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&=&u&u@~&&U~
&=&E& Et ~&=&E ~
&=&E ~&=&E #~
&u&5 @~&&U~&=&E ] Error in arguments following 2Cannot do regression on lists of different lengths UX*XƆ Ɔ Ɔ ~ &}&& Eu{~ &}&=&& EueƆ Ɔ W P P~ &u&uWS W PF*P~ &}&=&u&5~WS W PF*P~ &}&=&=&u&5~WS W PF*P~ &}&=&=&=&u&5~WS >< t~1&&E ~&} ub~&} uX~&} uN~&EPW*t:~&EPW*t&~&EPW*tvv@u ~ &E01ҿ*P~ &}&u&5 @RPE
@~&&UFVľ&=&&UFV~&&UFV~&&U~1&&EssXQ~&M&u&}
o*~&M&u&}
]*~&E&]&U
~ &}&u&5Z >< t~1&&E6,6,vv @RP ?ƆW PF*P~ &u&uWS ľ&}t ~ &}&& Et<WW *~ &E01ҿ*
8 W * 4~ &E01ҿ*PF*P~W/ K& t W Ɔ~ &}&& EuƆƆW PF*P~ &}&u&5WS ľ&EP#W*t ľ&EP#W*t>< t` u @ u @7PE
@~&&U( 11ľ&E&Uľ&E&U t2 t(ľ&&Uľ&&Uċ u
tH t W t W ~1&&EvWCW * Q>< uľ&}t?ľ&} t4~ &E01ҿ*P11RPE
@~&&U t*ľ&E&Uľ&E&U1ľ&}uľ&E&U~ &E< t t t
t t~&E&]&U
111*v*>,&}&E&]&U
~&M&u&}
*vL~&E&]&U
111*r{>,&}&E&]&U
~&M&u&}
*sN~ &E O&~W~ W~W @~ W~ W)@~W~ W~W @~W <7tF W PF*P~WS ~&} tƆ[~&}u~ W> O&~ WW P( *~W W PF*P~WS ~&} tƆ ~&}u~ W> O&~ WW P( *~WW~W @~WW~W @WW W-@vW WvW @WJW)@~WJW~W @W4W)@~W4W~W @ľ&&U~W tľ&&U*>,&} W~ W>,&} W @>< tX tN~ &E<8t < t-~ &EPvW*t
~W ~1&&E W P P~ &u&u~WS ~ &}7u% W P P~ &}&u&5~WS 1FF>< u1~ &E01ҿ*PvvvvE
@~&&U ~W ~W ~1&&E u u ~W ~W ~W t W t W ]
U *~
&E&UFV~WP ~&=1&E&E~&=1&E F Fu >< t FV~
&;UuI&;EuC W PF%*Pvv~&= WS ~&=&E&UFV6 W PF%*Pvv~WS ~&&UFV~&}u*~&E& Et ~&=&E ~&E ~&=&E
~&=&E ~&&UFV ~&=&E& Eu ~&=&E >< t
~W ]
%%Sublist limits not correct5Error in substring limits--use s[a:b] for a substring Beginning sublist limit too big Second sublist limit is too bigUF*FF Fu5 W PF*Pv v
~WS FVFV W PF*Pvv~WS ~&=&}u+~&= WW *uvv @FV* W PF*P~&u&5~WS ~&} u!~&} u~&}t
~&}t ~WP W PF*Pv v
~ WS FVFV~&E&UFVF FtO>< uH W PF*Pvv~WS ~&&UFV~&&UFV멋FVFV ~ W( @u ~ W( @t{~
&}u%~&E&]&U
~&M&u&}
*wL~
&}u ~&E&]&U
11*r%~
&}t~
&} u~
&}u>< t 1FF~WW * a~
&}u~&=&& EtV~W W PF*P~&=&u&5~WS ~&} t~W FV~ W~Wu#@~ W~Wu#@>< u;~t5~t/Fы^ӋVչ 1 *rF^V 11*v W< W P *1FF ~W P ~&E P?*~&E&UW~
&}WFы^ӋV՚**PF^VNыvӋ~՚c** *P@ *~&}W P *FVFV~
&E&UFV~&E&]&U
**F ;F(FFF Ft~&&UFVF;FuF Fu ~W W * 1FF.~&=&}uR~&= WW *u:F*Pvv~&=&u&5FVFVFV~WP F*Pvv~&=&u&5~&E&U~&}&}u%~&}&E& Et~&}&E ~&E ~&E ~&E&UFV~&E&]&U
**F~&E&]&U
11]***;F~ FFF Ft~&&UFVF Fu} F*Pvv~&=&u&5~&&U~&=&}u*~&=&E& Et~&E ~&=&E ~&E ~&E ~&&UFVF;FtRF Ft>< uFVFV&1FF~W ~W W * ~W ~W FV]
! %% is not a listU*F~W PF* *P~
&u&u~WS >< t ~&&U~&}u/F* *Pvv~
&}&u&5~WR =&~&}t~&} u=~&}u3F* *Pvv~
&}&u&5~&&UM~&EP2 W*t ~WP ~ tFV~&=&E&Uvv @~&=&E&U~&=&E&UFV~
&}&&UFVF Fu ~&}u,~ WR W *uvv @~&&U& W PF* *Pvv~WS ~&&UFV~&&UFVvP> ~&&UW~
&u&u P< PPY U W * ~ t
~W ]
is not a list%%) must be a single list entry, not a range is out of range ,9 includes undefined or non-integral or negative parameter out of range or undefined U.*.~&u&u P~W[ >< u*~&=&}&}uvvvv~WW =&>< u~&=&}&}t)W~&= W *"W * q~&}&&UFV~&=&E&UFVF ~& ~
1&F Fu9F Fu.>< t$~&=&}u~&= W"W *t-Wvv P PP'Y "W * ~&}t-Wvv P( PP'Y "W * FVFV~&E&UFV P Pvv~W >< t~W( @u
Fߋ^V111*w F Fߋ^V㚏*ȋڋFܙ;|R;sNF FtFFVFV~&&UFVF~&}u~
&~&E ~
&~
&뒋FܙRP1P~W P *"W~W * ~ ~W"W~W *P P
*͍W~W *"W *~W *~W2 P *-Wvv P PP'Y "W * ~&=&&UFV>< uF Fu-Wvv P2 PP'Y 3#W * ~&E&U;Vu0;Fu+FV~&E&U~&&U~&}&&U'FV~&&U~&&U~&=&&U~&}u~&E& Et ~&E FF ~&}uF~&+E FN܍~W ~&}&&UFV~&=&E&UFV~&E F~&E F Fu ~&=&& Eu >< t ~&E F~&E ~&E&UFV P Pvv~W Fߋ^V㚏*N#*Fи ;F FF~&&UFVF;Fu~&=&&UFVJ~W P P
*] "POS must be applied to two stringsUP *P~W~W P( *~
W~W P( *~u~t) W~W P( *~Wf(W * @~&= u, W~W P( *"~W~W **RSP~W ] U * ~
W~W P( *~W ~u ~&= u ~&&U ~&=u%~&E01Қ*RSPG ~&&U ~WP ~&E01Қ*RSPG ~&=&E&U~&=&E&UFV~&0F ;FOFFF虿8)*~&01Қ*RSPG ~&&U~&&UFVF;Fu~&0~&=&E ] U * ~W P vv @u ~ &E&]&U
11*rx~ &E&]&U
1 *wZ~&=&E P?*~&=&E&UW~ &E&]&U
*P$
*~&=&}W P *~ &}t\~&=&E P?*~&=&E&U~&=&}& ~ &E&UFVF Fu W PF{**Pvv~WS vv~WF{**P~&}u<W~&=&}W *~&}W *~&=&}W P *^~W ~W W PF{**Pvv ~WS P~&u&511RPE
@~&&U{~W ~W ~&&UFVR~W W PF{**Pvv ~WS P~&u&511RPE
@~&&U]
U*~
W~W P( *~t W~W P( * ~& P?*~&E&U~&}& ~&0F ;FaFF荾W~&}W *WF虿-*~&Pc!*P$
* *~&}W P *F;Fu] VAL must be applied to a stringU帘 * ~
W~W P( *~thW-W * u~ WW~&0P *~&0䉆WWW P P~W W t W ] U*~W P ~&=&E P?*~&=&E&U WF.*PPvv ~WS Wvv P P PY ~&=&}W P *~W ]
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J m !U!g!!!!"+"W"""""_#{#####k$$$$$$$%%3%K%%%%%&&&'&D&N&S&&&&]''( (^((((((( ) )#)0)I)_)i)}))))))&*7*?*******&+,+A+e++++,,$,0,:,O,`,x,,,,,,,-/-H-[-------.-.C.H.g........ /1/L/a/k/{/(Wrong number of variables for a function%%U4 *4F Fu~
1&&E* P?*~
&&U~W~
&=W P( *~&E< t ~&}u7 P?*~
&=&E&U~&}W~
&=&}W P *>~&}u4~ W~
&= W/ O&~
W~
&=
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&= W~W<t F Fu ~
&u&5 PT*FVFV~&EF ;F(FFF Ft~&&UFVF;FuF Fu,~W W * ~
W ~
1&&Evv11RP~
W~W< u#~&u&5vv~
&=W~W
~
W ] U1*~&vv11RP~
W~W] BUG -- empty control stackU * FVF Fu~WW * 0>&E &U ~ W vv
PT*] U *FV
P?*FV>&E &U FV>&E&UF
