MFNWtKUb<ob<R=MDLCdNVZZJ:tN>H:xXVErps:;BNSDOETlMXlgwgiW;mD[UUUWUsKitUf]Wfv_ivmixoYKEVcsIyuyvayvUIv_ioixoOWkgxwiywOveCHwgIxiIxmyqAYs]IwgYtUiuIXpCIFiSIaBAAsa;GbYyvcixqyxeYweyuYyuWdMWTuUYuyyyyA;:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::ZjifDqEtk]`N\\@Nd\\QgqxH`jwhSWDQVyPxPLAIXU`wyyySUun`r[DNZ]WmUjPuJZ]Y_lSLqqWioSxwwtLEQl@UNGiOC@XyQjXLYbIvN<xwaLnAt=uOZdQnAtE<SIdQnQJLYRIdq:`xJYryqJBhyNFvL?^^YoOA[yYelofiGbt?w[w[PhdK?gSO^DGpLYeJp]t?fjHo\\I_:yo;H]\\`\\:GoDF]`hqEht=w[F_alS=wUToTtOHPwCborY[w:=EpYdRYrYMChKdE?BDmidKG=QsC_YRmHnQBLYr?QeE_X_krige:[iBYcf_DDaGeSs\\eTPOb_wYrwsXirdIviGbNwG];TYeTKmgywvJGBsyCy]VlmFeyEQwcX=jjyx:`sQMP^\\YPho_Tk>xMsmtsIPMhKmYLwMXwIWXqMxqPIUkEQT?moDhtHEo_lY@mQHQpZDyLUrYHpn<yRutnHUv<lpxKYPWwIXR_p`I`pXfWOyy>eMy_JWu=qaR>ppVxO^funr?G`Hv^Qia]vuuocJpwUQdTgd`_mex]Tvf\\xfrhdbXvpIe_Hs[IiH>nUonv@bKpiZHtX`ibhfKO`JFdPPkIqvy^q<?m@vuvA[k`fDhbkYdNqxj_c>_fOfv_wdx^_E?uYXyQ@olFqYIf;_e]IyPVqnosfPyJA^=asuq[j`ZR?kE^yjHtHQgOHxSn\\wYoIh`TY\\Fg`Rx`Iq[Vwq:@]TyybQxv@]k>kivdaY\\ui\\dWirn[PqrTgpPYbx^tvFfkWZbihlYa>^bK@wTwsQhvOyb@?]gqhwomng_>og=>wpGarAc]hibAyX@eLogQnhlykD?s<_c\\>b@QuvA^kxm^ppAXvjVZsF^AFo^_nVVflixrifhaqi?bHI\\Jf_]O]s^`lyssAsp_b=IZ]akdPmJniAv^PnaNAw:Gi>VqmfvRIuyF_[NmpQjc?pIq^PWjiFdUYrc>glPqhP[B?jLNqKAwyxnVhq\\ajYQ^ZFVQxk?e;_f@UbISs??T<aBw=fK]UyYy[oRAMyR=HwiwEUHfmRPSty]TsStbAHxSuYMs^yGKUu=IB=QxemUA=rrwI;aIX=BJ?b^ss[_TXEYTCeEkuGgCNgeEKY:yxEKBLWbmuBHkvjOgvacI_W=_dGktRegYwr]WFQ?yTKBBUwI[HTYrByGjyF\\Wbwgvw]SxawaaWs;yAwTCAS^yxd?Xd=sBgyRaDW=DjsT:=h\\KgmMG[av\\Kd]sTJEcv[dV;fvch;wS:_DkYu]QwOCdO;sg=yoeytSG`kImsFyog^?xEOBLCFViDIgI@Gy]ot^irP;HK?hZOsjgS\\oH?EUSuDGMUAuFJIHi_FKSWUwRT[ho=Succ^;Is_VTUE=ICoSIswCWqRZQG<_iUacrCehOcaIRWuspqRfYT@ccfMuhsyCWrYmIPKIbQhdCehqx\\st?]DG]EqMIFYfW]rgUCbqvIGSgofLWg`aHJKdluEqEeu=ixkwQStrSWtWgcgwJSIGku^oxgKVyQWZEt^gBeKGZKxced=IdTOhJEfR[xrMBkKg^mGJ]Hc[trOT:_R?eFd_FVCXZCD?QCqSX]YetGF<EuQeUfcCLMhjGvVKs_STkUw^]CEUEl[f<?hNEwdoH?MWf]FbesPKU]kgH]bSES;QVV?hHqdT=ce?bp_h=GGuqGD[y@SU=IFKExEeUWAhNMX^wdRYFIMevKeHYWSsCl[HGau[AEZiR_iTJUDS]YckXsoV>]GBqb@;VM=DluVHgVuQeDqxLUE]]WSAR_oB?oxLgr==vqkR?McPAEG]WBKVP[HVOI>IrEuBkUcqSckCwpsFo_Rc?eB[hhCXYSrFChVASt[UUWWs]ceYBhyD>aUTMWZ;vDoR<MigQDu_TtCUuQeTqXLOI>QV_CiI]w_CruEHosRwoFf?EcQiJ?bh<rTuX[Xm>QN?YtNdpPQMSxUM<Lq=q@INBAKETJBhxStLsEq:\\VmYMcEJvLM`\\joAWKlvL`oTExbqR``uRqK;=PX<LAusChO?@mNEjeaP]ISWhp@yWl\\Wc=y<QlPXJQuSwlW=xtYyvJHOTtK;TW>lOIDODTJZyNoUPRLxHlwPelKxT;toREv\\Alc]kbppf`yolyvPvOMkxDK>]u\\EVC]NAanAYc=F^K_udgd[Q^Vi^Dr>[tR=H\\aG_?GT[rtSru[XBuGDsUKag?QUEGEKCigcGMeYoGB<URBIb[ebvYFAKbGyGK=CMQCQ]C^[UkUTFcXVEh=]g<[VDoBAIgOyXCgsQsd`CFc=ujQHK]Yc;xOOi@YxlOFXEbxOGeCs<khaIRVIgOms=eTOIyPyrfyBtqtVuyREy:orPce\\IgqkbVMUZAX>sHsUuOkYqAgC=syoYAsv`KChAX^WR]_xvcF_kRgAc^IcP[SI_D[Uf=MerofcQGoYBfcca[TiETvae;=HGctaqvuWHd;IbAiJEYdytG?hBordUTXWC;ebcisL[UxYDC[gkQrHMgHqebmrikvj?HrSiPyrckxkCwQADCoIeEvbUbGAboQhXEh[;d\\KHHmb_OFtWu_yb_UcROtnwbQUHjEuL=Up_Rb=UYAgUME>gCAgCiySEosEQUGqdWMWq=c?ErKMWIGFwOCeGw_?c@YBM=s`Qes?U`GvDIGu]Dh_U\\aECQCkig`KY^Id<UrFSGdidCQd?wvjsgjoc`av?ABUcCqkDbgUQmYdWTyUHIEI^?vO=xrIY@_IXKxyey:Wy]YRruxDiGiSv?uiHGbVQl:DK[HmrpPHPq^PlE\\kAMkvmLLylFAokljcev=lqi<YWtRLewqIQP]nuTjSqvo]xgtr:`TDeos`qsXoUts^<QVAKd=lHEwRQOVYqEyTo`Y:aYNPKh\\V>AsNQx;TxrdW^YJ^tja\\vHdnlUkRekoYJvXOVesOqlUMN@mPnUPoXmT@jtmUdpKoHxhmuD=QHewk\\nBlOhuqWXowys<\\VPdkZAJgERo`R@ev[evpTq`aSx<NUAvyUra]nvtRiHuBTQITs\\qV\\yLl]raXt\\@PCHS@tr;\\XmDS;XmFpVRyXuHjIMKB`mZivW=NHTSA\\srptgMmIANqeuY@qJMOFhrxELi]vomrP@kg]TEMSNEXrelmyroxkU\\YyMlm=K`AvvaXWmKQqmA<QTIU^IQhmw^IYHQq^\\sWllE]skls=QYwARtpUPHVWin>TKyeq`DLkYPD=VYxOUiu<QTo=u=PUcYXLykEMmBHYwuOSdsmuu_dRm]WlpLI\\xKlqy@K^AO:IJ\\ao;YsdHxRHpO@yD@L?IpLxrdUp_Hvcpvg]uEQVKXwvdnp`VNqVV@t[lL_io;qOIUNwLSfiJ:mt>yVTqNgMVoaoP]RNiVDQO`@VDisdHywtY;@VftLqYlstrE<vhmrBimUMr>EkJAuGxvYiYJmWxxYqdjGxKl]T@QPVYOY`LJ`m`ajN\\MBMVQmysLNDYsq<opYySDm`AvP@qBHlPiO\\Ax<qo\\@YeXrSHPR@VeYVGASrxQZYPGttsPk]eLEhWo<PGAP?QxZLXX<ucMS\\lJydSSMwG@kQLvjAMWTyUtoxULkUPXTu<PQ\\hsaPkdPKNhuHdkAtuCQPZQMKDSvQVPYypLRTxyMTPVMUUhqsmmDpncYlX=NqlqkxRpdPOekRxMp@kSlU]HW;xt?