atGF+F$F
$F$,
I'tcisum:F$6$F\]m%&mapitGF$F$C)@%F\]l-F]bl6#%4Sum~has~no~argumentG>F+5Fgfm-F:6$
FablF<@$Febl@%F+-Fen6#-Fcz6%%$sumGFablFgbl-Fen6#-Fi\oF_el@$Fj[n@%F+-Fen6#-Fcz6%
Fi\oFabl/FgblFg\n-Fen6#-Fi\o6$FablFc]o>F.Fe]n@$Fg]n@%F+-Fen6#-Fcz6%Fi\oFablF.-F
en6#-Fi\oFf[m@$Fjhl@%F+-Fen6#-Fcz6%Fi\oFabl/F.Fh^n-Fen6#-Fi\o6$FablFh^o-FenFcel
F$F$F$,
I(tciprod:F$Fh[oF$F$C)@%F\]l-F]bl6#%8Product~has~no~argumentG>F+F`\o@$Febl@%F+-
Fen6#-Fcz6%%(productGFablFgbl-Fen6#-F\`oF_el@$Fj[n@%F+-Fen6#-Fcz6%F\`oFablFc]o-
Fen6#-F\`oFg]o>F.Fe]n@$Fg]n@%F+-Fen6#-Fcz6%F\`oFablF.-Fen6#-F\`oFf[m@$Fjhl@%F+-
Fen6#-Fcz6%F\`oFablFh^o-Fen6#-F\`oF\_oF]_oF$F$F$,
I(tcidiff:F$F$F$F$@%F`\o-Fen6#-Fcz6$%%diffGF6-Fen6#-F]]n6#-Fcbo6#F6F$F$F$,
I(tcifunc:6$%"fGF\]m6#FdoF$F$@%F\\l-Fen6#-FczFb\l-Fen6#-F^p6#-F`pFdpF$F$F$,
I(tcizmat:6$%&nrowsG%&ncolsG6#FgelF$F$C&>F.-%%bandG6$7#Ffq-%$maxGFb\l@$2FepF`p>
F.-%(delcolsG6$F.;,&FepF/F/F/F`p@$2F`pFep>F.-%(delrowsG6$F.;,&F`pF/F/F/FepFdanF
$F$F$,
I(tciimat:FjcoF]doF$F$C&>F.-Fado6$7#F/Fddo@$Fgdo>F.Fido@$F_eo>F.FaeoFdanF$F$F$,
I.tcidelodeproc:6#F\bnF$F$F$@%2F/(FjcnF`p>Fffo,&FffoF/F\yF/C%Fi_n-F\`n6#Fffo-F\
`n6#(FhbnF`pF$F$F$,
I(tciasgn:6%%&fnameG%&vnameG%&pnameGF$F$F$>F`p-%(unapplyG6$-.%*getodevalG6$Fep-
F^dn6#Fa[nFa[nF$F$F$,
I*getodeval:6$%(thenameG%'thesetGFbglF$F$C$?(F.F/F/F[dnF1@$/-%$lhsG6#Ffcn.F`p-F
en6#-%$rhsGFjho-F]bl6#.4%&foundGF$F$F$,
I)tciJBmat:6%%%diagGF[doF\doF]doF$F$C&>F.-%,JordanBlockG6$F`p-Fedo6$FepFabn@$2F
abnFep>F.-Fjdo6$F.;,&FabnF/F/F/Fep@$2FepFabn>F.-Fbeo6$F.;F]eoFabnFdanF$F$F$,
I(tciBand:6%%*entrylistGF[doF\doF]doF$F$C&>F.-FadoF]jo@$Fajo>F.Fcjo@$Fhjo>F.Fjj
oFdanF$F$F$,
I(tcicorr:F$6)FeoF[_mFgelFccm%#jjG%&list1G%&list2GF$F$@%3F`elFgfmC(>F4Fabl@$4-F
:6$&F46$F/F/Facn>F4-Fbeo6$F4;F/F/>F.Fhy>F+-Fip6$F.F.?(FhoF/F/F.F1?(F_tF/F/F.F1C
%>Fjo-F?6$-FerFeclFA>F\r-F?6$-Fer6$F4F_tFA>&F+6$FhoF_t-Fh`n6#-&%)describeG6#%2l
inearcorrelationG6$FjoF\rFd`mFddnF$F$F$,
I)tcicovar:F$6*FeoFaoF[_mFgelFccmF[\pF\\pF]\pF$F$@%F_\pC)>FhoFabl@$4-F:6$&FhoFg