01ҿ:*>&] 0 @ -IF or WHILE or FOR does not have matching endU0 *0F ~&=&EQ&US~&&U~&=&}gu ~&=&}_&EPW*tFP~&=&}gu~&=&}_&}NuN-~ t'~u!~&=&}gu~&=&}_&}PuN~&& EtN~&=&EgPW*u7~&=&}gt8~&=&}_&EPW*u~ t~&& Et~&=&EgPW*t~W
W * ] &INPUT@ can only be used while graphingError in INPUT@ X'Too many characters specified in INPUT@xxU市 * > u*~WzW * W~W P *8 P P~
&u&u~W P P~
&}&u&5~W P P~
&}&=&u&5~W ~W~Wz &t$~W( @tF^V111*w*~WW * W~W P *}vvvᚬ &Fvvv˚ &FF^V**F~WW *U&1ҋȋڋF+Ӄ |)=
s$~WW *U&
1ҿ*F~WW * &1ҋȋڋFD *ȋڋF ȋڡ~E;| ~ ;r ~WW * &1ҋȋڋFD *ȋڡ~E- +Ӄ |2= s-W~W P *~WW * :=~WW * &1ҋȋڋFD *ȋڡ~E- +ӿ*F1F1F1F1F~WW *U&1ҋȋڋF+-
*1F1F1~WW * &1ҋȋڋFD *ȋڋF *1F W~W P *F ~W &~W~W P~Wv F ~W &F1F1F1F1] after INPUT is not a variable0Computing interrupted--press any key to continuexx @ U
*
>< t ~&EPj
W*t%~&}&=&}u_~&}&=&E& EuK~&EP
W*u ~&}&=&=&=&}u ~&}&=&=&=&E& Eu ~&EPj
W*t4W~&}&u&5 P PPY
W * 8W~&}&=&=&u&5 P PPY
W * : FV< ~&EP
W*tvvTWum W PP~&u&u~WS >< tWvv PF P PY ~WP P *~W ~WTW, TW
W *u$>< u.W
W * T u W< W P * ~&EP W*tNUWWT0P *T0䉆WNW~W ~&}u
. W5 4~&E P?*~&E&UTW~&}W P *>< tTW
W *tcTW
W *tv>< uo~&EPj
W*t ~&}&u&5 PNW[ "~&}&=&=&u&5 PNW[ >< uFVľN&E&U
~W ] U*Ɔ ~&E&UFVF Fu >< t ~&} uH~&}u>~&E& Et1WW *~&}W *W P * W PPvvWS >< uVWW *W *WP P P'Y *W *W P *W ~&&UFV>< u W5 ] U1* W PP~
&u&u~WS ] :Command GRAPHICS can be used only in the subroutine window X Push to stop graphingU< *<> t > t>< t~WW * 2P)W*t>1 uu &4 _&1
P&HHP]& P1P&
P&HHP&P~WIW *U&1RP&HHY[+ӿK*P&SW WO P * Wd&]Press to continueU *> u ~WbW *P\ &] UJ *J ~&&U~&=&E P P~
&}&u&5~W P P~
&}&=&u&5~W P P~
&}&=&=&u&5~W FPW*t'FPW*tFPW*t>< t~&=&EG~
&u&u P~W[ vv~W RP TP11RPcF^VNՋv~ٚ*sF^V111*r/F^VNՋv~ٚ*vF^V111*v ~ W11RP* >&E&U~W FVP>&u&u @RPvvE
@>&}&&UsXQNv~Úo*NՋv~ٚ]*FՉ^Vٍ~W >&}&=&&U]
is undefinedU* P P~
&u&u~W ~t@ ~&&UW~
&u&u P< PP'Y W * YF^V111*t) ~&&U~&=&EOP11RP ~&&U~&=&E ] U * P P~
&u&u~W ~t ~&&U~&=&EgeF^V111*t5 ~&&U~&=&E QP~
&u&u @RP ~&&U~&=&E
] UNTIL without matching REPEATU4 *4 ~&&U>&=Rt~WW * \ P P~
&u&u~W ~t
~&=&E.F^V111*t
~&=&E ~&=&E] U1* ~&&URP11RP~&=&E] 0 Function or Procedure heading has been changed ANS
Parameter not matched by function name
The function includes undefined parameters"Incorrect number of variables for "Value following WHILE is UNDEFINED$Value following WHILE is not boolean Unexpected END in REPEAT loop!Value following ELSE is UNDEFINED%ELSE IF not followed by boolean valueUnexpected end to Parameters in return incorrect value cannot return a valuesenil fo dne ffo narU帰* ~&&U>< t ~
&EgPwW*u,PWW *~
W *W *
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V * , FV,,LWW *11RP* F؉Vvvذ P~W[ vvظ PT* ~&E&U~
&}gu`P11RPb
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&}_&E&UFVF Fu~&}tF Fu>< t}~&}%u vv P~W[ ,,FV,,FV W PPvv~WS FV,,FV,,F܋V~&E&U~1&E&E ~&&UFV~&&UFVPW~ W P P@ *11RP* F؉VvvذP~W[ vvظ PT*,,FV,,FV~&}t0PWW *~ W *W * ~ Wr FVF Ft
~&}t/PWW *~ W *W * `~&E~&E~&u&u~ WQWC瀾Q u-PWW *~ W * W * FV,,FV,,~&&UFV~&&UFVVF FuF Ft PW*W *~
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&EQ&US* , F>* &}Y~>* &EQ&US* , * , u>* &}gu&>* &}_&}Nu>&PMW*td>* &EgPwW*tL>* &}gu>* &}_&}Uu/>< t%>* &Ec& Eet>* &}gu6, 6* dW~WZY >< t~&} t=~&EPmW*u&~&E<
t>&&u&u~W ~u,WW * L~t*WW * /F^V111*t>&E&U* , E&u&u P~W[ P P>&}&u&5~W FPW*u ~&}&E&]&U
Nv~*s*F^V>&}&=&=&M&u&}
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*r0~W~&} W P( *>&E&U* , #&E& Et* , >&E&U* W P< u* , >&E&U<
u* W P>< th<u* , >&E&U< t * WP>* &}_&}Pu" P P>* &}_&u&u~W W~W P( *~u.WW * ~t*W5W * >< uFË^ŋV111*uX>< t>* &}_&}Pu OP11RP..>&E&U <u* , >&E&U <u2 <u>&E&U* , z< u * W Pt>< tZ<t<u!PW[W *~
W * 1<u-PWnW *>* W *}W * ~W i>* &}gu^>* &}_&}[uO~
&}gu ~W FV~&&U)PW~
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* _&2] U1*~&& Eu9~WUI>2 u&Eڋȋ~;u;uEEEEM~&=&Xxu4~&=ZWU>2 u~&=&Z&\~&&U ~&=&X] x #Error in writing last graph to diskU$ *$>2 u E WP >2 t F
*>E&X*>E&MN>E&X*>E&MN>E&X*>E&Mi>2ub1 WF
RP1P *H*1 WF1RP1P *H*1 WF1RP1P *H*~WW * P/ -&] x #Error in writing last graph to diskU*F ~&0;F}2PW*u >2 u E WPy>2 ux>E&X*>E&E W~WvF@@P@ *>E&X*>EW P *F Fk>2ud1 W 1RP1P *H*1 WW~WvF@@P@ *1P *H*~WW * P/ -&F F] U *vvv vg*Fv
vvg*FF1ҿo*PF1ҿo*P2g*P& &Pvv] U *vvv *Fv
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1P P&1P1P P&22*P &226 . 1ۺ 3*RSPE EEE6E>Ec*RSPE EERSPE EEY^_]*Y^_u*3*Y^_u***,,~1*,~ ,@@*dž* 1ۺ 3*RSPE EEE6E>Ec*RSPE EERSPE EEY^_]*Y^_u*3*Y^_u***,,~1(,~ ,@@(dž( (*6 6E6E6EW WW- 0W2 P *6E6E6EW WW- dW2 P ***6 6E6E6EW WW- ~W2 P *6E6E6EW WW- ~W2 P *.*6 6E6E6E\6E6E6EH 6E6E6E
6E6E6EzE EE111*v
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&- P