=S_Lm=Atn`LqUQEEVBAWBUnn=tBLXxptF`NSATdUNGHTE<WNINPxWNIRGewJTNwHu=MYV@uE@K<MM_eSGEk_DP@aV@ml@=L\\EuCPvcywSpka@u[tQhDp<eS@Avm@U\\Mv=AQZDW;MMwUkQ=m=aTMAY]LouuS:MN\\yPs\\QXmPVIwvqJoPMTIprAs^QRvlsS]tNdKCEl?xTwmn[prj]WMxKODNIIL^@sn<YfEkXHQNdQMtWLaPMQLqUT?MyZtWTaRCUlk@X;@mWdK?mnVDlF@xvtLVQQsIm^TWs<oX=KaEuEhYELt`]Qr@yTHXRtxBXuvDrZdt^MnVHXIaRxqLKLSGASMHw]@jdyrNTM==se]r`]oG<K\\=VP`YKDjXuTuIjE@wCQSxdM^@wPPS=Msb=k>LO[\\o;tsm]UCILdEVj<S;PTEiNUMVMmoPuJGLTHTNGpXKPKgDpJlUTHKsuo<PcJn_cxp@FwagZNY_WpeM`qAWg]h\\fIsA`bZ^atituw`>Aiayh[PrEQigpbMOwyvaJvx:HgbYg;Xm<OrMogdPw\\>^??kNFaVXqGP^dyZwFrWGxKn[kfgL>`GYnPYkdwbKqbYXpphhOGs>y[[FsuV]Av:GuVKGX?rtmbU=UAyBXQVIOwDqEKIEsoe:ad]kXJavRGdd[BwMcuEY\\eEDex][dxOe]AuRIdBKvS[D>CXgAVH]BwUUGsBYixByfVwvrkSa]BmGWgcfq_il;hgig<ARuarHuhNQdqkHkKWqAdpEcGoGCMI^iwaWcWyFSmSlqsI_WmgGcqeVismqboWhYWGdWSFGCnwvkOH?kFPCsjohaaDoygB;cesRR=HPAcA[ivarNgrGQyf;ce[cSab>oF<eXJ]bA?rgIUJKetmscqCqEULmU<MfeQwrytKsXtsvgwfR=ssee]eVr=iXgTusREKIrawVaesoD[]yqAgT=VE;XwgTX;CsicmshZIyh]tf;D>agYkSZ;cEeeOUbpgBK]C^cch=X[Wcw?TK]D_kwZcr^aIMaiv]gC?uR[iAeGn=gWIRDYxaAgLyiU[cosfTMs`WHECeWihZSi[SSH?vD]CCSyJSeLawp=dB_xOOxKqg@cy^?bb_wJSC`UYT[bNEGd]HZiIOAbVOrJeEcKIj?FnaWgAelSCA_WK]t\\AUAqSMMDhSVRgep?BFMu]kRDkvOKw`]iy]SsAxnUt>Sfi;IWuuuGev=rhWd@qggYFHucr=ffovLQB_[e>=ieAwjAd\\ihDUtOSHFeW^wiAeWnMCcsXsmh]oxC?g_?fYgrnsSvguuMb[If?Cf`mRPEvYusl;XQ=SqmDRAsuctPGvsgxHgBKui\\;Fv]GLAD^[CoME>?SOWUigTKUYTYDTcIVCGt;`FO]UfkWV^GwkaW`ufkKPZt?\\Dw^oO_\\^iw@bn_mvN^]?vKqc`v`tVs<@yfN_e`\\DvsFg`iYcLHtw_bKwZk^hKVnhVfmg\\sIwQPfAG`Pnhuikjww=atXPbdweN@jNWuG`agib^ViYfeaPir?g;_[=Or:x\\vqi=iqZiZTvk@afXvpdqlSW\\ipydarYG\\JFm=Y_xge?_ZBqcDH_NwrNXxkPn=W[lYn=a_=HZ[in?PnAayT?yxviixbhXr;igdHiooQ]eDWfbiF@Sx=ctvwu[QWIiI^sE]WrP[EbMugWRnsBd[yR[d?YU=MybchadqR=loMvwDSWYPWxR\\=LOdWj<LImuL]w<XNAEROhwKHLxmKftSxYUf<KEMxxtLNlYKxr>uQtpTVYUt\\mudTa\\t]enZDQp`YkqSI@o]qOp`lo]PCxxxAkrxx_DsTImQHSayThaRE\\JLtptqRAuQyXONdUyUN;ax[MWsxxN=t?=J_yU?PK?Qx:Hn_YNk<SLIy\\UUDYOhhv:MufmMkIOrUJqXslDrU@wYqQEhLKAk[Xnkqv_]xcUKl=TaEnUENPmvHipVpSHYtcPQKxTIUw`XXeAq[iXyhqXdW]quSlkuUNTQw[hyWalRESQhKudMPuRNHQVTpZ<VAHnsHlYxv^mmVHJtDYoTw]at\\XX^Yy<LjJ`kV@o]tS=XJqMQ]Epq`sVIJ^pWtPKcLmkdNIhuZ=WYyvhTNrpTPiMwTQaqqZERnXje=nI`Ux=pPutt]X^@wGUKLxj[=qJQnY]VMLUFMrq`wIDsXhPc@Q\\AyrtTuHN=IkfdUeqO[lLqQpHtv=qJ>qNNmRUUL^]wRTLD@q]`sWhxkTK<hN^drxQmkARFQrVApJXYrlLWhVKqs`pxRLTwuQjdqf<wR=lOmu_]N\\aXCisgmJtDXsdUtUL<Pk`Xp^<URPuE\\Ty@UGDKXMKlQM:pt<`nHyvg<kEyn^lVFIQ>qPnuwBeyruTmHYmXJ_urDpKqIRpPLLxRV]JtLSkujxmokElxMuxAXNYWchP=hRXxUjpvqqnGEnv=YjQrZTP^epTqja\\PFDYnucSPdiflVg[jw[Hw\\j^_owuVPdfg_CVgdXnHhhkQwMVshgZTxolYbh`ojHqw_`eXZ\\>wXOne`m?goL_wOn`Bw`a_vfyyXGuJGugfso`mgivtHmX^cSpmQaf\\^]nyh=oZx_wPXnOitrib:XwYOhpWy]qdlWvu`cX>]Jgsm>tdqssn_F?anfyNhZKgg\\NgDyp;Ah:_lhAs[vtDF\\Mwh\\gwBAl[ybMX^?We]YdEnZwhy:Qw>aut@_lOl:>hfgaoxuFQbKnbYHpHQobw^C_nW@qDnpcQqEGawV\\`@rnpclhck>^XGdN@qdAu[FfUI^u_\\:`qfvq?_soG\\UguAA\\An]kPlFNdB@sKVpdNtH^gAfoipdaGdEGlPwbJPt[OsQn^UN`mFZZvlnob>ygL^wWYm\\VheVeMGjPhrJHenIbp@x\\we]Xoc``hpe`xp:vuXweMYg[PqTpniH`oo[Jg]t?si@`pvofItsn\\^Id`ovVagAqlaIxV@]jV]dvaQFal_hbowAOxD`_aYjJhloqkWYlJ^fAfbi>lMP`QNf[grX>r@_nH_j_a^TNvoxiJVrs^euPco@\\QO[O_pE>gYPm@_moP^UQ_BpfENcH`jMnZiYtmx`VOgxv\\fOqhod@yoWAoHNk^WbCYdsOhrygJndKvqVXbR@]i>jAHyW^]h?]fxgCIcNn]Io^lNwHFf>@gYAkQVcD@iB?\\UGrTV^hfjDifg^ytAyIv\\Q`myVx`v_DQZ\\Hxt`^Qq_sQm@hdCntT@c=xfg@`UYo\\YxxfpgYjHI`dggYo_q`thI^W`a=GrBheUVoPwkhxydGZS^np?yF^mGhhvh]TI^<qhwq^HF\\sQpVGtoo[GabIV\\f@fBywC?jOwoGF\\cFyqnmmNhewn:wkfxoaOipho:w_^w]GXi@^xiQeqFiOn_gA^oVpUYn<NxEgl?Iigi`ZQhlGuWovA_xna\\XNs:yb_PprX^Giv;Fhqxg<Ite^dDFajHfSvoQYi?WxZPdcI_NGm=iZ^Iv`>dY?p=qhmPp=>]O`bIQwNgelQd?VbY@i_O`\\IbDIeZfrmpblvlZfZy^svnsnIhmNh[apjVbmVfUfZ[At=`fBgvKfgWxkb?cfojdGvrhiLfv`Y_C_dipgXwoCXtsHl\\n]NPZmO`yW\\e^hT_xDFlh`[PI^ZnpWpmDgZ=_cGfccVvZnnJYkVofg^hlWw>pa\\`lMpfHPjCPj>GfnO`T>icv][fj@vktPronymPTgdbPp>yNdTnpdorQmTay:DoCxr`iP>QLchN@DXDTryXyI]jG<uEhL@TuA=leyOf\\XrPtZpOimYiqQgQrqXvrlWquqtLPvQyp]r?QYNur`uNWeR`xq^HjFipgUYXDsAYxNTrm@OJqPIYn:eoFMXYEtcLPRqLGHwKlnaUMpHocMwN=yZVfE^^_Iq\\FnC_cTHhnWsW?oN@nbP]]hrvGbs?oqnmB_a[xvn>fc@_EOi>XhNfpuVa@xhNIc^ormIqffoF_mfHcgydgN]__v:H[p@_R^^K`]eaoMijRW\\ZOy`hhApeUpmBh`@@mQ`n[fhMqbT_oOfhEphtAl`?lnidb@vhwbq^xVGcmo`nhuJavkNZI^`<gghHoD?