\pFacn>Fho-Fbeo6$FhoF[]p>F.-FcqFhjl>F+-F_qFhjl>F4F^]p?(F_tF/F/F.F1?(FjoF/F/F.F1
C&>F\r-F?6$-FerF^^pFA>Fas-F?6$-FerFatFA>&F46$F_tFjo-Fh`n6#-&Fc^p6#%+covarianceG
6$F\rFas@$2F/F.>Ff`p*(Ff`pF/F+F/,&F+F/F\yF/F\y-Fen6#-F^pFNFddnF$F$F$,
I(tcimean:F$6%FgelFhelFccmF$F$C$@$FfcmFdq@)FgfmC&>F.Fabl@$4-F:6$&F.Fg\pFacn>F.-
Fbeo6$F.F[]p>F+-F?6$-FhenF7%)listlistG-Fen6#-Fh`n6#-F[jl6#-Fcz6$&Fc^p6#%%meanGF
+Fa\o-Fen6#-Fh`n6#-Fdcp6#-F?6$FablFA-F:F^dp-Fen6#-Fh`n6#-FdcpFcelC%>F.-Fby6#;F/
F0?(F4F/F/F0F1>&F.FN&F6FN-Fen6#-Fh`n6#-Fdcp6#-F?6$F.FAF$F$F$,
I*tcimedian:F$FiapF$F$C$@$FfcmFdq@)FgfmC&>F.Fabl@$F`bp>F.Febp>F+Fhbp-Fen6#-Fcz6
$&Fc^p6#%'medianGF+Fa\o-Fen6#-FdfpF\dpF_dp-Fen6#-FdfpFcelC%>F.Fgdp?(F4F/F/F0F1>
F\epF]ep-Fen6#-FdfpFcepF$F$F$,
I(tcimode:F$6&FgelFhelFccmF[_mF$F$C$@$FfcmFdq@)FgfmC(>F.Fabl@$F`bp>F.Febp>F+Fhb
p>Fho7#-&Fc^p6#%%modeG6#Fjil@$2F/Fgil?(F4F[blF/FgilF1>Fho6$Fho7#-Fbhp6#-F[jl6$F
4F+-FenFhjlFa\o-Fen6#-FbhpF\dpF_dp-Fen6#-FbhpFcelC%>F.Fgdp?(F4F/F/F0F1>F\epF]ep
-Fen6#-FbhpFcepF$F$F$,
I(tcisdev:F$FiapF$F$C$@$FfcmFdq@)FgfmC&>F.Fabl@$F`bp>F.Febp>F+Fhbp-Fen6#-Fh`n6#
-Fcz6$&Fc^p6#&%2standarddeviationGFbblF+Fa\o-Fen6#-Fh`n6#-F^[qF\dpF_dp-Fen6#-Fh
`n6#-F^[qFcelC%>F.Fgdp?(F4F/F/F0F1>F\epF]ep-Fen6#-Fh`n6#-F^[qFcepF$F$F$,
I(tcimdev:F$FiapF$F$C$@$FfcmFdq@)FgfmC&>F.Fabl@$F`bp>F.Febp>F+Fhbp-Fen6#-Fcz6$&
Fc^p6#%.meandeviationGF+Fa\o-Fen6#-Fc]qF\dpF_dp-Fen6#-Fc]qFcelC%>F.Fgdp?(F4F/F/
F0F1>F\epF]ep-Fen6#-Fc]qFcepF$F$F$,
I,tcivariance:F$FiapF$F$C$@$FfcmFdq@)FgfmC&>F.Fabl@$F`bp>F.Febp>F+Fhbp-Fen6#-Fh
`n6#-Fcz6$&Fc^p6#&%)varianceGFbblF+Fa\o-Fen6#-Fh`n6#-Fc_qF\dpF_dp-Fen6#-Fh`n6#-
Fc_qFcelC%>F.Fgdp?(F4F/F/F0F1>F\epF]ep-Fen6#-Fh`n6#-Fc_qFcepF$F$F$,
I+tcipolyfit:F$6*Fgel%$degG%"CGFd[l%"SGF[_m%$keyGFccmF$F$C.@$4Fjhl-F]bl6#%:wron
g~number~of~argumentsG>F.Fabl@$4-F:6$F.Fip-F]bl6#%;selection~must~be~a~matrixG>
F+Fgbl@$34-F:6$F+F`x2FfqF+-F]bl6#%Edegree~must~be~a~nonnegative~integerG@$4/-Fc
qF7F[bl-F]bl6#%Dselection~must~be~a~2~column~matrixG@%Fabp>F\r7$FdoFgzC$>F\r-F?