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@@P0WT &@@PHH+PdWT &1P1P&2] Graph not savedCannot open 2d graph file Error in copying graph to Copying graphics image to Cannot read last graph from disk *Error in copying graphic from disk to diskError in last graph fileBGraph not saved--press , Shift-F9, redraw graph and try again Graph savedU\*\2N*0 W W WWWFV*P PFV*P* -& t^WD W P *H= u6~ u@V*PWnW *0 W * W'1RP1P *H* W&RP1P *H* W&RP1P *H* W2RP1P *H* W2RP1P *H* W W1P *H* W6E6E6E PP
*H* W6E6E6E PP
*H* W6E6E6E PP
*H* W6E6E6E PP
*H* W\ RP1P *H* W^ RP1P *H*WW *0 W *~ u@V*P/ -&>2u<>2 u$ W P~ u@V*P >2tWW *0 W *WP P *W5 1 We*WW *~ u@V*P/ -&>2u1 W
*t>2t 1 W *** W1RP1P *H* u41 WW P** WW1P *H*l1 W *** W1RP1P *H*1 W *** W1RP1P *H*xWW *~ u@V*P/ -&1 Wo* W% -&WW *~ u@V*P/ -&* +~ u@V*P`W,W * N*2Ɔ W% -&oWD W P *] U *F;Fu2F*F F
+FF2@ȋڋF1Қ_ *ȉڿF*FF1ҋȋڡ2+ӿF*F2ȋڋF1;u);u%2@ȋڋF@1Қ_ *ȉڿF*FƋFFF] Error in loading # Error in reading graph file x #Error in writing to last graph fileU*~ W **F**~ W **F**~ W **F**~ W **F**~ W WO P***~ W&
*E EE**~ W&
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**tR>2uH~ W **F**WhW *0 W *~
u@ *P/ -&>2uF𘙿*FF< u ~ W~W P***t< t<t <t<
t ~ W **F**F*RSP&*Y^_u*RSPF*Y^_o***F~ W **F**F*RSP&*Y^_u*RSPF*Y^_o***F<t<tl~ u ~ W **F**~u0F*PF*PF*PFF*F~ W **F** ~ W **F**F*RSP&*Y^_u*RSPF*Y^_o***F~ W **F**F*RSP&*Y^_u*RSPF*Y^_o***F~ u@ *F#<uo~ W **F**F*PF*PF*PDF~ W **F** <un~ W **F**~ W **F**F*PF*PF*PF>~ W **F**~ W **F**WhW *0 W *~
u@ *P/ -&>2u>2 u E WP>2 u7~W>E&X*>EW P( * >2t 1 WFRP1P *H**~ u 1 W~W1P *H**<1 WF1RP1P *H**1 WF1RP1P *H**~WW *~
u@ *P/ -&~ W% -&* >2u* _&~& V1 F*RSP&*Y^_u*RSPF*Y^_o***\ F*RSP&*Y^_u*RSPF왚*Y^_o***^ ]
x Error in writing graphics file U& *&| W5 ~ t4 -&2EEFVF F FuF~&;X~w>2umF *~&} ug~
WF *~&ERP1P *H*~
WF *~W1P *H* ~
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WF *~&E1RP1P *H*~W W *F *P/ -&FF~&;X~~&Z&\FVF n~
W% -&~ t* _&>2t22 * ] Error in opening last graph file *Error in transferring last graph from disk x U. *. W5 1RP t W5 * 2 1 We*~W W * P/ -&1 W
*t>2 tE W P>2 tc1 W */ *F*~W7 W * P/ -&>2 t&Fj *>E&Xb *>E&M>E&Xb *>E&} u;1 W>E&Xb *>EW P**z1 W *r *>E&Xb *>E&M*1 W *r *>E&Xb *>E&M*~W7 W * P/ -& W5 2Z1 W% -&>2u* _&* ]U1*E EEE EEE EEE EEE EEE EEE EEE EEE EEE EEE EEE EEE EEE EEE EEE EEE EEE6E>Ec*.F 0F2FE EEE6E>Ec*4F 6F8FE*E6E>Eo*.F60F>2Fu*RSP|E*Y^_c*E FFE*.F60F>2Fu*F FFE*E6E>Eo*4F66F>8Fu*RSPE*Y^_]*
F FFEؙ*4F66F>8Fu*F FFE*RSP|E*.F60F>2Fo*Y^_u*RSPE EEY^_c*F FFE*RSP.F 0F2FY^_u* F F FE*RSPE*4F66F>8Fo*Y^_u*E6E>E]*"F $F&FE*RSP4F 6F8FtY^_u*(F *F,F] Cannot load last graph from disk x Cannot move last graph to disk Cannot save last graph to diskU6 *661&6h1P6j&>1 u 2}%*P&2}%*P &
P P P P& P P P P& P
P P P& P P P P&
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vG FVvvvvvvvvP-~W ~W ~W ~W EEFV1EE~&& Eu >< t ~&=&E<.u!~&u&5~W/ ~W <,u#~&u&5~WP4 ~W n< t:
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h1F@@d1 h1 d1 1ۺ 3*RSPE EERSPE EEY^_]*3*Y^_u**4*F 1ۺ 3*RSPE EEE6E>Ec*3*Y^_u**4*FF;F~F+F FF F;F~ F+Fj11j1~~
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E EE~&E &]&UFʋṾT V F;F~FFFFFFF;F~FFFFFFv RSPvRSPvZRSPvPRSPUW~&~1& F ~ tZ~&=muP>t6\ 6^ >EW P&CP Piр>t6\ 6^ >EW P&7~ t~&=gu W5 ~ t~&=hu P P4 Z&~ tw>tp~ tU6\ 6^ >EW P&\ F\ ^ F^ ~ t\
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t~&=t~&=t ~ tI~ u">t*6\ 6^ >EW P&] U *~W~W P( *~W( @u W~W P( *F^V*>?*PL] Lines on graphs will be THIN Lines on graphs will be THICK Text on graphs will be THICKText on graphs will be THINU1*~u ?WD W P *Y~u ?WD W P *8~u?WD W P * @WD W P *] Push to stop graphing U *> u >R u >1 u$2P@W*t> u
>R u)[>1 u> uM>R uF4 _&>1 t5E W EEEEEE>R u
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1ҿ@*P&P& W P% _&>1 t1>Y t*>X u >2 ~2222;2tX (>1t!>Y t>Z u@ Z 2;2tE@*P1P@*P&P@*P@*P訿/1P1P@*P&P1P@*Pw2@*P &P2@*P1PN] !Error -- Push to continueGraph completedUv *v~W~WP P *> u4>u >R u> t
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W~W P( *~W~W P( *F1F1FЃ~|i~|`~ uW2*~^V~W~W~Wf@vv~~W ~W~W~W-@~W~W~W @6,6,~W RP P Pvv~W P Pvv~W ~W~Wu vvvUFvvv蟵Fe&1ҿI*Fvv &1ҋȋڋF;uB;u>vF@P &1ҋȋڋF;u#;u vFHP &1ҋȋڋF;u;tFF FF͘I*FF] :Incorrect limits for graphing or too many points requested U * ~W~W P( *~W~W P( *~
W~W P( *FP]KW*tLFP]KW*t<~W( @t.F^V111*vF^Vù 1 z*v&W}KW * -~ t!v vvv~W~Wt6,6,~W RP ~W~WfWf@fW~W~Ww@ P Pv v~W P Pvv|W >< uR~W|Wst?~ t vvvv}轸Ɔevvvv}
Ɔe F^VÚ*- K* }bb>< tb ~(>,&} W~W>,&} W @ ~W>,&} W P( * P Pv v~W P Pvv|W >< us~W|Wft`~ t@e tvvvv} Ɔevvvv}芷vvvv}߶Ɔe b t] Polar graph: r = U帾*ƆY>1 t~&E<t<
t < t<t~&}&u&5 @FV~&u&u @FV6E6E6E~W 6E6E6E~W ~&E<t<
u ~E+|E*RSP~W J< u"~E+|E *RSP~W $<u ~E+|E *RSP~W ~&}uƆY BW~&u&u P2 PPY ZWP P *P<t~&u&u @FV~&}&u&5 @FV P P~&}&=&=&u&5~W P P~&}&=&=&=&u&5~W P P~&}&=&=&=&=&u&5~W BW~&u&u P# PPY NW *BW~&}&u&5 P# PPY *ZWP P *A<t:P~&u&u @RPP~&}&u&5 @RP11RPE
@RPE
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@RPE