`h_mIQyIHqFVg[q_T_n]Xb^H\\Sf^]nt`wfWo_VnvLHfSnbsYyui`AQgcq]D>sK@fqf[ChiS_Zvff[HtBRlgF`?sOSSrqvdAIH?xtmU]uW]GGDaRiSF?MTpKvokhbYF>QhhKUN?Dy=Vfwv=EVGWivoeK_uLagD]rVCtM?d?=s=GRQoYfIY;=UqoerMDsgILoS>EX<mCk_GFAY\\iEvIDggEAqehqgdWhSaSOUdAUBqeyMMco;gf]wO_slsGEaIlUtoegg?EaITkSu`QrwovxKy^keL]r]Gvj[WJshO_igADBwg]`vSmLLIsRHoCdLlHMFPxfpkLPr`]jmPOFQxvIkdLn>xVQysDtsEMptxvKaN``thlRl`qI`XiimSeJ:\\SiLU<mR]Hrb]xAmudTkWePQiuQ<lourv]tMtWUajiyo:pnW=PE=oLDQ^yL>`oG`jXtLplxs`mj`t[HODPnkDOtettHqVHKU=TglNadR^xUKYR;Xn;<YG`PtQYXTOlPtSDQNEliMw^dsvIpftPUikHal>LVqxkXxRShUC`TipvaAN;pssPOEQptlL^mrK=MKyTC`uc=mEdpR`u=Aqexjr@RkUPqXUGALn]l>HvcXKD@ycIv;QWKtSUmU_URB`kR`MBDlXTnbLnq=YXUnVPtutyO`Qx`JfmUbmQGxKlQmTQlLUMi=RZXmFeN`lXU<uQatxDYXqQLaVUXrdyUKMyAhkMQqTDjuqSTxpJTKBqv^QynlK]dXl@sXpogxR^qOXdvGxmYYWIMnf\\OYuueLM?iRneRwywcQRrPnFLPG=VRPO^iK]<RqpMYlquAxWpYwqKmufyfiq?^c@_DNnnYw@o]k>[^iuBfhQIyrNu@inlp[_Wfu^_Yp]EAal_y^ve_`bP^agga=AeRwaHAjQoeDOyV^e]oqUG`y?chw]=NxxO\\wVwZndk?bV>pPVjPYjDng@xc=qpQ_cOH\\Q>\\_f`Gfm^odnQ`>XZdWe\\GmFFvsPuapp=`lFVthi[Bya=NqqFxYYcmq\\pfsaGx;A\\DQldPwBPqMf\\UonsVuhHhX^fcNoQoceOkhIsti^;qtZGtOnxX?^vqdYPpjo]hPl<qc@VkTheGOwEokn@[Naiy^mBQj\\IrcOmOnk<ok]qt=qr=VoIV_d_jXvuqiowXw[ncxH_LY]tgpundPNeGpik>v[ivRFt_GuKnqFIw\\n[Dpht`vgIkZav_Q]NqvbAkmHqAqgUOq_H^ZXjE>c@ObIXjtnofGo?qq^gek>ut@iu`tp?l\\IpOhwCas\\aonfiIvm?PdqQgMNhVQjFgeDAdSFf\\VeDAghqlRG\\UFqMYepp^xvlPPv^G^e@dF?^L@mKIurQ^^yxKFiKnmXGj:IvRymv>lgOlr?q<htJI]lw[^quL@_\\Gfugp<?xGw[l_w?ieg_ijn\\D^\\eInBw[<gZnH\\oQ_FAbVnaFaaR`_>G`rHna^skP[@Fjhih>`bBpbgvvrAaBxp=Aqoqb@w_j^q;qa\\VuFq[@x[V@[?AgJ^[kxerPenhqfWafWy@qfmqvcwZkng[awq@ona^EG]KgrbY]_`]Nx^fGZrOxeA`RFh:@wFNjfhZ]Ncgiq=YddW\\b^m@@erFcgq[LQmRApeA[qAxA>rTGrBHmJpxoxayqqiagVO`cIn[>[^Xr@IhK>b:Ywm^koNxqg[X`g<QyC_gM`[x_fy>t\\@fbxb;A`h^hdQiKXufFnFH]Lhqchj^fyOeC[fcowYsvRqI;kW[;teGV^?TIUwW[etGDOmhlUf[ubfcyi]IMogiwH^Uh:owAwfWaRpmtCCu=IFdAe^OhsKrueeZESZUB^cinMIfwE_mfskxJsEn?fOac@?GJ=uXkDIiB:qYOWBUKR?=u?qgNath?vdGFP?u`Uyw]fCccUOtvUGYci?Cu=gXp]xIcIyOrAmyxYxIcUNKFpQDYYR;CwB=sPqiF?eF?C>UTYef>=RJMT\\EBCGUDihhKUR]vgAenUvZiCeibWkCcUBoqdoocwyCC_r@if;Ssqksw_DVoBuyY;yrdqfuSchAYAUgqSySkgZuWmkD=QcvYwY[bksrJsEaKWiWuM=u_gc:Eg_YfMYtnqHogRisEi=xpsXq]grIhrWFiECySU:mRe_xgEBs[C\\yRo?c:sifCgn[XHeDUgWKoiicEPYIqqHxkWwAgYchqgDjgI;aFpKDWQv_OBZYt>WwdAUYuRL;coyqNuVh]Uqptdik;pXdykxTQGlTQtvX`YV=q:@Vm@rfTrITlTyjYtxo@jnUSSHSs]q_uyq]sCeWNMuHmK>\\jW=lwdNZdoB`WspoPDLoImBUJaaXXmXPaLSeon=UuamQqmpEUWHsLTyvEXTeOiiYyiqy=qq]XHARH`M_IQc<YAenHyQTInyMlRYKKxkfEXyAmYyQT=pthy[duxAmCAmAyYwUosdyA`PkQkUtOyxr`IR^tmMLvePL;DYZenryvu<YGuNr`xkPqPxMrmmC=S@\\vayJkMxnutcav>@jVDv`lqdmL;iwfTkBeLqlUWQPfUXQXyZuLgmsOyQ=HV@uNxeQuumr@QOMykDMcLms=OH@sQIU=HQm]rxujluyGqpxYuNqUD]Yxar;avC`mH\\U;tP;lWkuQsIJmxMGMLvMNaYPS`mrYOhqYJ@SreQx]TbHOrHlcIm?EypIjnhlkEwgYnFtXohJSUslLrw<kq`XcXuHmS:IPPMW^\\neLNrEYTELkhyWDW:pv@PRNASAqoq`YLxUytXZMvr`TjlmkUq=hQPQRvdtSEXTYUuULq@YxAT?ySLmUVdNoQNV\\oKQwoUX=myJ@v^yrfIsJdOR=X>=WX@URHjyIVIuXILLS`nk\\LsdLJxVXpmjPrpyJ:YqgMSUurFXqeaWDxpW`Y:=RpPLLao?TQMDNl`PdYp<mX>yXXELE`wQmT>]QetyZEUExkr=R?yraIXTIYjuufinriK\\@ySqKExX^]x]`rX=R:LVhpPBlPeYY\\dLbUNT@PXeS^awZiwAukjXW<<medjwP`qweXNrkoh_Yo=hbkW]w`wE@eNWblwkhX\\h^rNobMQrywiKYkYy`yWt]ifhylt^hyAx\\x\\yHkTYkBxsk_yjAh=hv[_^yfua_d\\?ktxar>jowbYyZlQaPVmj^iwPq?`[AH^^Q`pAy`wdZ`cMpyvi^;FrmxqywtPpwWN`qqa[QdlXxJ_hwgZL_rHxkiGaZWq\\xqMHw`xvNAhI_pjwsL@pMWrx^ohqiZ?ohyw^xx<OtQW[cqlrFcZoa\\N]SWbKwq?hykwj=y]`_feNsf_Z[@i^xvxX`iv^w^fXWdQv`t?bqYvfV^qphkgnm_hOIlfn\\fynmpxP?yfvpuiepnhyfruyi?>qYo^rxuxAu;hxeia_wyYf[Iv]`Hiq?nHWxDy^IPZyhm?QaVojWapPgmnI_x`n_yim@`jyr?OyyW\\`xqA@uXNaHW\\?pdAykuveI@c;AqmIyCw\\eAf?OoWapPGxIHpxyjRfjyakN`gUFxaOcSvyYAl?qefnu;fvI`xtowHHrpWh^icYOitqy<pdyOmS>yin`\\ya=hntvo[gtmpyYVjkyiO?btFfuaxe_etyhlXZyyZ?xpAxy\\>kYFv;P[to`bIvl@n_ifMIa]P`Iyy`Pcw^xjyqEnks_b:ojdIi<fxpVyqQtKYryyabHsKv\\E?lYgvjouu>dw^etHyjX`s?yTqZUYuR^^X`Z?ykxoit?qn?sL`_;hlj?]^xdshgsyqmAoNw[w^yyN[Bv_<AgOftih`SIa=h_fpbx@uIAdIvlHV^f?bdYf@hwS__:vh^Iw_IoyPoVYbIv\\=V_J>p;FmhYeJ>xan]bYoxoitCV[bBKeqqroeGBCI=MHlQycIw[Qv;?cAaxJ=Rxay_EfXKYryy:oxvcdr=TVYCCuCw?X:IX;CIrIiAoEhSEtiWkqEt=w?tKw\\x<vjXniu^yAv]AYcNiedPgjD:;j^PNaLNQENjD5BMore Powerful Mathematics in Maple 9.5\251 Maplesoft, a division of Waterloo Maple Inc., 2004