6$-F^r6$F.F/FA>F.Febp>Fho-F<6#,&F+F/F/F/>F4Fhbp>Fjo&FhoFbbl>F_t<#F`dq@%/F]ilF/C
$?(FasF/F/F+F1C$>Fjo,&FjoF/*&&Fho6#,&FasF/F/F/F/)&F\rFbblFasF/F/>F_t-FD6$F_t<#F
[eq-Fen6#-&%$fitG6#&%,leastsquareG6%F\r/&F\rFhblFjoF_tFNC$?(FasF/F/F+F1C$>Fjo,&
FjoF/*&F[eqF/)F^fqFasF/F/>F_tFaeq-Fen6#-&Fheq6#&F[fq6%F\r/F_eqFjoF_tFNF$F$F$,
I,tcimregress:F$6)F`aqFd[lFghl%"dGF&FgelFhelF$F$C)@$FcaqFdaq>FjoFabl@$4-F:6$Fjo
FipF\bq@$-F:6$&FjoFg\pFacn-F]bl6#%9columns~must~be~labelledG>F.-F?6$-F^rF_vFA>F
jo-Fbeo6$FjoF[]p@%/F]ilFfqC&>F+-FerF_v>F\r-FjdoFghq@%/FgblFfqC%>F4-F`gm6$F\rF+>
FhoFfq?(F_tF[blF/-FcqFjdmF1>Fho,&FhoF/*&&F.F]uF/&F46#F]fmF/F/C'>F4-F<6$-F_qFjdm
F/>F\r-%'concatG6$F4F\r>F4Fciq>Fho&F4Fbbl?(F_tF[blF/FgiqF1>Fho,&FhoF/*&F[jqF/&F
4F]uF/F/-Fen6#/&F.FbblFhoC&>F+-Fer6$FjoFgiq>F\r-Fjdo6$Fjo;FgiqFgiq@%F`iqC%>F4Fc
iq>FhoFfq?(F_tF/F/,&FgiqF/F\yF/F1>FhoF\[rC'>F4F`jq>F\rFdjq>F4Fciq>FhoFijq?(F_tF
/F/F`\rF1>Fho,&FhoF/*&F[jqF/&F46#,&F_tF/F/F/F/F/-Fen6#/&F.6#FgiqFhoF$F$F$,
I,tcistatplot:F$F]doF$F$@%F_\pC'>F.Fabl@$Fjbq-F]bl6#%;matrix~must~have~2~column
sG@$Fabp>F.-%'putkeyG6$F.Fbcq-%+regressionG6$F./Fgz,&Fc[lF/*&Fd[lF/FdoF/F/-%)st
atplotG6$F./Fgz-F`\n6$%""GFe^rF]cqF$F$F$,
I,tciquantile:F$6'FgelFhel%%fracG%"qGFccmF$F$C&@$2F0F[bl-F]bl6#%;quantile~needs
~2~argumentsG>Fho&F66#F0>F4-F?6$Fho%)rationalG@)FgfmC&>F.Fabl@$F`bp>F.Febp>F+Fh
bp-Fen6$Fho-Fcz6$&Fc^p6#&%)quantileGFNF+Fa\o-Fen6$Fho-Fj`rF\dpF_dp-Fen6$Fho-Fj`
rFcelC%>F.-Fby6#;F/,&F0F/F\yF/?(F_tF/F/FiarF1>F[jq&F6F]u-Fen6$Fho-Fj`rFcepF$F$F
$,
I*tcimoment:F$6'FgelFhelFeo%%origGFccmF$F$C&@$2F0F[il-F]bl6#%9moment~needs~3~ar
gumentsG>F4&F66#Fiar>FhoFj_r@)FgfmC&>F.Fabl@$F`bp>F.Febp>F+Fhbp@%-F:6$FhoFacn-F
en6#-Fcz6$&Fc^p6#&%'momentGFeclF+-Fen6#-Fcz6$&Fc^p6#&F^dr6$F4FfcpF+Fa\o@%Fecr-F
en6#-F[drF\dp-Fen6#-FcdrF\dpF_dp@%Fecr-Fen6#-F[drFcel-Fen6#-FcdrFcelC%>F.-Fby6#
;F/,&F0F/!"#F/?(F_tF/F/FjerF1>F[jqF\br@%Fecr-Fen6#-F[drFcep-Fen6#-FcdrFcepF$F$F
$,
I,tciaprxarea:6'%%exprG%#vvG%%rngeG%%nintGF:6#F\]mF$F$C%@%Fgam>F.-F^hmF_p>F.Fep