@FV P P~&}&=&u&5~W P P~&}&=&=&u&5~W P P~&}&=&=&=&u&5~W BWNW *BW~&u&u P7 PPY *ZWP P *~&E<t<
t < t<t<u~&}&u&5Z <u~&}&=&u&5Z >< t W P Pvv~WS ~W W P Pvv~WS ~W >< uqvv @>E&&U>E&&UEEvvvv~W~W~WYN*P PV ZWP5 ~W ~W ] #Error in step parameter after FIELD Surveying vector field Direction field: (,)Ut*t1 Z S*Z Ɔ >1 t1~&}&=&u&5Z >< t
~&}&=&=&=&u&5Z >< t
P P~&}&=&=&u&5~W P P~&}&=&=&=&=&u&5~W >< ux~W( @tj~W( @t\FՋ^V111*vFF^V111*v0FՋ^Vٹ 1 H*wF^V﹆ 1 H*vhWSW * W PP~&u&u
WS >< tu W PP~&}&u&5WS >< t< Ɔvv @>E&&U>E&&UEEE EEE6E>Ec*Nv~u*E EEE6E>Ec*NՋv~ٚu*dž dž dž dž dž dž 11u*E6E>E]* F^V*S* ;~kRPF^V*Y[+ RP PW2 P *WSW *W *W2 P *u
W5 W\6 >,&u&u G RP 11u*E6E>E]*FՋ^Vٚ*S* ;~->< t* 6,6,G RP P P
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~W P P~W FPSW*uFPSW*uF^V111*uF^V111*uF^Vu*RSPF^VÀu*Y^_*sDF^Vu*3* 1 @u**RSPfW BF^VÀu*3* 1 @u**RSPfW ~WPW)@PW~WPW-@~W:W)@:W|W:W-@PW:WPW @PWPWV0@fWPWfWw@fW~W~W-@fW~W~W-@FPSW*u'FPSW*u Nv~Ú]*RSP塉Nv~]*RSP Nv~Úc*RSP蛡Nv~c*RSPС++ Nv~Úc*RSPNv~c*RSP Nv~Ú]*RSPNv~]*RSPf Nv~Ú]*RSPNv~]*RSP*~I +o*RSP*o*Y^_]**ȋڋӿS*PRSP*~I +o*RSP*o*Y^_c**ȋڋӿS*PRSPn Nv~Ú]*RSPNv~]*RSP*~I +o*RSP*o*Y^_c**ȋڋӿS*PRSP*~I +o*RSP*o*Y^_]**ȋڋӿS*PRSPv]*;tZ ]* ;tW TW *W
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@~66P~6611RPE
@~66~6 u@|b*~6] )Function to solve is undefined or complex(Equation does not converge to a solutionUv *v P P~66~W >< uFPyeW*u~WeW * rF
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&u&u2F~WeW * N>< uF;FuF;Ft ~ t>< uD>,&}&} W~PW P( *>,&} W~:W P( *] %Error in step number parameter after #Error in step size parameter after $Initial value for first variable in is not real%Initial value for second variable in Singularity at beginning of Trajectory through field: (,)=U*Ɔ Ɔ Y h*Y >1 t菸~ &}&=&u&5Z >, W@W P *>< t ~ &}&=&=&=&u&5Z >, W2W P *>< t{ P P~ &}&=&=&=&=&=&u&5~W >< u<~W( @t.FՋ^V111*vFՋ^Vٹ 1 z*v=2WhW *~ &E01ҿh*
8 W * P P~ &}&=&=&=&=&=&=&u&5~W >< u@FPhW*t0F^Vù 1 *rF^Vù 1 *v=2WiW *~ &E01ҿh*
8 W * W PP~ &u&uWS >< t
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8 W *\iW * )
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8 W *\iW * fW >,&E&U|W$W P( *fWW P( *~ uPE
@>,&}&E&U,, PW>,&=&= W% P PW>,&= W% RP11RPE
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@ P P~W P P~W U>< uLFPhW*tEWFCw*P&PFҙCw*PFЙCw*P\PFCw*P1PE]
;histogram cannot be drawn while subroutine in GRAPHICS mode !Incorrect arguments for HISTOGRAM 0List did not contain any real data for histogram XUn*n~1&&E~ t > tVWxW * ƆW PP~ &u&uWS P P~ &}&u&5LW P P~ &}&=&u&56W P P~ &}&=&=&u&5 W >< t ľ&EPxW*u LPxW*ts6PxW*tb79;MOQ*vC W( @t4!#%111*v!#% 1 H*v*pWxW * t W V
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@FF>< t
~W ] /Submatrices do not have the same number of rows%Too many columns in one row of matrix$Too few columns in one row of matrixUJ *J~1&&E1F1F1F1F~ u~ u~
&E&UFV~&&UFV W PF*P~&u&u~WS >< t
~W ~&}uA~ u ~&EF F~&;Et~WW * ~&EFF.~ uF ~t~WW * F@F~ ~ F;F~~W
W * >< t~W ~W ~&&UFV~ u~Wvv~ u~WFFPv>< t~ uhFF ;FOFFFF ;F1FF~WvvvvvvBRP_F;FuԋF;Fu~Wp~ ujFFFF@;FOFFFF ;F1FF~WvvvvvvRPF;FuԋF;Fu~W1~&}usFF ;FZFFF+FF ;F9FF~WFFPFFPvvvvURPrF;FűF;Fu~W~WF@PF@Pvv>FF~&} u~ uFF(F;Ft ~W ~W3W * FFF~&& Et]
Incorrect limits after MATRIX U\ *\~1&&E W P P~ &u&u~WS W PF *P~ &}&=&u&5~WS W PF *P~ &}&=&=&u&5~WS W PF *P~ &}&=&=&=&u&5~WS W PF *P~ &}&=&=&=&=&=&u&5~WS W PF *P~ &}&=&=&=&=&=&=&u&5~WS W PF *P~ &}&=&=&=&=&=&=&=&u&5~WS >< t~&} t ~&} t ~&} t ~&} t ~&} t ~&} u{~&EP W*tg~&EP W*tS~&EP W*t?~&EP W*t+~&EP W*t~&EP W*t ~ &E01ҿ *Pvv~ &}&u&5 @RPE
@~&&UFV~&=&&UFV~&&UF܋V~&&U~ &}&=&=&=&=&u&5 @~&&UFV~&=&&UFV~&&UF؋V~&&U~1&&EksXQ~&M&u&}
o*~&M&u&}
]*~&E&]&U
sXQ~&M&u&}
o*~&M&u&}
]*~&E&]&U
~ W~ W~Wf@~W~܁ W~Ww@~tFË^ŋV111*s~W W * >FË^ŋVǚ* *F~ W~ W~Wf@~W~ W~Ww@~tFË^ŋV111*s~W W * FË^ŋVǚ* *F~ &}&u&5Z >< t|6,6,vv @RP ~ &}&=&=&=&=&u&5Z >< t 4~Wvv >< tFF ;F~ FF6,6,vv @RP FF ;F~ FF>< t W PF *Pvv~WS ~Wvvvv>,&} W~ W>,&} W @F;Fu>,&}&} W~܁ W>,&}&} W @F;Ft>< t
~W ~W ~W ~W ~W ~W ~W ~W ]
U *~1&&E W PF#*P~ &u&u~ WS >< tT~ &}t~ &}t
~ &}t ~ &EF~ &EFFfP~&&U>< t
~ W FfF ;F~ FF~u5 W PF#*Pvv PvRP~WS 3 W PF#*Pvv v PrRP~WS ~WvvvvtދF;Fto>< t
~W +~ &}t 1F~ &E&UFVF FtF~&&UFV~ ~v~&&U ~&&U~ W >< t
~ W ~ &E&UFVFF ;F[FF W PF#*Pvv~WS ~&&UFV~WvvvvZF;Fu>< t
~W vv @~&&U~ W ]
+You cannot make a vector from an empty listU: *:~1&&E~ &}G u@&*F W PF&*P~ &u&u~ WS >< t|~ &}t41F~ &E&UFVF Fu!~ W ~W&W * 0F FtF~&&UFV~ t~W Pv~Wv P>< t
~ W ~ &E&UFVFF ;FlFF~&&UFV~1&&E~ t~W Pvvvy~Wv PvvaۋFVFVF;Fuvv PT*;~W P P
>< u~W P Pvv
~ W ]
U1*]h ~ KQd
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k
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"'"."M"Y"""""0#j############$)$$$$ % %O%%%%&(&f&s&&&&
' '_'n's''i(((Ul *l~