Continuing the tradition of providing powerful solvers and standards-compliant algorithms that deliver maximum accuracy, Maple 9.5 significantly expands the type and complexity of problems you can solve. The following Maple enhancements are highlighted:: \342\200\242 The new Logic Package \342\200\242 Enhancements to the SolveTools package \342\200\242 Updates to simplifications \342\200\242 Updated summation \342\200\242 Differential equation routines for exact ODEs \342\200\242 New Toric Ideals of Groebner Bases \342\200\242 Updates linear recurrence equations Package \342\200\242 Enhancements to the QDifferenceEquations Package

The new Logic package is a suite of routines for manipulating and transforming expressions using Boolean logic. It uses a two-valued logic system, while standard Maple logic is three-valued (true, false, FAIL). All Boolean expressions in the Logic package are expressed using the operators &and, &iff, &implies, &nand, &nor, &not, &or, and &xor. with( Logic );

NiM3OUklJmFuZEc2IkklJmlmZkdGJUkpJmltcGxpZXNHRiVJJiZuYW5kR0YlSSUmbm9yR0YlSSUmbm90R0YlSSQmb3JHRiVJJSZ4b3JHRiVJMEJvb2xlYW5TaW1wbGlmeUdGJUktQ2Fub25pY2FsaXplR0YlSS5Db250cmFkaWN0aW9uR0YlSSVEdWFsR0YlSSxFbnZpcm9ubWVudEdGJUkmRXF1YWxHRiVJK0VxdWl2YWxlbnRHRiVJJ0V4cG9ydEdGJUkoSW1wbGllc0dGJUknSW1wb3J0R0YlSSpOb3JtYWxpemVHRiVJJ1JhbmRvbUdGJUkoU2F0aXNmeUdGJUkqVGF1dG9sb2d5R0YlSStUcnV0aFRhYmxlR0Yl

Simplify a Boolean expression.BooleanSimplify( ( a &and b) &or ( a &and ( &not b) ) );

NiNJImFHNiI=

Find a truth assignment that makes an expression true.Satisfy( a &nand (b &xor c), {a, b, c} );

NiM8JS9JImFHNiJJJmZhbHNlR0kqcHJvdGVjdGVkR0YoL0kiYkdGJkYnL0kiY0dGJkYn

Determine whether a Boolean expression is a tautology (always true) or a contradicton (never true).Tautology( ( a &or &not a) &or b );

NiNJJXRydWVHSSpwcm90ZWN0ZWRHRiQ=

Test whether two expressions are logically equivalent.Equivalent( a &and ( a &or b), a );

NiNJJXRydWVHSSpwcm90ZWN0ZWRHRiQ=

For some Logic commands, you can ask Maple to provide a counter-example for the tests that return false..Equivalent( a &implies b, b &implies a, 'p' );

NiNJJmZhbHNlR0kqcHJvdGVjdGVkR0Yk

p;

NiM8JC9JImFHNiJJJXRydWVHSSpwcm90ZWN0ZWRHRigvSSJiR0YmSSZmYWxzZUdGKA==

Ask if the first expression logically implies the second.Implies( a &or b, a &or ( &not b), 'p' );

NiNJJmZhbHNlR0kqcHJvdGVjdGVkR0Yk

and see the counter-example.p;

NiM8JC9JImFHNiJJJmZhbHNlR0kqcHJvdGVjdGVkR0YoL0kiYkdGJkkldHJ1ZUdGKA==

With the Logic package, you can also generate random Boolean expressions, create truth tables, convert expressions into normal and canonical forms, and more.

The SolveTools package now provides a submodule for solving linear inequalities rigorously.with( SolveTools:-Inequality ):To solve a linear inequality in one variable, use the LinearUnivariate command.LinearUnivariate( a*x < 1, x );

NiMtSSpQSUVDRVdJU0VHNiI2JTckPCMySSJ4R0YlKiRJImFHRiUhIiIyIiIhRiw3JDwjMkYrRioyRixGLzckPCNGKi9GLEYv

You can also solve under assumptions on variables.LinearUnivariate( a*x < 1, x) assuming a > 0;

NiM8IzJJInhHNiIqJEkiYUdGJiEiIg==

To solve systems of linear inequalities in one variable, , use the LinearUnivariateSystem command.eqs := {x+1 > 0, 2*x-1 < 0};

NiM+SSRlcXNHNiI8JDIiIiEsJkkieEdGJSIiIkYrRisyLCRGKiIiI0Yr

LinearUnivariateSystem( eqs, x );

NiM8JDIhIiJJInhHNiIyRiYjIiIiIiIj

eqs2 := { a*x+2 <=0, 2*x-b >=0 };

NiM+SSVlcXMyRzYiPCQxKiZJImFHRiUiIiJJInhHRiVGKiEiIzEiIiEsJkYrIiIjSSJiR0YlISIi

LinearUnivariateSystem( eqs2, x );

NiMtSSpQSUVDRVdJU0VHNiI2JzckPCQxSSJ4R0YlLCQqJEkiYUdGJSEiIiEiIzEsJEkiYkdGJSMiIiIiIiNGKi1JJEFuZEdGJTYkMiIiIUYtMUYxRis3JDwiLUY3NiRGOTJGK0YxNyQ8IzFGK0YqLUY3NiQyRi1GOjJGMUYrNyQ8I0YwLUY3NiRGRjFGK0YxNyRGPS9GLUY6

For multivariate systems, use the LinearMultivariateSystem command.LinearMultivariateSystem( {y < x-1, y > 1-x}, [y, x] );

NiM8JDckPCMyIiIhSSJ5RzYiPCMyLCYiIiJGLUYoRi1JInhHRik3JDwjMUYoRic8IzIsJkYoISIiRi1GLUYu

The simplify command is faster and more powerful in Maple 9.5. Below are a few simplifications that could not be done with earlier versions of Maple.Simplifications involving absolute value have improved.abs( x*y )^2 - abs( x )^2*abs( y )^2;