@%/F.Ffq>F.FdoF$@)/9(F/-%*middlesumG6%F`p/F.FabnFibn/FggrF[bl-%(simpsonGFjgr/Fg
grF[il-%*trapezoidGFjgr-F]bl6#%<no~such~integration~formulaGF$F$F$,
I-tcipotential:F$6)F&FeoFc[l%$vecGF'%%possGF[_mF$F$C(@$Ffcm-F]bl6#%;no~argument
s~for~potentialG>F4Fabl@)F[cl@'/FfyF/>Fho-F^r6$F4F//FhyF/>Fho-FerFeir-F]bl6#%Bn
on-vector~argument~for~potentialG-F:F@>Fho-F?F;F9>FhoF4-F]bl6#%;bad~argument~fo
r~potentialG@'Fjal-F]bl6#%Emore~than~two~arguments~to~potentialGFebl>F_t-F?6$Fg
blFAC'>F_tF,?(F.F/F/-Fa^lFhjlF1>F_t-FD6$F_t-F"6#&FhoF7>F_t-F?6$F_tFA>F_t-%%sort
G6$F_t%)lexorderG@$0-FhilF]uF][s-Fen6#F^[m>Fjo-%*potentialG6%FhoF_t.F\r@%/FjoF1
-Fen6#-F^p6#F\rFdqF$F$F$,
I-tcivecpotent:F$6(F&Fc[lFhhrFihrF[_mF'F$F$C%@'Fj[nC&>F+-Fby6#;F/F[il?(F.F/F/F[
ilF1>&F+F7F5>F4-F?6$Fc]lF<>FjoFh\nFeblC%>F+Fabl>FjoFgbl@)-F:6$F+Fip@'/-F_qFfnF/
>F4-F^rFcv/-FcqFfnF/>F4-FerFcvFdq-F:Fcan>F4-F?6$F+F<-F:F__s>F4F+Fdq-F]bl6#%;mus
t~have~2~or~4~argumentsG>Fho-%*vecpotentG6%F4FjoF_\m@$/FhoF1FjtF$F$F$,
I,tcijacobian:F$6&F&Fc[lFhhrF'F$F$C&@$Ffcm-F]bl6#%:no~arguments~for~JacobianG@$
2FfqF0C$>F+Fabl@)Fa^s@'Fd^s>F4Fg^sFh^s>F4F[_s-F]bl6#%@Nonvector~argument~for~Ja
cobianGF\_s>F4F^_sF`_s>F4F+-F]bl6#%:Bad~argument~for~JacobianG@%FeblC$>FhoFgbl@
$-F:6$FhoF<>Fho-F?6$FhoFAC&>FhoF,?(F.F/F/-Fa^lFNF1>Fho-FD6$Fho-F"6#&F4F7>FhoFja
s>Fho-Fi[s6$FhoF[\s@%0FgjlF_bsF_\s-Fen6#-%)jacobianGFeclF$F$F$,
I+tcihessian:F$6#F'F$F$C%@$4F`el-F]bl6#%:Not~1~argument~in~HessianG>F.-F?6$-F"F
celFA-Fen6#-%(hessianG6$Fabl-Fi[s6$F.F[\sF$F$F$,
I-tcichangevar:F$F\grF$F$C&@$4Febl-F]bl6#%=Not~2~arguments~in~ChangeVarG>F.-FG6
$F\ds-F"Fdil>F.Fdep-Fen6#-%*changevarG6%FablFgblFb[rF$F$F$,
I(tcigrad:F$FbcsF$F$C%@$Fecs-F]bl6#%7Not~1~argument~in~gradG>F.Fjcs-Fen6#-%%gra
dGFadsF$F$F$,
I(tcifrob:F]do6$%"PG%"FGF$F$C$>F+-%*frobeniusG6$F`pF``m-Fen6%FfanFc]l-F_yF7F$F$
F$,
I*tcijordan:F]do6$Fefs%"JGF$F$C$>F+-%'jordanGF[gsF\gsF$F$F$,
I&tciGS:F]do6'Fd[l%&vectsGFghl%"DGF&F$F$C->F.-F?6$FgenF[cp?(F_tF/F/FcinF1>(%#gs
GF_t-F?6$-F[jl6$F_tF.F<>F+F,?(F_tF/F/FcinF1>F+-FD6$F+<#Fbhs>F+Fban>F+-Fi[s6$F+F