&=&EFvH =&~&&UFFF ;F~FFF F F F F F FF ;F~ FFF;Fu ~
&u&5vv* =&ǎ W~W @F^VNŋvNj~ɚ]*F^V~
&u&5vv* =&ǎ W~W @F^VNŋvNj~ɚ]*F^VF;FtUF^V6>*wF^V6>*wF^V 11u*F܉^މVF F F F^VNv~]*F^VF^VN܋vދ~*s>F^V湂 11o*F^VF^V 11o*F^V멋F^V 11o*F܉^މVF^VN܋vދ~*v>F^V湂 11u*F^VF^V 11u*F^V멸3333sNv~o*RSPF^VNv~]*Nv~u*Y^_*rDF vvv~W 11ҋNv~u*F܉^މVvvv܍~W FF ;F~ FF~
&u&5vv* =&ǎ W~W~
&u&5vv* =&ǎ W-@~
&u&5vv* =&ǎ W~W~
&u&5vv* =&ǎ W-@F;Ftb~&u&5vv* =&ǎ W~W~&u&5vv* =&ǎ W-@F;Ft,~ u ] U *~
&}t(Pv v
@RP11RPE
@~&&U ~W~
&u~
&u/ =&>< tn~
&EF ;F\FF~
&EF ;F:FF~Wvvv v
vv* =&RP@RP4 =&F;FuˋF;Fu] U *~
&}t(Pv v
@RP11RPE
@~&&U~W~
&u~
&u/ =&~
&EF ;F~ FF~&=&EF ;F~ FF>< urPv v
vv* =&RP11RPE
@FV W PF*Pvv~WS vv PT*~Wvvvv4 =&F;FtyF;FtN>< t~W ~1&&E]
U *~W~&u~&u/ =&~&EF ;F~ FF~&EF ;F~ FFF
01ҿN*Pvvvv* =&RPvv E
@FV W PFV*Pvv~WS vv PT*vvvv* =&ǎ1&&E~Wvvvv4 =&F;FtUF;Ft->< t~W ~1&&E] U *~ W~W P( *~ u6F^Vi*RSPF^Vi*Y^_]*RSP~W F^Vi*RSP~W ]
U帨 * ~
1&&EFFvvvv* =&ǎ W~WU<~W~W P( *~&EXF@;X~ FFvvvv* =&ǎ W~WU~W~WP~WZ@Fߋ^V111*t~W~W P( *FF~W~W~W@F;XtrF^V111*u~&uH =&~
&&UF;Fu vvvv* =&ǎ W~W P( *vvvv* =&ǎ Wvvvv* =&ǎ W P( *~Wvvvv* =&ǎ W P( *~W~W P( *~W~W~Wf@~WZW P( *ZW~WZWw@B WZWZW @ZWZWV0@B WZWZW @ZWpW)@~WpWpW-@~WpWpW @pWpWV0@B WpWpWw@~W~&u P/ =&>< t@FHX ;X)FF~Wv PT@RP4 =&F;Xuvvvv* =&ǎ W~W P( *~WZW~W-@~Wv P~W RP4 =&~&EXF@;XDFF~Wv Pvvvv* =&ǎ W RP4 =&F;Xu~&EXF;XTFFvvv P* =&ǎ WpWvvv P* =&ǎ W-@F;XuP~&uH =&RPP@RPPvvPvv @RP11RPE
@RPE
@RPE
@RPE
@FV W PPvv~
WS ~W F;Fu`~
&=&EX ;X~ FF~
&u&5vv* =&ǎ W~W P( *~
&u&5vv* =&ǎ W~
&u&5vv* =&ǎ W P( *~W~
&u&5vv* =&ǎ W P( *F;XtPvvvv* =&ǎ W~W P( *vvvv* =&ǎ Wvvvv* =&ǎ W P( *~Wvvvv* =&ǎ W P( *] Orthogonalizing Ud*dvv~Wf =&vv @~&&U~&uH =&~
&&U~&=&EF~&=&EF, W~W P( *FF ;F~ FFFF ;FeFF~&u&5vv* =&ǎ W~W @F^VNӋvՋ~ך*v~W~W P( *F;FuF;FuFӋ^ՋV111*u6~&uH =&~
&&UPvv~W9 =&~W FF ;FvFFFF ;FXFF~&u&5vv* =&ǎ W~W~&u&5vv* =&ǎ Ww@F;FuF;FuF F F;F|F;F~F+FRP1P~W P *W8W *~W *~W P *~W5 FFF~ tXF;FP~&u&5vv* =&ǎ W~W @F^V6>*sFF 뢀~ tF ~&u&5~WvvPvv~&u&5~WP ~W FV~&&UPvv~W~W vv~W~W P~
&u&5vv~W ~
W ~W FV~
&&UFFFFF;F?FF, W~&u&5vFHP* =&ǎ W P( *F;Fuƚ* FFF;F~ FF~&u&5vv* =&ǎ W~W @F^V6>*s-, W~&u&5vv* =&ǎ W P( *F;FuFF ;FvFFFF ;FXFF~&u&5vv* =&ǎ W~W~&u&5vv* =&ǎ W-@F;FuF;Fu~W ] UB *Bvv~W~W> =&~ uOPvv @RP11RPE
@~&&UPvv @RP11RPE
@~
&&U'~ t! ~&&U ~
&&Uvv~W~WC =&~ u~ uvv @~
&&Uvv~
Wf =&~
&=&EF~
&=&EF~ tD, W~W P( *FF ;F~ FFFF ;FeFF~
&u&5vv* =&ǎ W~W @F^ߋVNNjvɋ~˚*s~W~W P( *F;FuF;FuF^ߋV111*u FF ;FvFFFF ;FXFF~
&u&5vv* =&ǎ W~W~
&u&5vv* =&ǎ Ww@F;FuF;FuF F F;F~F;F~, W~W P( *1FFFF;F~ FF~ ti~
&u&5FF+FPv* =&ǎ&} u'~
&u&5FF+FPv* =&ǎ&} tB W~W P( *FF[~
&u&5vv* =&ǎ W~W @F^ߋVNNjvɋ~˚*s~W~W P( *FFF;Ft(F^ߋV6>*wJF;Fu FFF;F~ FF~
&u&5vv* =&ǎ W~W P( *~
&u&5vv* =&ǎ W~
&u&5vv* =&ǎ W P( *~W~
&u&5vv* =&ǎ W P( *F;FtQFFF@;FrFF~
&u&5vv* =&ǎ W~
&u&5vv* =&ǎ W~
&u&5vv* =&ǎ W @F;Fu~ u ~
&u&5vv* =&ǎ W% O&~
&u&5vv* =&ǎ&E P~
&u&5vv* =&ǎ W9 O&4 W~
&u&5vv* =&ǎ
W P( *4 W~
&u&5vv* =&ǎ W P( *-B W~
&u&5vv* =&ǎ W P( *FF ;F~FFF;FuFFF@;F~ FF~
&u&5vv* =&ǎ W~
&u&5vv* =&ǎ W~W-@~
&u&5vv* =&ǎ W~W~
&u&5vv* =&ǎ W@~u
~W% O&F;FtR~ u ~
&u&5vv* =&ǎ W% O&~
&u&5vv* =&ǎ&E4 W~
&u&5vv* =&ǎ W P( *4 W~
&u&5vv* =&ǎ
W P( *4 W~
&u&5vv* =&ǎ W P( *-, W~
&u&5vv* =&ǎ W P( *F;Ft!F%FFF;F~FF~ u ~
&u&5vv* =&ǎ W% O&~
&u&5vv* =&ǎ&E4 W~
&u&5vv* =&ǎ W P( *4 W~
&u&5vv* =&ǎ
W P( *4 W~
&u&5vv* =&ǎ W P( *-, W~
&u&5vv* =&ǎ W P( *F;FtFPT@~&&UFH*~&=&E&]&U
] U1*~6}W ~W ~6}W ~6}W ~ t; ~6}&&UT@~6}&&U ~6}&&U0~6}1&&E~6}1&&E~6}1&&E* ] LU Decomposition3You cannot invert a matrix with non-numeric entries.This operation applies only to square matricesLU Decomposition U帢*? W`W P *`W5 ~ u,WP W * ~ t5 ~&&U ~&&U ~&&U* ~&E~&;Et0W W * >< t,~1&&E~1&&E~1&&E* Wv v~
WWC =&~
&= u uv v @~&&Uv v~Wf =&~W~&u P/ =&~W~&u P/ =&@~&&U>< t PUM~&=&EFF^ ;^~ FF, W~W P( *F\ ;\~ FF~&u&5vv* =&ǎ W~W"@~
&= t ~uɻ{κ@RSP~W Fً^ۋVNËvŋ~ǚ*v~W~W P( *F;\twB W~W~W; @~u
PUL ~Wv P~W RP4 =&F;^t* F^ ;^~FFF+F@RP1P`W P *^W W *`W *`W P *`W5 FH\ ;\~DFF~&u&5vv* =&ǎ W, W~W @FHZ ;Z~} FF~&u&5vv* =&ǎ W~&u&5vv* =&ǎ W~W-@~W~W~W@~u
~W% O&F;Zu~&u&5vv* =&ǎ&}u$~&u&5vv* =&ǎ W% O&~W~&u&5vv* =&ǎ W P( *F;\t, W~W P( *F\F;\~FF, W~&u&5vv* =&ǎ W~W @FHZ ;Z~} FF~&u&5vv* =&ǎ W~&u&5vv* =&ǎ W~W-@~W~W~W@~u
~W% O&F;Zu~&u&5vv* =&ǎ&}u$~&u&5vv* =&ǎ W% O&~W~&u&5vv* =&ǎ W P( *~W~W @~u
~W> O&~Wvvv P* =&ǎ W~W-@~
&= t ~uɻ{κ@RSP~W F^VNËvŋ~ǚ*rFF~W~W P( *F;\t F;Fu F\ ;\iFF~&u&5vv* =&FV~Wvv~&u&5vv* =&RP4 =&~Wvvvv4 =&F;\u~&=&E&]&U
t~&=&E&]&U
vvv P* =&ǎ Wvvv P* =&ǎ W P( *~Wv PT@RP4 =&F*RSP~&u&5v P* =&ǎX[Z&E&]&U
~&u&5vv* =&ǎ W~W P( *~tb~
&= uDF^V6>*s%~ u4F^V6>*r~
&= t~ u~ u PUp F\F@;\YFF~&u&5vv* =&ǎ W~W~&u&5vv* =&ǎ W @F;\u* F;^t~W F^ ;^MFF~&= W~&u&5vv* =&ǎ W~&= W@F;^u]
Back solving UD*Dvv~W~W> =&~ u/Pvv @RPv v
@RPE
@~&&Uvv~W~W~W~WFߘ&*PFޘ&*P>< t~1&&Evv>@t ~&&Uov v
@~&&U~&EF~&=&EF ;F~FF~&=&E+F@RP1P~W P *W'W *~W *~W P *~W5 1FFF ;F~FFvvv P* =&ǎ&E&]&U