NiMsJiokLUkkYWJzR0kqcHJvdGVjdGVkR0YnNiMqJkkieEc2IiIiIkkieUdGK0YsIiIjRiwqJi1GJjYjRipGLi1GJjYjRi1GLiEiIg==

simplify( % );

NiMiIiE=

Simplifications involving logarithms have improved, including better handling of the branches for compositions of the form ln @ exp: ln( exp( 33/5*I) );

NiMtSSNsbkc2JEkqcHJvdGVjdGVkR0YmSShfc3lzbGliRzYiNiMtSSRleHBHRiU2I14jIyIjTCIiJg==

simplify( % );

NiMsJl4jIyIjTCIiJiIiIiomXiMhIiNGKEkjUGlHSSpwcm90ZWN0ZWRHRi1GKEYo

Expressions involving powers are now simplified more quickly ( up to 2 orders of magnitude for some complicated expressions), and more cases are handled.(-1)^a-(-1)^(-a)-2*I*sin( Pi*a );

NiMsKCkhIiJJImFHNiIiIiIpRiUsJEYmRiVGJSomXiMhIiNGKC1JJHNpbkc2JEkqcHJvdGVjdGVkR0YxSShfc3lzbGliR0YnNiMqJkkjUGlHRjFGKEYmRihGKEYo

simplify( % );

NiMiIiE=

There are also enhancements in the simplification of int, sum, product, and limit and in their inert counterparts Int, Sum, Product, and Limit:diff(s(t), t)*Int( f(x)*x^( s(t)-1)*ln( x), x = infinity..0) + int( f(x)*x^( s(t)-1)*diff(s(t), t)*ln(x), x = 0..infinity );

NiMsJiomLUklZGlmZkdJKnByb3RlY3RlZEdGJzYkLUkic0c2IjYjSSJ0R0YrRi0iIiItSSRJbnRHNiRGJ0koX3N5c2xpYkdGKzYkKigtSSJmR0YrNiNJInhHRitGLilGOCwmRilGLiEiIkYuRi4tSSNsbkdGMUY3Ri4vRjg7SSlpbmZpbml0eUdGJyIiIUYuRi4tSSRpbnRHRjE2JCoqRjVGLkY5Ri5GJUYuRjxGLi9GODtGQUZARi4=

simplify( % );

NiMiIiE=

Combinations in sums now take into account that the indexing variable is an integer.z := k*(2*ln(k+1) - ln(k) - ln(k+2));

NiM+SSJ6RzYiKiZJImtHRiUiIiIsKC1JI2xuRzYkSSpwcm90ZWN0ZWRHRi1JKF9zeXNsaWJHRiU2IywmRidGKEYoRigiIiMtRis2I0YnISIiLUYrNiMsJkYnRihGMUYoRjRGKA==

combine(z, ln); # k is an arbitrary complex variable, so no combination is valid

NiMqJkkia0c2IiIiIiwoLUkjbG5HNiRJKnByb3RlY3RlZEdGK0koX3N5c2xpYkdGJTYjLCZGJEYmRiZGJiIiIy1GKTYjRiQhIiItRik2IywmRiRGJkYvRiZGMkYm

s := Sum( z, k = 1..infinity ); # but now k is an integer from 1 to infinity

NiM+SSJzRzYiLUkkU3VtRzYkSSpwcm90ZWN0ZWRHRilJKF9zeXNsaWJHRiU2JComSSJrR0YlIiIiLCgtSSNsbkdGKDYjLCZGLUYuRi5GLiIiIy1GMTYjRi0hIiItRjE2IywmRi1GLkY0Ri5GN0YuL0YtO0YuSSlpbmZpbml0eUdGKQ==

combine( s, ln ); # combination is therefore valid

NiMtSSRTdW1HNiRJKnByb3RlY3RlZEdGJkkoX3N5c2xpYkc2IjYkKiZJImtHRigiIiItSSNsbkdGJTYjKigsJkYrRixGLEYsIiIjRishIiIsJkYrRixGMkYsRjNGLC9GKztGLEkpaW5maW5pdHlHRiY=

The combination of logarithms is now more general.-ln(5) + ln(abs(x)) - ln(x);

NiMsKC1JI2xuRzYkSSpwcm90ZWN0ZWRHRidJKF9zeXNsaWJHNiI2IyIiJiEiIi1GJTYjLUkkYWJzR0YnNiNJInhHRikiIiItRiVGMUYs

combine( % );

NiMsJC1JI2xuRzYkSSpwcm90ZWN0ZWRHRidJKF9zeXNsaWJHNiI2IywkKiYtSSRhYnNHRic2I0kieEdGKSEiIkYwIiIiIiImRjE=

ln(x)-ln(y);

NiMsJi1JI2xuRzYkSSpwcm90ZWN0ZWRHRidJKF9zeXNsaWJHNiI2I0kieEdGKSIiIi1GJTYjSSJ5R0YpISIi

combine( % ) assuming x > 0;

NiMsJC1JI2xuRzYkSSpwcm90ZWN0ZWRHRidJKF9zeXNsaWJHNiI2IyomSSJ4R0YpISIiSSJ5R0YpIiIiRi0=

ln(a-1)+I*Pi-ln(1-a);

NiMsKC1JI2xuRzYkSSpwcm90ZWN0ZWRHRidJKF9zeXNsaWJHNiI2IywmSSJhR0YpIiIiISIiRi1GLSomXiNGLUYtSSNQaUdGJ0YtRi0tRiU2IywmRi1GLUYsRi5GLg==

combine(%) assuming a > 1;

NiMiIiE=

The sum command provides more closed form solutions through accurate summation. Sum( Psi(x)^2, x) = sum( Psi(x)^2, x );

NiMvLUkkU3VtRzYkSSpwcm90ZWN0ZWRHRidJKF9zeXNsaWJHNiI2JCokLUkkUHNpR0YmNiNJInhHRikiIiNGLywoKigsLCokRi8iIiVGNSokRi8iIiQhIzsqJEYvRjAhI0BGLyEiJSEiIyIiIkY9LCZGL0YwRj1GPSEiIkYsRjAjRj1GMComLCpGOSIiKkYvIiM4RjZGPEZARj1GPS1GLTYjLCZGL0Y9Rj1GPUYwRj0qKkZHRjAsKEY5RjVGLyEjQ0Y/Rj1GPUY+Rj8tRi02IywmRi9GPUYwRj1GMEZA

More partial results are available through partial summation techniques.Sum( 5^x*(3*x-2)/x/( x+1), x) = sum( 5^x*(3*x-2)/x/(x+1), x );

NiMvLUkkU3VtRzYkSSpwcm90ZWN0ZWRHRidJKF9zeXNsaWJHNiI2JCoqKSIiJkkieEdGKSIiIiwmRi4iIiQhIiNGL0YvRi4hIiIsJkYuRi9GL0YvRjNGLiwmKiZGLkYzRixGLyIiIy1JJHN1bUdGJjYkLCQqJiwmRi4jRi9GLUY+Ri9GM0YsRi9GM0YuRi8=

Maple 9.5 yields nicer results for many definite sums.Sum( binomial( n, 4*k ), k=0..infinity) = sum( binomial( n, 4*k ), k=0..infinity );

NiMvLUkkU3VtRzYkSSpwcm90ZWN0ZWRHRidJKF9zeXNsaWJHNiI2JC1JKWJpbm9taWFsR0YmNiRJIm5HRiksJEkia0dGKSIiJS9GMDsiIiFJKWluZmluaXR5R0YnLCgpIiIjRi4jIiIiRjEpXiRGOkY6Ri5GOSleJEY6ISIiRi5GOQ==

The int command now uses differential equation routines for exact ODEs to compute integrals when the integrand contains unknown functions and is a total derivative with respect to those functions. (Note the usage of the compact notation for typing derivatives now available in Maple 9.5).PDEtools[declare]( u(x), v(x), prime=x, quiet ): U := DEtools[diff_table]( u(x) ): V := DEtools[diff_table]( v(x) ): Int( ( 3*U[x]*V[]^2 - U[x]^3)*sin(U[]) + (-6*V[]*V[x] + 2*U[x]*U[x,x])*cos(U[]) + 8*V[x]*V[x,x], x );

NiMtSSRJbnRHNiRJKnByb3RlY3RlZEdGJkkoX3N5c2xpYkc2IjYkLCgqJiwmKiZJI3UnR0YoIiIiSSJ2R0YoIiIjIiIkKiRGLkYyISIiRi8tSSRzaW5HRiU2I0kidUdGKEYvRi8qJiwmKiZGMEYvSSN2J0dGKEYvISInKiZGLkYvSSR1JydHRihGL0YxRi8tSSRjb3NHRiVGN0YvRi8qJkY8Ri9JJHYnJ0dGKEYvIiIpSSJ4R0Yo

value( % );