[\s>F4-%,GramSchmidtGFfn>FhoF_jl?(F_tF[blF/F]jlF1>Fho-%&stackG6$Fho-F[jlF]z>Fho
-FhenFhjl-Fen6$-F^pFhjl-F\z6$-F_yFhjlF`pF$F$F$,
I,tcisingvals:F]do6&FhelFd[l%&svalsGF&F$F$C'>F.-F\z6$F`p-%+htransposeGF_p>F+<#-
%*eigenvalsGF7>F4F,?(FhoF/F/FgilF1>F4-FD6$F4<#-%%sqrtG6#-F[jl6$FhoF+FdapF$F$F$,
I(tcinorm:6$Fgel%#tpG6%Fd[l%&maxsvGF&F$F$@%3/Fep.F[blFh[lC$>F.-FdjsF_p@%/FcinFf
qFdqC%>F+-F[jl6$F/F.?(F4F[blF/FcinF1@%/F+Ffq>F+-F[jlF\^m>F+-Fedo6$F+Fd]tFZ-Fen6
#-FjdnFb\lF$F$F$,
I'tciSVD:F]do6)%"UGF[hs%"VG%"EGF^oFghlF&F$F$C(>F_tF[_l>FjoFj^l>Fho-FhcoFg`p>F+-
Fh`n6#-%$SvdG6%F`pF.F4?(F\rF/F/-%$minGFg`pF1>&Fho6$F\rF\r&F+F[]s-Fen6%FfanF`js-
FhenFNF$F$F$,
I*tcifsolve:F$FbcsF$F$@'F`el-Fen6#-Fd^mFcelFeblC$>F.F\ds-Fen6#-Fd^m6%FablF.Fgbl
-F]bl6#%DWrong~number~of~arguments~in~fsolveGF$F$F$,
I+tciparfrac:F$6%F&F]oFdoF$F$C$@$5FjalF\]l-F]bl6#%Cparfrac~needs~one~or~two~arg
umentsG@%FgfmC%>F4Fabl?(F.F/F/FfyF1?(F+F/F/FhyF1@%F`el>&F4Fft-%,tciparfrac2G6#F
eat>Feat-Fgat6$FeatFgblFdap@%F`el-Fen6#-FgatFcel-Fen6#-FgatF_elF$F$F$,
I,tciparfrac2:F$FbcsF$F$@%F`elC$>F.F\ds@%FbinC$>F.Fdep-Fen6#-F?6%Fabl%(parfracG
Fb[rF[[m-Fen6#-F?6%FablF_ctFgblF$F$F$,
I*tciterate:6%F]coFc[lFeo6%FccmFhhr%%nextGF$F$C&>F+-F<6#Ffjo>&F+FbblFep?(F.F/F/
FabnF1C%>F4-F^p6#-F`p6#Fh]s@$4-F:6$F4Facn>F4-Fh`nFcdt>&F+6#,&F.F/F/F/F4Fd`mF$F$
F$,
I&tciQR:6#%"ZG6$FgelFb_rF$F$C$>F.-%)QRdecompG6$F`p/%"QGF[jn-Fen6$Fc]lFfanF$F$F$,
I)tciprime:6%F]coFifrFeo6)FdoF[_m%&ftempGFccmF[\pF\]mF[oF$F$C(>Fjo-F[jl6$;F/F\y
Fep@$-F:6$FabnFA-Fen6#--&F[hs6#-F[jl6$FgftFabnF_pFjdm@$4-%)assignedG6#-F`pF7-Fe
n6#---%#@@G6$F[hsFabnF_pFjdm@%5-F:6$FhgtFip-F:6$FhgtF<>F4-Fcz6%FcboFhgt-%"$GFeb
n>F4-F]]n6#-Fcbo6$FhgtFiht@$2Ffq-%+searchtextG6$Fcbo-F?6$F4Fajm-F]bl6#%EMaple~c
annot~do~this~differentiationG@%FhgqC%>F+-Fip6$FbjqFgiq?(FhoF/F/FbjqF1?(F_tF/F/
FgiqF1C$>F.&FjoF^^p>F]^pFfapFd`m-Fen6#-F`\n6$/F.FjoFfapF$F$F$,
I-tcilaplacian:F$FbcsF$F$C%@$Fecs-F]bl6#%<Not~1~argument~in~laplacianG>F.Fjcs-F
en6#-%*laplacianGFadsF$F$F$,
I*tcimixnum:F^co6$Fd\mFh\mF$F$C%>F.-%&truncGF_p>F+-Fa_rF_p@'FcgrFZFb]t-FenF7-Fe