*'*F~&u&5vv* =&RP @FV~&u&5vv% =&~Wvv~&u&5vv* =&RP @RP4 =&~ u FHFF;F~ FFPvvPvvvv* =&RP~&u&5vv* =&RPE
@RPE
@FV W PF&*Pvv~WS ~&}&u&5 PT*~ W vv PT*>< t~1&&E,F;Ft:vv@uF ~&u&5vv% =&~Wvvvv4 =&F;Ft4F= }FN~&u&5vv* =&RP @FVFFF@;F~ FFPvvPvvvv* =&RP~&u&5vv* =&RPE
@RPE
@FV W PF&*Pvv~WS ~&}&u&5 PT*~ W vv PT*>< t~1&&E F;Ft:Pvvvvvv* =&RPE
@FV W PF&*Pvv~WS ~ W vv PT*>< t~1&&ED~&u&5vv% =&~Wvvvv4 =&~tK* F;Ft~W ~W ~W ] U * vv~Wv v
~WF[,*Pvvvv~Wj~W ~W ~&}tFV~&&Uvv~W9~W ] U *@~&&U~&EF ;F~FF~&EF ;F~FFF
01ҿ-*Pvvvv* =&RPvv vv* =&RPE
@FV W PF -*Pvv~WS vv PT*vvvv* =&ǎ1&&E>< u]~&} tS~W ~W F
01ҿ-*Pvv @RPvv @RPE
@~&&U >< u2~&}u(~W ~W ~&&U R>< uK~&}uA~&E&]&U
111*u%~W ~W K@~&&U3F;FtoF;FtG>< t~W ~1&&E] U *~W~&u~&u/ =&>< t ~&EF ;F~ FF~&EF ;F~ FFF
01ҿ$/*Pvvvv* =&RPvv vv* =&RPE
@FV W PF,/*Pvv~WS vv PT*vvvv* =&ǎ1&&E~Wvvvv4 =&F;FtHF;Ft >< t~W ~1&&E] U *~W~&u~
&u/ =&>< t~&EF ;F~hFF~
&EF ;F~@FFT@FV~&EF ;F~ FFPvvvv* =&RPv v
vv* =&RPE
@FV W PF0*Pvv~WS vv PT*vvvv* =&ǎ1&&EPvvvvE
@FV W PF0*Pvv~WS ~W >< t ~W 7F;Ft~Wvvvv4 =&F;FtF;Ft>< t~W ~1&&E] -Only square matrices can be raised to a power-Matrices can be raised to integer powers only U: *:~&E~&;Et&~1&&E~WY2W * pm~
&} t/Pvv @RPv v
@RPE
@~&&U4v v
@u&~1&&E~W2W * ~
&E&]&U
1 *uW~
&E&]&U
11u*t*2*FF2*Pvvvv~W3vv @FV~
&E&]&U
*2*F~
&E&]&U
111*r vv~W~W> =&~ u(Pvvv v
@RPE
@~&&U F2*Pvv~&uH =&RP~Wp~W FVFV~&uH =&~&&U~ FsFF2*P~&u&5vv~Wz~W FV~&&UNEF2*Pvvvv~W8~W FVFVF Fb] U *>< t~1&&E v v
~W~W> =&~ u"Pv v
11RPE
@~&&Uv~ t ~&&U]v v
~W~WA~WP FV~&=&E&U~&=&E FV~&&U~1&&E]
U * >< t~1&&Evv ~W~W> =&~ u7F
01ҿW6*Pvv @RP11RPE
@~&&U~ t ~&&Uvv ~W~W~W~WF_6*PF_6*P~W F
@tFV~&&U~WP ~&=&E ~&= W~&u~&u/ =&~&=&}W~&u~&u/ =&>< t~1&&E~&EF ;F~pFF~&EF ;F~HFFF;F| ~&= WvvT@RP4 =&~ u ~&=&u&uvv* =&ǎ&E4 W~&=&u&uvv* =&ǎ W P( *4 W~&=&u&uvv* =&ǎ
W P( *4 W~&=&u&uvv* =&ǎ W P( *~&=&}Wvvvvvv* =&RP4 =&!F;Ft~&= Wvv蚚@RP4 =&~ u ~&=&u&uvv* =&ǎ&E P~&=&u&uvv* =&ǎ W9 O&4 W~&=&u&uvv* =&ǎ
W P( *4 W~&=&u&uvv* =&ǎ W P( *~&=&}Wvvvvvv* =&RP4 =&~&= Wvvvvvv* =&RP4 =&~&=&}WvvT@RP4 =&~ u ~&=&}&u&5vv* =&ǎ&E4 W~&=&}&u&5vv* =&ǎ W P( *4 W~&=&}&u&5vv* =&ǎ
W P( *4 W~&=&}&u&5vv* =&ǎ W P( *F;FtF;Ft~Wa =&] U
*
v v
~W~W> =&~ t~ t'Pvv @RP11RPE
@~&&Uc~
W~W
~WP ~&=&E v v
@~&=&E&UFV~&=&}&&U~1&&E]
U *>< t 1FF T@FV~&EFF~&;E~
~&EFFF ;F~ FFPvvvvvv* =&RPE
@FV W PF
Q<*Pvv~WS ~ W vv PT*>< t
1FFF;FtwFVFVFV] U
*
~&EF ;F~>FF~&EFF@;F~FFvvvv* =&ǎ&E&]&U
RSPvvvv* =&ǎ&E&]&U
Y^_*t vvvv* =&ǎ&EPvvvv* =&ǎ&EZ:urvvvv* =&ǎ&} u\vvvv* =&ǎ&E &]&UtRSPvvvv* =&ǎ&E &]&UY^_*tF F;FtF;FtFF] AThe characteristic polynomial is defined only for square matrices Un*n~&}u~&E~&;EtPW>W * >< t~1&&EM! W5 vv@FV~&EF~ tBvv~W~W> =&~ t ~ uvv~W~WC =&F F FF F F ~ t~ t~ u~ uvvMu ?*~
&~ tR~ uLPvv~W~W~&E&]&U
*?*F~W ~W
~&EF~WP @~&=&E&U1FF;F|0~&}t#FF*RSP~W PPF ?*Pvv[RP~W RPE
@RP11RPE
@FV~&=&E&U~&&U W PF ?*Pvv~&= WS >< t(~W ~W ~1&&E* $~
&= t%~&=&} W~&=&} WUN@~&&U~&=&}&&U~W F;F| ~&=&u&u @FVPvvPvvPvvvH =&RPE
@RPE
@RPE
@FV W PF ?*Pvv~WS ~&}W vv PT*>< t~1&&E* * W~&u&5 P2 PP'Y ~W< P *~W5 FFF@;FNFF~&=&E&UFVT@~&=&E&UFV~&=&}&&UF;Fu~&}t/~W Pvv @RP11RPE
@~&&U~W F@~&=&E * >< t~W ~1&&E ] U: *:~
&=&EFFFʋF;F~FF, W~W P( *FFȸ ;F{FF~
&u&5vv* =&ǎ W~WP@~W~
&u&5vv* =&ǎ W~W-@~W~W~W @F;Fu~W~WV0@FFȸ ;FXFF~
&u&5vv* =&ǎ W~W~
&u&5vv* =&ǎ Ww@F;FuFFȋF@;F~IFF, W~W P( *FFƸ ;F{FF~
&u&5vv* =&ǎ W~WP@~W~
&u&5vv* =&ǎ W~W-@~W~W~W @F;FuFFƸ ;F~ FF~
&u&5vv* =&ǎ W~W~W-@~
&u&5vv* =&ǎ W~W~
&u&5vv* =&ǎ Wf@F;Ft|F;FtF;Ft] &EIG must be applied to a square matrixACannot compute all eigenvalues. Try EIGENVAL to see partial list
Constructing eigenvector< t~
&}u~
&E~
&;Et:WsFW * NPv v
~W~W* K&>< u~ u"~W WFW * ~
&EF܍~
W~W
~WP vܚH =&~&=&E&U~&E&UFVF܉` ;`dFF~&= Wvvvv4 =&~&&UFV~&=&u&uvv* =&ǎ1&&EF;`u FΉ^ЉVvܚH =&~&=&}&&U~&=&}&&UFV~&=&E&UFVF F F >< tF;F~bWFW *F♿F* h W *FW *bW( P *bW5 F vvvv* =&ǎ W~W P( *FF;F~~ vvFFPFFP* =&ǎ&E&]&U
Nv~*uE~t9vvFFPFFP* =&ǎ&E &]&UNv~Ú*uFtv v
@FVF܉` ;`QFFvvvv* =&ǎ W~Wvvvv* =&ǎ Wf@F;`uiՔV1FF~W Pvv~W~Wxȡ 1 @o* Fܙ*~&M&u&}
*w };̿L*v~W Fܙ*~&M&u&}
*t"F+Fڙ*~&M&u&}
*v,~W ~W $WFW * sXQ*vFF F F;F~FF;F~2vvvvޚ* =&ǎ WN@u vvvvޚ* =&ǎ&E &E &E
F܉` ;`~ FFֿ, W~W P( *F܉^ ;^eFFvvvvԚ* =&ǎ Wvvvvޚ* =&ǎ W~W-@~W~W~W @F;^u~Wvvvvؚ* =&ǎ W P( *F;`t@FFNFF~W ~ ~VFF܉` ;`:FFֿ, Wvvvvؚ* =&ǎ W P( *F;`uNF뤀~ u~WvFHP%F؉F⚉* Y~&=&E ~ t
0! W5 ~W F^ЋVң ]
Matrix for contains undefined terms (Cannot compute singular values of matrix&The zero matrix has no singular valuesUX*X~1&&E>< t
vv ~W~W> =&~ u6~ u0F
01ҿM*Pvv 11RPE
@~&&UR
I~ tCWMW *F
01ҿM*
8 W *MW *
vv ~W~WC =&~ t vv ~Wf =&FVF V~ &E~ &;E ~@N*F~ t+vv ~W莴~ t
~ W FVF V~ &EF~ &EFԊFN*Pvv ~W vv~W2~W FN*Pvv vv~Wd>< t-~W ~W ~ u~ t
~ W ~
t FN*Pvv~W~W* K&~WP ~ Wvv֚/ =&>< t~&E&UFV1FڋF FtGF~ Wvvvv4 =&FVFމV~&&UFV~1&&Evv PT* FN*Pvv~W~W >< uCF Ft;~&}u1~&u&u~&}&u~&}&u* =&RP>@tB~W!NW * ~W ~W ~ u~ t