NiMsKComLUkkY29zRzYkSSpwcm90ZWN0ZWRHRihJKF9zeXNsaWJHNiI2I0kidUdGKiIiIkkidkdGKiIiIyEiJComSSN1J0dGKkYvRiVGLUYtKiRJI3YnR0YqRi8iIiU=

value( % );

NiMsKComLUkkY29zRzYkSSpwcm90ZWN0ZWRHRihJKF9zeXNsaWJHNiI2I0kidUdGKiIiIkkidkdGKiIiIyEiJComSSN1J0dGKkYvRiVGLUYtKiRJI3YnR0YqRi8iIiU=

The Groebner package can now compute the toric ideal of a Groebner basis. Both the Hosten and Sturmfels (GRIN) algorithm and the algorithm by Di Biase and Urbanke are available.with( Groebner );

NiM3OEkqTXVsTWF0cml4RzYiSSlTZXRCYXNpc0dGJUkwVG9yaWNJZGVhbEJhc2lzR0YlSSpmZ2xtX2FsZ29HRiVJJ2diYXNpc0dGJUknZ3NvbHZlR0YlSStoaWxiZXJ0ZGltR0YlSSxoaWxiZXJ0cG9seUdGJUkuaGlsYmVydHNlcmllc0dGJUktaW50ZXJfcmVkdWNlR0YlSSppc19maW5pdGVHRiVJLGlzX3NvbHZhYmxlR0YlSSpsZWFkY29lZmZHRiVJKGxlYWRtb25HRiVJKWxlYWR0ZXJtR0kqcHJvdGVjdGVkR0Y0SShub3JtYWxmR0YlSS9wcmV0ZW5kX2diYXNpc0dGJUkncmVkdWNlR0YlSSZzcG9seUdGJUkqdGVybW9yZGVyR0YlSSp0ZXN0b3JkZXJHRiVJKXVuaXZwb2x5R0Yl

A := Matrix( 4, 8, [[1, 2, 3, 4, 0, 1, 4, 5], [2, 3, 4, 1, 1, 4, 5, 0], [3, 4, 1, 2, 4, 5, 0, 1], [4, 1, 2, 3, 5, 0, 1, 4]] );

NiM+SSJBRzYiLUknUlRBQkxFR0YlNiUiKUcrQj8tSSdNQVRSSVhHRiU2IzcmNyoiIiIiIiMiIiQiIiUiIiFGL0YyIiImNypGMEYxRjJGL0YvRjJGNEYzNypGMUYyRi9GMEYyRjRGM0YvNypGMkYvRjBGMUY0RjNGL0YySSdNYXRyaXhHNiRJKnByb3RlY3RlZEdGOkkoX3N5c2xpYkdGJQ==

zs := [seq( z[i], i=1..8)];

NiM+SSN6c0c2IjcqJiomSSJrR0YlIiIiLCgtSSNsbkc2JEkqcHJvdGVjdGVkR0YvSShfc3lzbGliR0YlNiMsJkYpRipGKkYqIiIjLUYtNiNGKSEiIi1GLTYjLCZGKUYqRjNGKkY2Rio2I0YqJkYoNiNGMyZGKDYjIiIkJkYoNiMiIiUmRig2IyIiJiZGKDYjIiInJkYoNiMiIigmRig2IyIiKQ==

ToricIdealBasis( A, zs, plex( op( zs )) );

Error, invalid input: `Groebner:-ToricIdealBasis` expects its 2nd argument, vs, to be of type list(name), but received [(k*(2*ln(k+1)-ln(k)-ln(k+2)))[1], (k*(2*ln(k+1)-ln(k)-ln(k+2)))[2], (k*(2*ln(k+1)-ln(k)-ln(k+2)))[3], (k*(2*ln(k+1)-ln(k)-ln(k+2)))[4], (k*(2*ln(k+1)-ln(k)-ln(k+2)))[5], (k*(2*ln(k+1)-ln(k)-ln(k+2)))[6], (k*(2*ln(k+1)-ln(k)-ln(k+2)))[7], (k*(2*ln(k+1)-ln(k)-ln(k+2)))[8]]

Three new tools are available in the linear recurrence equations package, LRETools.The AnalyticityConditions command determines necessary conditions for the solution of a linear recurrence equation to be analytic, in terms of the initial values.with( LREtools );

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

AnalyticityConditions( n*E-1, E, f(n) );

NiM8Iy8tSSJmRzYiNiMiIiFGKQ==

The dAlembertiansols command finds all d'Alembertian solutions of a linear recurrence equation, that is, solutions annihilated by a product of first order operators.rec := (-n-1)*a(n)+(3+2*n)*a(n+1)+(-n-2)*a(n+2) = 1/(n+2);

NiM+SSRyZWNHNiIvLCgqJiwmSSJuR0YlISIiRisiIiJGLC1JImFHRiU2I0YqRixGLComLCYiIiRGLEYqIiIjRiwtRi42IywmRipGLEYsRixGLEYsKiYsJkYqRishIiNGLEYsLUYuNiMsJkYqRixGM0YsRixGLCokRjxGKw==

dAlembertiansols( rec, a(n), {}, output=basis );

NiM3JDckIiIiLUkkU3VtRzYkSSpwcm90ZWN0ZWRHRilJKF9zeXNsaWJHNiI2JCokLCZJI24xR0YrRiVGJUYlISIiL0YvOyIiISwmSSJuR0YrRiVGMEYlLCQtRic2JComRi5GMC1GJzYkKiQsJkkjbjJHRitGJSIiI0YlRjAvRj47RjMsJkYvRiVGMEYlRiVGMUYw

The IsDesingularizable command finds a multiple M of a given linear recurrence operator L, if possible, such that the leading or trailing coefficient of M has no integer roots.IsDesingularizable( (n-1)*E+n, E, n, trailing, output=operator );

NiVJJXRydWVHSSpwcm90ZWN0ZWRHRiQsKCokSSJFRzYiIiIjIiIiRidGKUYqRio3Ig==

This package has been enhanced with the addition of four new functions. restart;with( QDifferenceEquations );

NiM3LUkzQWNjdXJhdGVRU3VtbWF0aW9uRzYiSTBBcmVTYW1lU29sdXRpb25HRiVJLUV4dGVuZFNlcmllc0dGJUkrSXNTb2x1dGlvbkdGJUkzUG9seW5vbWlhbFNvbHV0aW9uR0YlSSxRRGlzcGVyc2lvbkdGJUkpUUVDcmVhdGVHRiVJOFFIeXBlcmdlb21ldHJpY1NvbHV0aW9uR0YlSTFSYXRpb25hbFNvbHV0aW9uR0YlSS9TZXJpZXNTb2x1dGlvbkdGJUk1VW5pdmVyc2FsRGVub21pbmF0b3JHRiU=

AccurateQSummation implements the method of accurate q-summationL := ( -q*(-1+q^2))*Q^2 + (q^2*( q^4-1))*Q + (-q^5*( -1+q^2) );

NiM+SSJMRzYiLCgqKEkicUdGJSIiIiwmISIiRikqJEYoIiIjRilGKUkiUUdGJUYtRisqKEYoRi0sJiokRigiIiVGKUYrRilGKUYuRilGKSomRigiIiZGKkYpRis=

Ac := AccurateQSummation( L, Q, x );

NiM+SSNBY0c2IjckLCgqJkkicUdGJSIiJSwqKiRGKUYqIiIiKiRGKSIiJCEiIkYpRjBGLUYtRjBGLSoqLCYqJEYpIiIjRi1GLUYtRi1GKUYtRitGMEkiUUdGJUYtRjAqJkYrRjBGNUY0Ri0sJiomLChGLkYtRilGLUYwRi1GLUYrRjBGLSomRitGMEY1Ri1GMA==

SeriesSolution computes series solutions of a linear q-difference equationeq := y(q*x)-(1+x^2)*y(x): var := y(x): sol := SeriesSolution( eq, var, 'data' );

NiM+SSRzb2xHNiIsJiZJI19DR0YlNiMiIiJGKi1JIk9HSSpwcm90ZWN0ZWRHRi02I0kieEdGJUYq

ExtendSeries extends a series solution of a linear q-difference equationExtendSeries( sol, data, 4 );