n6%F.%"#GF+F$F$F$,
I'tcilcm:F$Fj\lF$F$@%F\]lFfqC%>F+Fabl?(F.F/F/F0F1>F+-%(tcilcm2GFb]lFc]lF$F$F$,
I(tcilcm2:Fb[lF$F$F$@%Ficl-%%ilcmGFb\l-%$lcmGFb\lF$F$F$,
I'tcimod:6$FdoF^]mF$F$F$@'Fh[l-Fcz6%%(tcimod2GF`pFepFj[lFh]u-Fj]uFb\lF$F$F$,
I-tcicompanion:F$6(FdoFc[lF&FeoFaoF^]mF$F$C'>Fjo-%'expandG6$FablF\bm>F+-FMFjdm>
F.Fjil@$FghpC$>Fho-Fe[m6$FjoF.?(F4F[blF/FgilF1C$>F_t-Fe[m6$FjoF^ip@$2FhoF_tC$>F
_tFho>F.F^ip-Fen6#-%*companionGF[_uF$F$F$,
I,tcisimplify:F$F$F$F$@%F`\o-Fen6#-Fcz6%F]]nF6F\bm-Fen6#-F]]n6$F6F\bmF$F$F$,
I*tciexpand:F$F$F$F$@%F`\o-Fen6#-Fcz6%Fb^uF6F\bm-Fen6#-Fb^uFd`uF$F$F$,
I(tcisort:F$6$F\]mF]]mF$F$C$@'Febl>F.FgblF`elC$>F+Fail@%Ffil>F.FjilF[[m-F]bl6#%
Kpolynomial~sort~needs~one~or~two~argumentsG-Fi[sFf[mF$F$F$,
I(tcimod2:Ff]u6$Fc[lF`oF$F$C$>F.-FMFdp@'F[]t-Fen6#-Fb_mFb\lFbinC$>F+F^]t-Fen6#-
Fh\m6%F`pFepF+-F]bl6#%Fmodulus~can~have~at~most~one~variableGF$F$F$,
I+tcidiverge:6$Fc[lF'6#FhhrF$F$C$@)Fh[l@'Fegl>F.FhglFjgl>F.F]hl-F]bl6#%BNonvect
or~argument~for~divergenceGF_hl>F.FchlFj[l>F.F`p-F]bl6#%<Bad~argument~for~diver
genceG-Fen6#-%(divergeGFgcnF$F$F$,
I(tcicurl:FbcuFccuF$F$C$@)Fh[l@'Fegl>F.FhglFjgl>F.F]hl-F]bl6#%<Nonvector~argume
nt~for~curlGF_hl>F.FchlFj[l>F.F`p-F]bl6#%6Bad~argument~for~curlG-Fen6#-%%curlGF
gcnF$F$F$,
I*tciexpden:6$Fdo%#muGF$F$F$C$@$2FepFfq-F]bl6#%6mean~must~be~positiveG-Fen6#-Fh
`n6#*&-F`bm6#,$*&F`pF/FepF\yF\yF/FepF\yF$F$F$,
I+tciexpdist:FjeuF$F$F$C$@$F^fuF_fu-Fen6#-Fh`n6#,&$"#5F\yF/FgfuF\yF$F$F$,
I*tciexpinv:FjeuF$F$F$C%@$F^fuF_fu@$52F`pFfq2F/F`p-F]bl6#%:argument~must~be~in~
(0,1)G-Fen6#,$*&FepF/-Fhbm6#,&FdguF/F`pF\yF/F\yF$F$F$,
I*tcihypden:6&Fdo%"NGF_aqFeoF$F$F$-Fen6#-Fh`n6#*(-%)binomialG6$FabnF`pF/-Fbiu6$
,&FepF/FabnF\y,&FibnF/F`pF\yF/-Fbiu6$FepFibnF\yF$F$F$,
I+tcihypdist:Fjhu6#%$totGF$F$C$>F.-Fi\o6$-Fh`n6#*&-Fbiu6$Fabn%"kGF/-Fbiu6$Ffiu,
&FibnF/FgjuF\yF//Fgju;FfqF`p-Fen6#*&F.F/FhiuF\yF$F$F$,
I*tcihypinv:Fjhu6$F]juFgjuF$F$@%2F`p*&FabnF/FepF\yC$>F.Ffq?(F+FfqF/FibnF1C$>F.,
&F.F/-Fh`n6#*(-Fbiu6$FabnF+F/-Fbiu6$Ffiu,&FibnF/F+F\yF/FhiuF\yF/@$1F`pF.FZC$>F.