~ W ^1F܋F;F}*~&u&uF@PF@P* =&RP@uF~ t ~
uoF֙*RSP~W Fԙ*RSP~W < t~
uF։F ;F~ FFڋF܉F ;F~ FF~
u8~ Wvv~&}&u&5vvؚ* =&RP @RP4 =&{~ Wvv~&}&u&5vvؚ* =&RP @RP4 =&~&u&uvvښ* =&ǎ W~&u&uvvښ* =&ǎ WP@F;Ft9F;Ft~&}Wvvܚ/ =&>< tF܉F ;FaFFڋF܉F ;FCFF~&}Wvv~&u&uvvؚ* =&RP @RP4 =&F;FuF;FuF܉F ;F[FF~&}&u&5vvښ* =&ǎ W~&}&u&5vvښ* =&ǎ WV0@F;Fu~
t ~tF;F}F;F} ~&&Uf~&}&u&5 P P* =&ǎ W~&}&u&5vvܚ* =&ǎ W~Ww@~W ~&&U~W ~W ~W ~ u~ t
~ W %FN*Pvv~&}&u&5~WLڍ~W ~W ~&}&=Wvvܚ/ =&>< tFԉF ;F~ FFڋF܉F ;F~ FF~&}&=Wvvvvvvؚ* =&RP @RP4 =&~&}&=&u&5vvؚ* =&ǎ W~&}&u&5vvؚ* =&ǎ W~&}&=&u&5vvؚ* =&ǎ Ww@F;FtMF;Ft)~W ~
t FV~&&U~ tw~&=&E&UFV~&=&}&=&&U~&=&E&U~&&U~&=&}&&UFV~&=&}&=&&U~1&&E~&=&E F܉F ;F`FFڿB W~&}&u&5vvښ* =&ǎ W~&}&u&5vvښ* =&ǎ Ww@F;FuFN*P~&}&=&u&5~&}&u&5~WFN*Pvv~&u&u~W׀~ t-~&u&5~W7~W FV~&&U~W ~W ~ u~ t
~ W ] U *F
< t ~ &EF ;F~ FF~ &EF ;F~ FF>< t F
01ҿEY*Pvv vv* =&RP11RPE
@FV W PF=Y*Pvv~WS vv PT*>< u~Wvvvv4 =&F;FtbF;Ft:>< t
~W ] $Matrices cannot be used as exponents 2 is an illegal operator with a matrix and a scalar4You cannot combine matrices of different sizes with 6Matrices not right size for multiplication or division!You cannot combine matrices with U * F ~&}teF VFVFVF VFVFV~
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P4P>PTPmPPPPP"Q1QKQQQQQQQQQR&R3R< tl, W~W P( *~&E= |MFN~
W~W~W-@vv Pv* =&ǎ W~W~W @~u] ;EVALPOLY must be applied to a non-empty list and a constantU` *`~1&&E W PF *P~
&u&u~WS >< tK~W PF *P~
&}&u&5~WS >< u~&}u0~&E& Eu#~W W * ~1&&E ~&}u
~&} t8~ uvvܚ@F܉VްPvvvvܚE
@~&&U GPvv11RPE
@FV W PF *Pvv~WS vv~܁ W~W~W ~&&U~W ~W ~ t
~W ]
U6 *6, W~W P( *~&EFʸ ;FxFFvv Pv̚* =&ǎ&}uFFFpkvv Pv̚* =&ǎ W~W @~W~W~W @F;Fu~uFFFpFϋ^ыVӉF^VF^V] UR *R~
1&&E~1&&Evv @FV~&E~&;E~"T@~
&&UFV~&&U~
W P~&E~&+E@P/ =&>< tivv P~&u* =&ǎ W~W P( *~
&=&E= }FNvv PF~&EHP* =&ǎ W~W~Ww@~
W Pv~W RP4 =&~&EF ;F~ FFvv Pv* =&ǎ W~W~W-@vv PFFHP* =&ǎ W~Wvv PFFHP* =&ǎ Wf@F;Ft{~t~&EHFvv6 >u*F^V~ ~jvv Pv* =&ǎ&E &]&URSPvv Pv* =&ǎ&E&]&U
Y^_]*Nv~*wN됃~ uT@~&&Uk~W Pv/ =&>< t[~&=&EF ;F< t ~
&=&EF ;FuFFFH*RSP~W ~W~
&u&5 Pv* =&ǎ W~W-@~W PFHP~W RP4 =&F;Fu] U6 *6~&u&5@~&&U~&=&EHF̸ ;F~#FFB W~W P( *F ~&=&EFʋF@;F~ FFF+FȋFHfFF*RSP~W ~W~
W~W-@~W~W~W-@~W~&u&5 Pv* =&ǎ W~W-@~&u&5 Pv* =&ǎ W~W~&u&5 Pv* =&ǎ W @F;Ft&F;Ft~&=&EH*RSP 11Y^_u*RSP~W ~&u&5 P P* =&ǎ W~W~WA@~W~W @~W~W P( *~&=&EH= |lFN~&u&5 Pv* =&ǎ W~W~&u&5 Pv* =&ǎ Ww@~W~W~W-@~u] U0 *0~
W~W P( *~W~W P( *~&=&EFи ;F~ FF~&u&5 PvҚ* =&ǎ W~W~&u&5 PvҚ* =&ǎ W-@~&u&5 PvҚ* =&ǎ W~W~&u&5 PvҚ* =&ǎ W @F;Ft^] U6 *6~W P~&=&u/ =&>< t+F F ~1&~ tF~&=&;E~~&=&}x~&=|l~&u&5 PvΚ* =&ǎ W~W P( *~W~W)@~&=&E+Fs~W~W@F F+F= } FF~&=&;E~ ~&u&5 PF+FP* =&ǎ W~&u&5 PFFP* =&ǎ W~W-@~W~W~W @~&=&E+FFs~W~W~Wf@~W~W~W @F3~t~WN@tF ~W Pv~W RP4 =&F]~ u~&=&}~ ~&=} ~W ~
W P~&=&EHP/ =&>< t*~
&=&E= } FN~&u&5 PvΚ* =&ǎ W~&u&5 PF@P* =&ǎ W~Ww@~W~W@~
W Pv~W RP4 =&~t|~&~W~
W~W~W ~
&=&E= }WFN~
&u&5 PvΚ* =&ǎ W~
&u&5 PvΚ* =&ǎ WV0@~&u&5~
&u&5 PvΚ* =&ǎ W~WR>< t~
&u&5 PvΚ* =&ǎ W~
&u&5 PvΚ* =&ǎ W@~&u&5~
&u&5 PvΚ* =&ǎ W~W>< tK~W~W @~W~W @~t ~t ~&u&5 PvΚ* =&ǎ W~&u&5 PF@P* =&ǎ W~
&u&5 PvΚ* =&ǎ Ww@~
&u&5 PvΚ* =&ǎ W~
&u&5 PvΚ* =&ǎ W@d~tF^VNыvӋ~՚*sE~
&u&5 PvΚ* =&ǎ W~
&u&5 PvΚ* =&ǎ W@~t] Perfecting rootPerfecting root U* 3*zgo*RSP|?UY^_c***^v v
XNPR~
W~W~&=&E, ;,~G \\\J,WW *\* h W *W *.W P *C\RP1P.W P *,WW *.W *.W P *.W5 v v
~&u&5 P\* =&ǎ W~W>< t* i1``vv~&u&5 P\* =&ǎ W~W>< t* ~W~W~Ww@~t|~&u&5 P\* =&ǎ W~W~&u&5 P\* =&ǎ W@v v
~&u&5 P\* =&ǎ W~W~W~W @~&u&5 P\* =&ǎ W~W @~WxW @~u ~u F^V 11*v&F^V 1 o*Nv~*rzF^V6>o*Nv~*w F^V6>*s`-y{}111*t`;^
>< u~u# 1 Ho*y{}*v 1ۺ H6>o*Nv~o*y{}*wb 1 Ho*Nv~*w: 1ۺ H6>o*Nv~o*Nv~*wY~&u&5 P\* =&ǎ&} t~&u&5 P\* =&ǎ&E&]&U
111*to~&u&5 P\* =&ǎ&E&]&U
sXQo*RSP~&u&5 P\* =&ǎ&E &]&UY^_*rTNPRsXQo*RSP~&u&5 P\* =&ǎ&E &]&UY^_*r~&u&5 P\* =&ǎ&E &]&U111*u#~&u&5 P\* =&ǎ&EXv v
~&u&5 P\* =&ǎ W~Wb~&u&5 P\* =&ǎ&E &]&UTVX~&u&5 P\* =&ǎ&E &E &E v v
~&u&5 P\* =&ǎ W~W~W~W @~W~W @~tFы^ӋVՋNv~*v;TVXRSP~&u&5 P\* =&ǎX[Z&E &]&U ~&u&5 P\* =&ǎ&E~&u&5 P\* =&ǎ&} tg~&u&5 P\* =&ǎ&E&]&U
111*u0~&u&5 P\* =&ǎ&E &]&U111*u~&u&5 P\* =&ǎ&E &]&UsXQo*RSP~&u&5 P\* =&ǎ&E&]&U
Y^_*rTNPRsXQo*RSP~&u&5 P\* =&ǎ&E&]&U
Y^_*r6v v
~&u&5 P\* =&ǎ W~W~&u&5 P\* =&ǎ&E&]&U
TVX~&u&5 P\* =&ǎ&E &E &E
v v
~&u&5 P\* =&ǎ W~W$~W~W @~W~W @~tFы^ӋVՋNv~*v9TVXRSP~&u&5 P\* =&ǎX[Z&E&]&U
/ W~&u&5 P\* =&ǎ W P( ** \;,t~W ] U: *:~&=&EHFȸ ;F~iFFFF~&u&5 Pv* =&ǎ W~W @~&=&EFƋF@;F~FF~&u&5 Pv* =&ǎ W~W @~&u&5 Pv* =&ǎ&}u7~&u&5 Pv* =&ǎ&}t*F^V幁]F o*Nˋv͋~Ϛ*s ~&u&5 Pv* =&ǎ&}u F^V幀EGro*Nˋv͋~Ϛ*r ~&u&5 Pv* =&ǎ&} t ~&u&5 Pv* =&ǎ&} ur~&u&5 Pv* =&ǎ&E &]&URSP~&u&5 Pv* =&ǎ&E &]&UY^_*sFF~W~W P( *F;FtT~&u&5 Pv* =&FV~W Pv~&u&5 Pv* =&RP4 =&~W Pvvv4 =&F;Ft] U * F F~
&=&;E|~
&u&5 Pv* =&ǎ&}t#~
&u&5 PF@P* =&ǎ&}u~
&=&EF~
&u&5 Pv* =&ǎ W~
&u&5 PF@P* =&ǎ W~Wf@~
&u&5 Pv* =&RP@tk~
&u&5 PF@P* =&RP@t, W~W P( *1~W~
&u&5 PF@P* =&ǎ W~Ww@/~W~
&u&5 Pv* =&ǎ W~Ww@~W~W @~u F^VpG'*r ~
&u&5 Pv* =&FV~W ~
&=&EHFF;F;FF~
W Pv~
&u&5 PF@P* =&RP4 =&F;Fu~
W P~
&=&u RP4 =&~u~
&u&5 Pv* =&ǎ&} t~
&u&5 PF@P* =&ǎ&} t~
&u&5 PF@P* =&ǎ&E&]&U
RSP~
&u&5 Pv* =&ǎ&E&]&U
Y^_]*sXQo*RSP~
&u&5 PF@P* =&ǎ&E&]&U
RSP~
&u&5 Pv* =&ǎ&E&]&U
Y^_c*Y^_*r~
&u&5 PF@P* =&ǎ&E &]&URSP~
&u&5 Pv* =&ǎ&E &]&UY^_]*sXQo*RSP~
&u&5 PF@P* =&ǎ&E &]&URSP~
&u&5 Pv* =&ǎ&E &]&UY^_]*Y^_*r~
&u&5 PF@P* =&ǎ&E&]&U
RSP~
&u&5 Pv* =&ǎ&E&]&U
Y^_]* 11u*RSP~
&u&5 Pv* =&ǎX[Z&E&]&U
~
&u&5 Pv* =&ǎ&E&]&U
RSP~
&u&5 PF@P* =&ǎX[Z&E&]&U
~
&u&5 PF@P* =&ǎ&E &]&URSP~
&u&5 Pv* =&ǎ&E &]&UY^_c* 11u*RSP~
&u&5 Pv* =&ǎX[Z&E &]&U~
&u&5 Pv* =&ǎ&E &]&UtRSP~
&u&5 PF@P* =&ǎX[Z&E &]&UF~1&~
&=&E= |9FN~
&u&5 Pv* =&ǎ&}u~&~ủ] #Cannot find any roots of polynomialU帔 * ~W~W@~ u'F~&=&;EulW$W * `! W5 ~W P~
&=&E+FP/ =&>< tP~&EHHF ;F(FF~W PvT@RP4 =&F;Fuݍ~W P~&u@RP4 =&~W P~&EHP~&u&5 P P* =&RP @RP4 =&vv P~&EHP* =&ǎ Wvv P~&EHP* =&ǎ W@~&=&E+FF ;F~@FF~&u&5 Pv* =&ǎ W~W P( *~W~W@~Wvv P~&E+F@P* =&ǎ Wvv P~&E+FP* =&ǎ W-@~&EHF~&E+F@;F~ FF~Wvv PF@P* =&ǎ W~W-@~Wvv Pv* =&ǎ Wvv Pv* =&ǎ W @F;FuF;Ft~
&u&5vv~W~Wۍ~W vv@u * ~W ! W5 F 2*F^V2*F^V~W~W @~W~W~Ww@~W~W~W~W1F~W~W~W~W >< t* ~W 4~W~W~Wvv~W#~W >< t* ~
&u&5~W>< t* ~&EF ;FwFF~&u&5 PF~&=&E+FP* =&FV~W ~W PF~&=&E+FPvv Pv* =&RP4 =&F;Fu~Wa =&~W3~W~W* F;F ! W5 ~ ~~
W~W1] %Non-numeric value following SOLVEPOLY:Polynomial is constant or zero polynomial and has no roots U帚 * ~&E&UFމVF1F1FF1FF~&} u~&EP)W*uF "~&} u~&}u~ށ W> O&~ t ~ށ WN@tF~ tF 1FF ~&&UFމVF Ft ~ tg~ u'zW)W * ~
1&&E8FH;F'fW)W * ~
1&&ERFHЋFF;|! W5 ~W PF+F+FP/ =&>< t~&E&UFމVFF ;F FF~&&UFމVF;Fu~&EF ;FAFF~W Pv~ށ W RP4 =&~&&UFމVF;Fuč~W~W~&EH= |kFNvv Pv* =&ǎ Wvv P~&u* =&ǎ Wvv Pv* =&ǎ Ww@~uB Wvv P~&u* =&ǎ W P( *vvvv~WRvvvv֍~W~W8֍~W ~W 2*F^ÉVŀ~ tF5F 2*Flj^ɉVˍ~W~W @~W~W~Ww@~W~W~W~W21F~W~W~Wzހ>< t~W * ~W ~W~W~WKݚ* vv~W~W~W~W~W >< t#~W ~W ~
1&&Esvv#ԉF^Vvv֚@FV~&EF ;F~KFF~uV~
WP ~
&=&E vvڸ Pv* =&RP @~
&=&E&U~
&=&E&UFމV=vvڸ Pv* =&RP @~&&U~
&=&E ~&&UFމV~&}~&}uvv~ށ W~WЀ>< t#~W ~W ~
1&&E=~W~W @F pG'Nv~o*NvË~Ś*w Fvvޚ @~&&U~
&=&E ~&&UFމV~W~W~W FVF։VvvY҉F^Vvv~ށ W~Wπ>< t7~W ~W ~W ~W ~
1&&E@~W~W @~ t.~W vv@F։VvvщF^VF;Ftvvڸ P~&u* =&RP>@ u@4**~&~W ~W ~W ~W J~
WP T@~
&=&E&U~
&=&E ~
&=&E&UFމVN~&FF ;F9FFT@~&&U~
&=&E ~&&UFމVF;Fủ] -SOLVEPOLY must be applied to a non-empty listU0 *0>< t~1&&E F~W PP~
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P~W~Wp~ t
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W ] 8EIGENVALUE and EIGENVECTOR apply only to square matricesBYou cannot find the eigenvalues of a matrix with UNDEFINED entries U帄 * ~1&&E~&}u~&E~&;Et~W2W * >< tvv~W~W> =&~ u*Pvv @RP11RPE
@~&&UH ~ t|W3W * (vv~W~WC =&~ t vv~Wf =&FVFV~&EF, W~W P( *FF ;F~~ FFċFF ;F`FFvvvv* =&ǎ W~W @FNj^ɋVˋNvߋ~*vFNj^ɋVˉF݉^߉VF;FuF;Fuvv @FVFF ;FnFFċFF ;FPFFvvvv* =&ǎ W~Wvvvv* =&ǎ Ww@F;FuF;FuPvv P~W~W9 F&~W >< t vvF^3*P~W~
W_~W >< t ~W J~&=&E&UFVF Ft.~ W~W~ W-@~&&UFVʉ] U *~W~ &u P/ =&vv @FV>< tB~ &EF ;F~ FF~Wv Pvv v~ &u* =&RP @RP4 =&vvv~ &u% =&~ &EH= |3FN~WvF@Pvvvv* =&RP4 =&~uҍ~Wv P@RP4 =&F;FtVFJ6*PvvP~W> F&>< tT~W PvvvvE
@FV W PFJ6*Pvv~WS ~W ]
` cannot be applied to a matrixUt*t~ &}~~W P~ &u/ =& ~1&&E>< tD~ &E*RSP~W ~ &EF ;F~FFF< t`~W PF<*P~ &}&u&5~WS >< t~ t
~W ~&}t~W<W * ~&} tQ~ tvv @FV~ tvv @FVIPvvvvE
@~&&Ucvv@t@~&E&]&U
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* =*Fvv @~&&U~&=&EF̸ ;F~FFR FHF~&u&5vv* =&FV~&} t\~&u&5vv* =&ǎ&} u@<*Fπ~ t[~ W~&u&5vv* =&ǎ WP~WZ@FӋ^ՋV111* u@<*Fπ~ uN~ u ~ tWFH;F ~&=&EFʸ ;F~ FF~&u&5vv* =&FVF@@FȋF;F|9FN~Wvv~&u&5FHPv* =&RP4 =&F;Fu~WF@Pvvv4 =&F;FtvF;Ftb~ t
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F t
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P?*~&=&E&U~&&U~&=&}&E&U~&=&E&U~&&U~&=1&E&EF
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P?*~&E&U~&E&UFVFV~&E&U~1&E&EFVN^_ *ȉڿ*~&FVN^_ *FVFVFV~&E&UFVF Ft~&E&UFV~We FV*PFV*Pvv~W~W/ FVFV~
&E&UF
V =~W ] U *~&& Eum~&=&E& Et~&=&E&U~&&U~&&UFV~&=&E&U~&&Uvv
PT*~&& Eu] digit index out of range *BUG -- digit index out of range for bignumU * ~W~W P( *~ |F;F|SWW *W~W8 *F*RSPm- ~WW * 1FFF~&1҉FVFV] -BUG -- Assignment to BigNumDigit out of rangeassigndigit i assigndigit x U6 *6~
W~W P( *~ |F;F}~ rW~WW * ~WW *F*RSPm- ~WW *F1Қ*RSPm- VF~&] :Insufficient memory to complete operation with big numbers U> *>~&EFFRP t)~WW * 4 W~W P( * F*P?*~&E&U] U1*~
~@b*~&~&E ~WF>< t ~W1PF
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W~W P( *>< t4 W~W P( *~ u~W~W~ u~W~WF2Ft9~ tF~W~W~WF~W~W~WfFFF;F~FF~Wa>< t?1FFFHF1;F~ FFF;F}~WvLFVFVF;F}~Wv,FVFV~WvFV 1ۚ_ *ȉڿ *PFV 1ۚ_ *FVF;FtsF Fu~W~Wq`F@~&E~W>< t_~W~&}WF *P *~W~&EHPFV쿝 *PN~WF *~&] U * ~W~W P( *~
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