NiMsKiZJI19DRzYiNiMiIiJGKCooRiRGKCwmISIiRigqJEkicUdGJiIiI0YoRitJInhHRiZGLkYoKipGJEYoRipGKywmKiRGLSIiJUYoRitGKEYrRi9GM0YoLUkiT0dJKnByb3RlY3RlZEdGNjYjKiRGLyIiJkYo

QHypergeometricSolution finds all q-hypergeometric solutions of a given linear q-difference equationEq := x*y(q^3*x)-q^3*x^2*y(q^2*x)-(x^2+q)*y(q*x)+q*x*(x^2+q)*y(x);

NiM+SSNFcUc2IiwqKiZJInhHRiUiIiItSSJ5R0YlNiMqJkkicUdGJSIiJEYoRilGKUYpKihGLkYvRigiIiMtRis2IyomRihGKUYuRjFGKSEiIiomLCYqJEYoRjFGKUYuRilGKS1GKzYjKiZGLkYpRihGKUYpRjUqKkYuRilGKEYpRjdGKS1GKzYjRihGKUYp

QHypergeometricSolution( Eq, y(x) );

NiM8IyomSSJxRzYiIiIiSSJ4R0YmRic=

Enhanced FunctionAdvisor command... More conversion knowledge about special functions... Differentiation knowledge for special functions... More series expansions for special functions... Enhanced plotcompare command... Better rational function decomposition... More flexible singular command ...Efficient forms of hypergeometric terms ...Better polynomial factorizations..