Fdgu?(F+FfqF/FibnF1C$>F.,&F.F/-Fh`n6#*(-Fbiu6$FabnFc\vF/-Fbiu6$FfiuF+F/FhiuF\yF
\y@$1F.F`p-Fen6#Fc\vF$F$F$,
I*tcibininv:6%FdoFeoF^]m6&FgjuFffs%&ratioGF]juF$F$C%@$51FabnFfq1F/FabnF^hu>F4*&
FabnF/,&F/F/FabnF\yF\y@%2F`pFabnC%>F+)Fc^vFep>FhoFfq?(F.FfqF/FepF1C$>Fho,&FhoF/
*&F+F/-Fh`n6#*&-Fbiu6$FepF.F/)F4F.F/F/F/@$1F`pFhoF`\uC%>F+)FabnFep>FhoFdgu?(F.F
fqF/FepF1C$>Fho,&FhoF/*&F+F/-Fh`n6#*&-Fbiu6$Fep,&FepF/F.F\yF/)F4,$F.F\yF/F/F\y@
$1FhoF`p-Fen6#Fe`vF$F$F$,
I+tcirandbin:6%FeoF^]mF[iuFccuF$F$C$>F.-&%'randomG6#&%(uniformG6$FfqFdguF`bn-Fe
n6#-F[jl6#-Fcz6&Fg]v7#F.F`pFepF$F$F$,
I-tcicauchyden:6%FdoFc[lFd[l6#%$denGF$F$C$>F.*(%#PiGF/FabnF/,&F/F/*&,&F`pF/FepF
\yF[blFabnF[frF/F/-Fen6#-Fh`n6#,$*$F.F\y$F/FfqF$F$F$,
I/tcirandpoisson:6$Fc[lF[iuFccuF$F$C$>F.7#-&Fcav6#&%(poissonGF_pFdp-Fen6#-F[jl6
#-Fcz6%F?F.%)fractionGF$F$F$,
I,tcicharpoly:F$6%FboFgjuF'F$F$C&@$5FfcmFjalFdaq@$4Fgfm-F]bl6#%6argument~not~a~
matrixG@&F`elC%>F4-FM6#-F?6$FablF_cn>F.%"XG?(F+F/F/F]jlF1@$2Ffq-%+SearchTextG6$
Fgev-F[jlFdjlF[[mFebl>F.Fgbl-%)charpolyGFf[mF$F$F$,
I+tciminpoly:F$FfdvF$F$C&@$FidvFdaq@$F[evF\ev@&F`elC%>F4Fbev>F.Fgev?(F+F/F/F]jl
F1@$FjevF[[mFebl>F.Fgbl-%(minpolyGFf[mF$F$F$,
I&tciLU:Fbet6%F^^tF^]m%"lGF$F$C$>F.-%)LUdecompG6%F`p/FefsF[jn/%"LG.F4-Fen6%Fc]l
FfapFfanF$F$F$,
I'tcimax:F$6%F'%%argaG%%argbGF$F$C%@$F`elC$>F.Fdev-Fen6#-Fedo6#-F[jl6$FgftF.@$3
-F:6$Fabl%(booleanG-F:6$FgblFbivC%>F+Fabl>F4Fgbl-Fen6#5-%&evalbGFfn-F\jvFN-Fedo
FiboF$F$F$,
I'tcimin:F$6'F'Fc[lFd[lFbhvFchvF$F$C%@$F`elC$>F.Fdev-Fen6#-F^_tF[iv@$F_ivC%>Fho
Fabl>F_tFgbl-Fen6#3-F\jvFhjl-F\jvF]u-F^_tFiboF$F$F$,
I)tciisvec:F^coFbglF$F$C$?(F.F/F/FfhmF1@$-F:6$FgjmF<-Fen6#F1-Fen6#%&falseGF$F$F
$,
I+tcirandmat:6&%#nrG%#ncGF:%&rangeG6%FgelFhelFgjuF$F$C$@*/FabnF/>F.-%+randmatri
xG6%F`pFep/%(entriesG-%%randG6#Fibn/FabnF[blC$>F.-F[]w6&F`pFep%*symmetricGF]]w@
$4/F`pFep-F]bl6#%8must~be~a~square~matrixG/FabnF[ilC$>F.-F[]w6&F`pFep%.antisymm
etricGF]]w@$Fi]wF[^w/FabnFjbmC%>F.-F[]w6&F`pFep%+unimodularGF]]w>F+-%+randvecto
rG6$-F^_tFb\lF]]w?(F4F/F/F__wF1>&F.6$F4F4&F+FNFdanF$F$F$,
I,tcipickunit:Fb[lF$F$F$C$@$-F:6$Fcp%"+G-Fen6#F]p-Fen6#FcpF$F$F$,
I+tcisetseed:6#FeoF$F$F$C%>%(assignsG%!G>%+conditionsGFf`w>%&_seedGF`pF$6%Fj`wF
e`wFh`wF$,
I.tcisetassigns:6#%$strGF$F$F$@%/-Faem6#Fe`wFfq>Fe`wF`p>Fe`w-%$catG6%Fe`w%#;~GF
`pF$FcawF$,
I1tcisetconditions:F^awF$F$F$@%/-Faem6#Fh`wFfq>Fh`wF`p>Fh`w-Fgaw6%Fh`w%&~and~GF
`pF$F_bwF$,
I+tcisatisfy:F$F$F$F$C%@&F]bw-%(tciloopG6$Fe`wF10FbawFfq-Fjbw6$Fe`wFh`w>Fe`wFf`
w>Fh`wFf`wF$F^cwF$,
I,tcidostring:6#'F_oFajmF^awF$F$C$>F.-Fgaw6%%/if~(0=0)~then~GF`p%%~fi;G-%&parse
G6$F.%*statementGF$F$F$,
I(tciloop:6$'F[jlFajm'%%condGFajm6#%&countGF$F$C%>F.Ffq-FacwF_p?(F$F/F/F$2F."$+
$C&>%'mycondG-F\dwFdp@$F_ew-FenF$Fidw>F.F_etF$6#F_ewF$,
I(tcirand:F$6(F_oFeo%#d1G%#d2GFc[lFd[lF$F$@'F\]l-F`]wF$F`el@%-F:FeevC'>F.Fabl>F
+Ffq?(F$F/F/F$0F.F,C$>F+F]dq>F.-FG6$F.<#Fb[r>F+--F`]w6#;F/F+F$&FablFfn--F`]wFce
lF$C%>F_t-F^_t6$-%&floorGFcel-FfgwFdil>Fjo-FedoFdgw--F`]w6#;F_tFjoF$F$F$F$,
I,tcirandproc:6#Fgev6'F_oFeoFhewFiewF^]mF$F$@&F\]lF[fwF`el@'F]fwC$>F_t-F?6$-%(C
ompSeqG6#7#-...%/tcirandfromsetGF_p%*procedureGF\uFa\o-F`]w6#;&FablFbbl&FablFhb
lF`gwF$F$F$,
I-tcirandmateg:6&Fb\wFc\w%&atypeG%'arangeG6&FgelFhelFgjuF]coF$F$C%>Fho-F^hwFa]w
@*Fh\w>F.-F[]w6%F`pFep/F^]wFhoFb]wC$>F.-F[]w6&F`pFepFg]wFdjw@$Fi]wF[^wF^^wC$>F.
-F[]w6&F`pFepFc^wFdjw@$Fi]wF[^wFe^wC%>F.-F[]w6&F`pFepFj^wFdjw>F+-F]_w6$F__wFdjw
?(F4F/F/F__wF1>Fb_wFd_wFfanF$F$F$,
I/tcirandfromset:F`hw6$F_oFeoF$F$@$F]fwC'>F.Fabl>F+Ffq?(F$F/F/F$FbfwC$>F+F]dq>F
.Fffw>F+FjfwF^gwF$F$F$