Legal Notice: The copyright for this application is owned by the author(s). Neither Maplesoft nor the author are responsible for any errors contained within and are not liable for any damages resulting from the use of this material.. This application is intended for non-commercial, non-profit use only. Contact the author for permission if you wish to use this application in for-profit activities. MFNWtKUb<ob<R=MDLCdNVZZJ:@L>H:TKGxMkJ:<O`Lo\\lQxlQWdMWpsHqShmWhYoeXOPmTPmV`mvqyxq=Xj=xXquXaxnaXcEWc=UR=UweYwELKDLqtPq<R:=r^av^uRAurZ@nZtVauVb=WbMYtMyvayvYyuYYxmYxqyxqYyuYyEYsEYpmXpyyyyypqxp=J:>::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::dy<TypC>qULCTJcDXoXusT<aupkcfWMX@JCeU`dNuTmWxyyyppuPCDSSuLClu><xTpQmlsb]MihUO`qTeXSQO;@JxV]wOl:@syFv<w\\t@tsNnQn\\V?w<w\\?FqJijXynZVvnyHErmiB__tWit[MyxYRIIXvWgtSS=;gQMwAIC]IYrGXRogc[EpqYtsxn=BVSUGuEA[WxKrWaSHssoYBPkynKctqgmyUKAYQYUw_rs=wboYTWXI?IQKyo[X@wydqytYRGAy`ixs[SlyXaSyquy:mel=dXqydIfvgRIeSUkUmUBGwuZitS;eQ?S>AdMasnkySGbDSuimbSabjytNAyMuXlaTWaCp;y?at;_txaTwath?cj=GbgYVGCA[eAkh^ihyaIGoVdGxyWeQatamVHYx:SEIewyacmcSBAvgOyyssEyBVWCwQFtYWxYdMgcY_y^Uy?gce[WXQCDcwGuwHMw?qwx[gacscGrwOtuKFXKsc[FZIBOqIrII]kuICfRosM_yTSEWWcKQs_qGHeIiaWBsvaAXWoFsYTyuIYSdWCet[fZpOYtv[\\XSMvN=Xhluxel]ylvUn;PYsqvkmmCxSEQPsMOeUpQEKN`yVAqcqRQpYxHr[xU\\AtgPVexmHHQYDXptL;ey_\\XHxyTpLQ=qJhJklqA=wPxqOtpPmwQ=kWdSSYjxhQt=li<X=Pr\\HoxMKxppdUPGxl`<RadWsEMUhnMinaqvy\\t]pJw\\Pttt:lw_hy;PxuElWpfypiQyg<IbgHqQ?wRwvFgcQnmtI]lXZoauvw\\]Vi\\?yuIjGqyA_]j^cia\\^vaYfmXYvV_foyd_wZa?yIPfNXpOimbInwiieQyZ@[jf[p_`s?\\N@qaw[<a_=qpdIu]>gnHpUi\\^a[AGcS_y]pnHg_oIi=XkM`bK^yUWjFhhCpif?llhelhkKqk=qgCqqIokJadZ@]IOspHjgQgUv^Mp^[akXNokxcFaxMX>Efx=GJyY]=uKWXuefcYCV_DO;X]oeDwI]UrhIXhKdtYgv=sYMxyMhEAbdKdFED;MBimUYgvNsfBuDgqw^sRZoieyiYEfEAsYOcU;uf_C^;g>EIUmWy]xZ[H?UTiwhayb<EWUAhmghUee]ODLyfkYdOQDNMsleg]mHGkynUrrUhjgbvstrICsOiU?upUhtME_cVUeywWrSeSvIwHqsEUvwaS`mv_kCEgDEEVOoyfSFYGXh[xe;wfsya?Hbcu_SiHUfrStqsgICUKmR;IEGGiEUxSSewkBRcic?f[GHs]WBCeFSXMec@qwQYiOCFi;bd_epghCcrSIbrUFfKXpOE>CdGUVH_ss=GaEF\\Mh_uDJcXeWGSkIA=T`[uhOiKOy;Ido_sBQgPGbiMxZIx[=RNQHCUwlIhVAs>Mxv=t;Iekec[iToeB]YSVsI]UGkMgC=xM_cv]rCkGlOyE=wVsymoRPERGUWoKs>?dNGcqOvL=DcgUUid=SdBYtacBcyT;sC??sXsBFEIPKdwUibUUuowtCxLERxGUPOc=eeWWDJ_tBIFj[RMWXoaIniFDYyvIfFYH;EifaWAAdkQgSuIoYHS?s\\aYnkYcCRXAy;=urSsUEGXovmkdU?bIkuvIhf;hHKRmsIqkGkCIEGSQiUy?r[chy]DW?UJweo_HI;I[iRPuYCce]yIQGSR=SFcY@IHNabEyhT;H\\gC[iiEubXIY[?FhkfAaRyccQ;D<MBLksUGvM]FOSWZaFnmUVOB]Mh`gu]ew:CSX[VU[d^iWCITMkingVmcY;EuIkFZgetaSlkeD_SlUd?SU[Wh`_IHkuNaIBEY@KhQ[IbSfl_CpgV]IBgcf:CrOWWliVPSDMuEkwBYQbgKxGiWfcdg_cCoXDyFoAF<CYd_fZSUKOXmUErmvpWgaQIeWGyMiuOfheFY[UWgdGwe[;X@Yh<owskTwUgjYdvEhnTP`LJatUmyo]xlkUpgPSHmSOiSXtM?HsHhWglnu=ypMosmPWQtXmlLDR^erappAPq@Twu\\mf<ytMo_tNQDmwuUBal[TKM]UZ\\VsUPg\\OhXU]iw>lT>TtolYUeM\\`q:iNFQkMeuB<Y^yq[TqwLxyYk^mPDhUTEL[mxdYTrUwHYpp`R]tsyhm<\\rdhN\\]VGejEyTBLlXhUidSklVcImkuJA\\OFAJxXTJ\\oRpUr\\qnEUf<POaocioXxYUTRxhmKHnoUuBavvxt]@ordyqIl`tycEyg=St<V;LY`DoDElChWYdkpIkSMophnhqkeMW<QX^dogEmM<kxAYM=mpPKmTTMmXeQLnuK?HMeIU``TqMSdeNqmxHeLK=OUpx^@kiYp`xXVdoU@L=PprAPIuR[Qp@YlvPWwQToMpG`jOXyFhxAETieRADKgioVPOyXUlXT:Iwc<NgeMNup\\XWrdQFPQvlP=Toseo>qXbiWO\\yE=PUiPAASgLtxXLG=STASAxj=@WixwX`XOAtHloIeoHiLvyuouMtLtTyJsAxBXr@TqWXOsEKopuAEU<uyO\\LTyPAXm=tOUQneaND]KOYyLyXbtxuhmcYrXMkh\\ylLo_eq`tSeAOH]lqUwiPnkPwlHPgHrehY^pKhPwGPJ;<O<`qU=tMxUUEPW@RdITfYjjaowTqMQjXHJS\\M<EvappT@mWMJ@iOVhyLQKq]T=Eyc=UhqNa]PJ\\X\\Lu[DsQ@O[XRw<Rb`P`tSuejceYX@UN=rFexuHmDmk]XRLaYElRmIP]Pech`rxma?araaCxvWQ[\\aZ`yiFAj?gvVVd^@mGy[hhjxQvjIwMVwPGyXW_EpjDNnsy^EhvE_d:PnkOaDA^CnxEAoCh_ewc;pb[I[ZwcU?kpGwxvcVV\\OWaYGZWqbGG^jVkAQ]mXckfwTVfovZVnZLwfoIeS>e@HtcvsgPn<YqDOxcqbdNmPxtqwhsfag>myOedhqCFkNWqspy]@_VQrIIu]ncLIb>_xdQ^[yw^`^YqbSxeyga>OkV@fpVfeNhmxeSwn^?_GOklf`QqgK_yK?yj@pxvwbHtI`yYai?HvJ^wvQvYngAVo=XhwcReBIMflKTU_b`qrFQC<UGRWY=kVWAiv]X<CSyMycyweoE>?ttksVgBTmtGIXvKDT;D`atpaGQEVA=efoH@]TgswsCfWGEbCCLIYtSwG;tRaC?]hi[TfwSPUcSQYZCuloE[KTnOSTuDPqfpQU_Yx[?UZ=b`yCuETUectcrsaWIGhPUVdCXo[Dn;GTof=AVBcYRGgaaYbsvt=UBuVIOeZKgGmhHQr]]umsifyTPWtneyZKydmHjoWRAsSQHewDS=Hj]C>qdH[XHIgkwTGuvI_sgYDgabSsiLYrb]Ic[uZUuCeGN]InyyjiVnMuJibq]E>=sH[thQDXgT\\qhNwTVmGdoSiKsD]DD]UOksO=fX;XvIdbUwRiisCEv?tEAS?eH[EHiOy[mcE?hY;ewKCr[x;ECpUEaItRMUeMI@wF=GuqIdriXmAiHouB]UEkvboD`]bDeu^UHOsxwKSogVE_GNQbBAduMYQ;Y_]XbqBe[FFYGF=tXgxryYpAFDoidIRHgUf?uXGg]WguGig]URQrp;u=MHYIXxcIamsqEl<uR<PMwtwNMqNYMB?\\aIiqvboxhknwDOv]^r:a\\[WhExsn_cdQo@Ng]orLPnCptE?wJqi:ad`?gjX\\Bol:@dJis[vel^pK>]TpcIHhoSZoXJOhw[WgsesuBfEg]=uuUY=qXZWVYMSZECHWHqeX<Su^EuvYX;AFQQC]]Fl]SNqIO=ILQwhIwZoeqEoOqVY@TTprWANqYsuxNA@WjlpuaXytmXMRkdpI]K\\LT@=Pd\\SxHJSXNhulFYQmtwJhWI<QsuRUpwm\\rQDLyuMgMv>@pS@pftRiUniTV:uRRil<lRY<wltSViLhHKD@vViS`DOfaTvAsyMuKmQUhvqlQuLW@qlr`RddRKIm^QYAaXxdP\\TuVlktMYmyPA`xRivRUoLxKmANalL`qV`eTDIO;MY\\HoQiYnMkHLNqhylUJ\\tS^uKJIMKAY[qufMrxAXfxJyXxe`RPqxOiorlJW]XEHXw\\lJqr=XwN<T>`nFPklHv^LTd]kviu:YwlhWkTyDpLSUVUqQCAuTTliPopuoTHNSQyRts>IqKYKhTNQMseAjoalrQvbIslMp=\\ojLUMDuDQymaoiQulmPMELwhpuplnIvypP`XlCDM>LY@`rdqtoyn@MLFTUUPo\\UWR\\WMetOAoEewLIUctRw@t]ERG@XtqKuHQWqjWLqZ`LTUOTusmHPcYk?DN=uT\\aXSeLNuKrttf@kIunUTXCMtYyRUQplXw`Xv=iXppuLmRUqwTMm[]qxhLElt>lNi@qQ=Q_lRL<NgerhhXwAryAL=iw]IxYTUyhj;poqXPmUgHG\\ganfWfF>hrAwtwy[Ys<VuGXhSGxePjM^exn\\vabHNjTffFYwDNre@qoheHWmoW`]P\\gfq]Ikxx\\?vknnc\\giupovIhMaZOIkjIdVqtv?efnhe`i=OixVueVopxjJOuNY`[W\\jX\\SNkeqrQ_pUghjNiNQtpG\\CIe_IabYs@wwBw\\L`xO?r`qZi?c@WsW`^@fjogeppjkIpnXkKPndGadGidocE>m?Fjf_bYf\\\\?p]HieNqWggeIuCAnhiZwaepYnkgeFyjvOhu_[GQkpioSNa?ndiprUFjcV\\pQngw]R?]WFeWx`>i_H@tAwdbny<x__O`FyggqujAtJhaiAnSAs=xwtp^aYnloln?eYQtA^mJvwD?k\\Ql]xqMPc`_sjV]gvreOsIOkpP^Vy^[Vw`O[gwmLqi]NmZ@hBAriP]O>[@HdmYZyir[Nn<YpeNfonso^]dnfIYuXwkEAcUyn^A`]VeyYulPogAn;?\\K?mt^gp^jXGxf>ysfZsgu=`seb_aIESSJcWewtmCrECfgERaqENChB;f^IvxYL=PS]=yKXmGeMYLmrTSBpL_`UAlmXmXlUTXEn^EsSmmfyREXsDEwelvQqlQaX@@tj<pkTYkDSNqxPQjlusiTJELXQ\\Rw`sPaSUYJwPjdes_QsK`j@Ij_DuFmJmPLmllh<SSPKV<W[eOaaTN@wLltv=qd@OOHrc<K>huhPP=ApSURP]mbIVSurlDLqpKuaVliV>IoOxJxLyGXOhqt=QPBQVItRjdV?]PFPPCyvs]YB]RXAsPLysQT^MuLUODMueDP=UPpHsFUx:XJ`hNlEYKykqQLQHSEur^aX_XJH]UyxtgMRCXtjuo?EQWML[aRSikidoeLsUduWEMthYZyQ[qwxHT[tOu<VGxqb`qp<OQAWOeYIIw^Tv`HrNyP;EKhDLiTqcXLq<NXejsEKseT;MYA<osmuf@U@txUMJYaMFuvVajUelv]xX`ncuThTxB\\wxtvCiu@HsQUQ:msJyUVXLOeUALmdaY]TMouqEExW`xK=QQLyGAyiHP\\xOf]tG>cJw`gxw^f]mIdJwgXiybX]_^\\]x]wXoovfJ`vgQklWrhq`sxqThd_AuXHotauxqvVPs>fXQEG_YGyujGWqaCOyE>WX[wuEwysMHsACawYfsIiqvWiWpWGoGYmqwAeh;_XqGSy[YQUW<kFaUGmuhqeYE;xdwbDUDdWV<OYjmwc]rL?TpuwF_snWumiiaAInyB[aUbyx\\yy`cSLmHxsInwYLwf=ob_ktxgUJWTB]TtIvKkDDMICMVZCH<WWF;vXeuOGe^QeLwik]HkCfrUXu_DgoC[OIyuh_Iyb[eEhqryQ?MwTexIuNbumv<sOiwy]uO>ie?oNXpnFb]iykyv@pnM?^bQbcOp]@pM_wOIZ\\i]tVpGIu=PdbHfMxcxXat?aWPZsww>xaDvv<wqQvyk^piAr_@fdYyfoxsactW_uvgBPmqvmK_ZMArZWZyAvCPmuYd\\AbZp]ZNgXwryXaxva>wfYpcZgem>uxiu[GiYnuwQu<aiJns?\\UNpqHgjfwhq[bahb@xCGbHVkk_nTPeiobfycUf`XnaxidlwiTHjmheF?sw>qWXxTWygQbupZtYpgqpkwwfWvcHZcAw[iuMiyb^mEfyh_yyXsIIosXdJfxvq]>yaR_ZVxy\\bS?EbAws]w]wvcOFoMhwSURagyCYdiTwABuAEGWFuSIGoEkKYIGFYUY]uw`uwXoGuAFVWkGwqyfb@qrrifj?sYpu=@_]on=g[Q@ltQbQNZDf\\FWe\\yquw[<pu^>lvQx\\Yw<w\\<VxRPn=yxiN[CNgB^irOpwGnEfyyWntqw:gwEfZSpi_G\\<?`QnxV?wygm<NZ^qyaGpxxiMpk_OhqYrWx\\t@t?@vAA\\eq_rQqv>uy@tya`Wyy:xvmysXwyYf[MWxoWmIgvoE:;B:MTKWDKWgJ;eZ1: