FUJIbaudXdata„LUUü<=•°B¶BÚZ¨ÃÂÄAµBµQµMµCµÆA¨ØÌËÓÊÅÔÁÐÇÑÒÏÈÉÎÖÕ×ÍB¤C¤XµÙA¤JµEµZµFµD¤YµAdD™™™™<data„UUüC ? A X5  @'fdata„UUü :!:P"#$–9x%&=data„UUü'@&(A#UP)_:* M >:A%,ÁÌÇÉÃÁÌÃ% (tm)M #Rational Algebra & Calculus programg Atari BASñdata„UUüIC versiong GCopyright (c) 1981, The Soft WarehouseBox 11174, Honolulu, Hawaii 96828 A A 6€-€&@bdata„UUübb8€,A@AAPA0AA€AA…A A 0A` 6‚-O:‚,( 6ƒ-O:ƒ,2 ädata„UUüƒ ‚6„-ƒ6ƒ-‚6‚-„< ƒ!…6‚-@$F(‚6‚-ƒ$P"6„-ƒ&‚$P:ƒ'‚,„6ƒ-‚"6‚-„Z$d 6„-O:ƒ,„!…$nHdata„UUü „ †6ƒ-$x„!‡AP‚#6ˆ-P:ƒ%†$„,O:ˆ&ƒ, †$„#6ƒ-ˆŒ$–6ˆ-P:ƒ%‰,O:ˆ&ƒ, ‰6ƒ-ˆ $ª, „-ƒ‚2data„UUü6Š-Š%@%6‹8Š,-‹8„,) „,$´B‚-Œ%@Š6‹8,-‹8‚,-6-%@1 ‚?6Œ-&@B$¾ 6‚-‹8Š,‚ @$Èi=data„UUü 6Ž-Š&‚6-‹8Ž,6-‘&‹8‘,/6‘-‘&‚%@7’-‘B6ƒ-‹8’,'K6‹8’,-ƒQ6„-’i“-Ž%@Š&@Í:6„-„%@$6‹8„,-‹8ldata„UUü„,&ƒ$‹8“,( “, ’76‹8‘,-‘&:$Ò!‹8‘, ‹8Š,6„-‘6‘-Š!6Š-„ÜA 6Ž-‹8Š,Ž @'6‹8Š,-@>6‹8Š&@,-@Adata„UUü$æH 6Ž-Š&Ž6-‘&‹8‘,6‚-‹8Ž,(6ƒ-‹8,2 @@=6-‹8,'‚H6’-‹8Ž,'‚ë,O:,!…)O:’,!…"6‹8Š,-@, A ðL6‚-rdata„UUü6“-3”-%@‘&@A6Ž-Ž%@L6ƒ-’$‹8”,õ O:ƒ,!…6“-‘&@ 6”-“úŽŠAp:6ˆ-$‹8Ž,Ádata„UUü6ƒ-ƒ&ˆ&O:ˆ,!…)O:ƒ,!…46“-‘&@:6”-“ 6‹8”,-ƒ(“*ƒ6“-” @@ ”“" $"$6‹8‘,-‘&“‹8“, èdata„UUü$6‚-6‚,1‚&@-“‘&@-6‹8,-‹8,'‚1 6 A@H 6-‹8Ž,6-‹8‘,6Š-Š%%26‹8Š,-%&@:6’-Š&bdata„UUüB6-Ž&H6‚-ŽEU!„-Š&@Š&‹8Š,6@-6ƒ-;6‚-‚&@A‚ G6‚-U6‘-‘&@J 6“-‘„ ’6Ž-Ž&@Ødata„UUüT; Ž!‚-‚Ž&@'6“-“&@76ƒ-ƒ%‹8,$‹8“,; ^ 6‹8„,-ƒ „$hT ApK•")”"@*–"@*—"ldata„UUü*"@*’"@Q6Œ-˜T$rII”")•"@*™"@*š"*"@*Ž"@A|g6‹8&@,-šdata„UUü%—6ƒ-•"6‚-–, @@46•-•'‚<6–-–'‚B6ƒ-”H6‚-™R @@g6‹8&@,-”'‚$•j6‹8&@,-™'‚$–6Š-Œ$6ƒ-*6‚-›4 ÿdata„UUüAp:6‘-Š@6ƒ-œF6‚-ŒP ApZ A`6‘-Œj A‚ 6Œ-‘6‘-› A6›-‘†U 6Š-Œ6ƒ-6‚-ž Ap%6‘-data„UUüŠ+6ƒ-Ÿ16‚-˜; ApE AK6‘-˜U A‹U 6˜-‘6‘-ž A6ž-‘%6Š-Œ+6Ž-›5 A ;6‘-ŒA6Ž-˜K A U `data„UUüA€!‹8Š,!‹8–,6„-Š6Š-–!6–-„šo6‚-6“-‹8Š, 6-–&“&6—-26-:6Š-Š&“JŽ-–&@X6ƒ-‹8Ž,%‹8Š,šdata„UUüa6‹8Ž,-ƒo6Š-Š%@Ÿ"ƒ @@6—-Ž("6-ޤ Ž6‘-‹8–,(6-—®H “&‘6-–&‘!‚@*!1Ž-&@]data„UUü:6ƒ-‹8Ž,D @@H ޏ (‚ $‹8, 6‚-6‚Ì)‚&@Ž-—%6‹8Ž,-‹8Ž,'‚) ŽÖ6—-—%@6‹8—,*data„UUü-—&$à Ap(”6Œ-˜$ê(•Aôe 6‚-™6ƒ-– @P!6™-™'‚)6–-–'‚/6‚-•56ƒ-”? @0G6•-•'‚O6”-”'µdata„UUü‚W6–-•$–_6”-”$™e6•-šù — •6•-—þI 6š-š&•6—-—&•6‘-Œ)-œŒ&@76‘-‘%@E6‹8‘,-‹8,$–I ,š-‘%@'data„UUü‘%š(6‹8,-, V6‘-‘%š%@6‹8‘,-’%š$6š-‚*6Ž-›06Š-Œ: A @6–-ŠF6‘-ŠV-Ÿ˜&@ L6‘-‘%@þdata„UUü6‹8‘,-‹8,$”# '—9-‘%@‘%—H6‹8,-L j6‘-‘%—%@!6‹8‘,-‹8˜,%—'6Ž-ž-6Š-–7 A A AFœdata„UUü(‚P A€g6‹8&@,-j$¦6‹8&@,-•%–&—6•-‚$6ƒ-™. @066•-•'‚>6™-™'‚O6‚-‹8&@,U6ƒ-•_ Œdata„UUü@@t6‹8&@,-•'‚$š”6‹8&@,-‹8&@,'‚$™š6Ž-˜ 6‘-Œ¦6Š-—g A 6™-Š6•-,6Œ-Š&‹8Š,&@6 A€¦data„UUü<6‘-ŒG6ƒ-—&‹8—,M6‚-—S6Š-™] Apg A#B 6‘-™ A6™-‘6‘-—) A/6Š-‘B6Œ-Š&‹8Š,&@&6 6-•†data„UUü A€6Š-™,6Œ-Š&‹8Š,&@6 A€0i 6’-‹8Œ,6œ-Œ&’"6ž-œ&@+6-‹8ž,36-ž&D6”-‹8&@,U6–-‹8&@data„UUü,f6—-‹8&@,i$:‡ A`6˜-&@$6Ž-‹8˜,,6Ÿ-˜&Ž:6›-Ÿ&@C6-‹8›,K6-›&\6•-‹8&@,m6™-‹8&@šdata„UUü,~6š-‹8&@,„6Š-Œ‡$D ApN'6-&@6Š-Œ6Œ-˜' A€X*6€-€%@ 68€,-@* A bZ data„UUü 0)6€-P6¡.2), operator, digit, decimal point, variable or (Z Ag6€-€&@l A 0v 0^@Ydata„UUü'€*6€-€%@ 68€,-@* A €Š Ap(”A€”++—"*"@*’"@Ažf7š8data„UUü)!@)Ž!@)™@)•@\6¡.numeric power because base<>1f A¨¬6‹8&@,-@16‹8&@>data„UUü,-@H6‹8&@,-W6‹8,-@n6‹8%@,-@…6‹8%@,-@“6Œ-%@¢6‹8Œ,-@¬ mdata„UUü@%²>6‹8&@,-6”6“-Œ!6Š-Œ'6Œ-˜1 A>(€A¼ 6Œ-“ APÆ” AÐ' 6Œ-˜'”"@Ôdata„UUü*–"@@%Ú= 6š-š'–$”š&P:š,36¡.integer powered result= Aä!!•)–"@APécY6¡.Ointdata„UUüeger power because base is negative or has a negative leading coefficientc Aîz6‹8&@,-š 6ƒ-•#+”'–,* A¶data„UUü;6‹8&@,-ƒG6ƒ-™#+”'–,Q Ab6‹8&@,-ƒz"@*"Ž@%ø6–&@,6¡.integer powered result6 *data„UUüA= 6•-›6Š-Œ A€6•-˜) A€3 A€= @% 6 6¢-Š6‚-•6ƒ-•&‹8•,$ Ap3‹8•,"@6$4™Rdata„UUü-@”6Ž-•6‘-Š#6Š-¢- A 1 ™4$ 7 A`(”6€-46¡.nonzero divisor7$*‡ 6‘-Š6‹8&@,-6—=data„UUü/6‹8&@,-O:”,E6‹8&@,-N:”,$–K6ƒ-œQ6‚-Œ[ Apa6ƒ-g6‚-žq Apw6-}6Œ-‘‡ A€4V 6ƒ-•6‚-œ @@Ëdata„UUü!6•-•'‚)6œ-œ'‚/6ƒ-56‚-™? @@I6•-'‚$•S6™-™'‚$œV$>€ A 6-‹8,"6œ-@56‘-›&‹8›,%@;‘ ›KŽœdata„UUü-‘›&@Q6ƒ-W6‚-–a @@k6œ-–'‚$œ|6-‹8Ž,$œ%'‚$”€ ŽH$R68€,-@ A0\[ Ap-—)Ódata„UUü@)’@Q6¡.numeric term. See topic 6.[ AfQ6ƒ-”#O:š, A6-ƒ)6ƒ-–#O:š,3 A96œ-ƒEš âdata„UUüK6œ-Q6-ƒhd A06-Ÿ6›-˜# A0)6ƒ-/6-œ56œ-ƒ? A D(™Z6¡.nonzero divisord Ak 6‹8&@Ídata„UUü,-•%6‹8&@,-™<6‹8&@,-K6‹8,-@b6‹8%@,-@y6‹8%@,-@‡6Œ-%@–6‹8Œdata„UUü,-@  A0p*6€-€%@ 68€,-@* A €u A @%z- A`*6‹8&@,-6‹8&@,-´data„UUü$„m 6‚-‹8š,ƒ-š&‚š&@,6‚-‚&@:6Š-Š%@L6‹8Š,-+‚%“,$‹8ƒ,P ƒ^6Š-Š%@j6‹8Š,-‹8š,m$Ž‚ A`6ƒ-Odata„UUüœ6‚-Œ6Š-Œ) Ap/6•-Š56š-ŠA6“-K A Q6™-Š_6ƒ-Œ%@e6‚-™o Ap‚6‘-Š&‹8Š,&@‘e A6÷data„UUü‘-• A#6•-‘)6‘-™3 A96™-‘D6Š-™&‹8™,Tƒ-Š™&@a6‹8ƒ,-6‹8ƒ,e ƒ”U 6‘-™6Ž-ž A 6–-Š%6“-—+6š-žldata„UUü96Š-&@C A I6‘-žO6Ž-•U6Š-–˜v A  A6š-‚.6ƒ-‹8&@,8 @0X6‹8&@,-š'‚$‹8&@…data„UUü,v6‹8&@,-‹8&@,'‚~+6‹8&@,-‹8&@,%–&—&@16Ž-Œ76‘-•=6Š-—G A Z6Œ-—&‹8—,&@`6-’data„UUüj A€t A 0~ A0¢6£-£%@¬ £!B:¤,6 .$¶6 .¤7£<£, 4 A 0À$  2 6¤.¤7@,$ 7data„UUüA @Å% /z* 1a%6 .>:@: ,&@2,Ê$Ô A 0 4+A €Þ 4-A€è 4(Aò 1A8data„UUü* /ZA•ü76ž-6“-'6Š-@7 4.A`J 10* /9$6“-“$@%A: ,26ž-£%@< A 0Ldata„UUüJž"£A0R(žH6¡.9+, -, semicolon, digit, decimal point, variable or (R A 0.A$6‘-ðdata„UUü.X6ž-£%@ A 0- 10* /9*ž"£;6Š-@$ŠN6‘-@$‘%A: ,X Ap8- 6ƒ-‘6‚-Š @@!6Š-Š'‚-6“’data„UUü-“$Š%‘'‚B¨6‹8Œ%@,-“%6‹8Œ%@,-Š<6‹8Œ%@,-S6‹8Œ%@,-@j6‹8Œ%@,-@6‹8Œ%@data„UUü,-@6Œ-Œ%@ž6‹8Œ,-@¨ A0G A(€AI A LÆ6ž-@: ,&@d 4X36‹8Œ%@¢data„UUü,-@J6‹8Œ%@,-@a6‹8Œ%@,-@x6‹8Œ%@,-@6‹8Œ%@,-@¦6‹8Œ%@,-@´6Odata„UUüŒ-Œ%@Ã6‹8Œ,-@Æ$VY 6œ-‹8ž,œ#6-œ&‹8œ,&@8ž-&‹8,&@œF6Œ-Œ%@R6‹8Œ,-‹8ž,V žY$`D6€-Àdata„UUüA6¡.+variable to be X or assigned. See topic 3D$j*6€-€%@ 68€,-@* A €t 4/A~"68€½data„UUü,-@" 4*A €ˆ 4(A’ 1A* /ZAœ!! 0.*+ 20) 39,@%¦ A ° Adata„UUü(€Aµ A º A` A@Ä*6€-€%@ 68€,-@* A0Î$  4+68€,-@$ A0data„UUüØ 4@APâ 4%A ì 0-@%ö68€,-@ A0 A A€ A068Ädata„UUü€,-@  A €( 6Š-Œ A (€A2 A<. -@@6! -% + -.$F-  (x Aîdata„UUü"ƒ!-  + ƒPƒ   - 6ƒZ 6ƒ-‚ A (ƒA d"ƒ!  + " An data„UUü - 6ƒ-6ƒxƒ&@ ƒ ‚ iŒ )›&@ ^›–$ 6ˆ*O:, †6ƒ-” 6‚-,6ˆ-ùdata„UUü6 AP¥X6ƒ-”'@6“-ƒ!6‚-ƒ$ƒ&-‚ 76‚-M:6‚,A APG6ƒ-“N6‚-6‚X APª$“ 6“-“&M:‚,$ Azdata„UUüp´6“-“%M:‚,¾1 6ƒ-“6‚- AP'6ƒ-'“1 APÈE 6ˆ-‹8ž,6-ž&ˆ6‚-‹8,%-ž36‹8,-‹8,'‚7 E6-½data„UUü%@ÍO6‹8ž,-5ˆ @)ˆ'@P:ˆ'@,A6ˆ-O6ž-ž&@Ò( "ž6ƒ-‹8,6‚-( APbdata„UUüÜ5%@"ž6”-‹8,+6-‹8%@,5 A@æ)6•-@6œ-@!6”-‰)6-”'œë6¥-ð6“-@6ƒdata„UUü-‹8,&”&6˜-26Ÿ-@B-%@žH6„-˜N6˜-Ÿ\6Ÿ-ƒ&”$˜&$„b6‚-“h6“-ƒy6ƒ-‹8,&”$“&$‚} 6Ž-˜$˜%„$+“&Ÿ,õK'Fdata„UUüO:Ž,!†$+O:“,%O:ƒ,%O:„,%O:Ÿ,%O:˜,,76•-+“$˜&ƒ$„,'ŽK6œ-+ƒ$˜%“$+“&Ÿ,,'Žúi 6”-”%•6-%œWO:œ,%O:•,%O:“,%O:ƒ, †$+@%O:”,%O¡data„UUü:,%O:‹8ž,,%O:‹8ž&@,,,_6¤.Yi A@ü%6¥-¥%@%¥ AA þP ¤46ƒ-”+6”-'+H:@,&?P,Fþdata„UUü6-ƒ'+H:@,&?P,P AT7 .No convergence yet. Continue until ÂÒÅÁË (Y/N);¤C¤4YJ6¤.T A4k ¤4data„UUüN6-&@'6ž-ž%@/6-ž&86‹8ž,-? (K6˜-@W6”-@a A@h )k$ A6U A@6ƒ»data„UUü-” A#6”-ƒ)6ƒ-3 A96-ƒG6ž-ž&@U6‹8,-‹8,&” K-%@ž=6‹8,-‹8,&”$‹8&@,&$‹8&@ data„UUü,A K A1 6-‹8ž,,”@)—*"@1 ”—! X"—!@ ^—,"@$-data„UUü6+6›-@6-ž&+ @A€@q 6ƒ-6‚-ž6Š-Œ Ap+6“-16š-Š; A I6Š-Š&@e6‹8Š,-‹8Š%Ëdata„UUü@,&@q6‚-Eh-š%@Š&@$6ƒ-‹8,. @@2 >‚&@V-š%@Š&@d6‹8,-‹8,'‚xdata„UUüh J* 6‘-š A*‹8Š,"@A€TF 6š-ŒŠ!‘6-Œ%@06Œ-Š&‹8Š,&@: A€@6Š-ŒF6Œ-š^5 6™-Š6Ôdata„UUüƒ-6‚-ž Ap%6‘-Š+6Š-™5 Ahv6ƒ-š%@6‚-‘6Š-‘' Ap-6•-Š@6Š-•&‹8•,&@J AP6‘-™Z AŽdata„UUü`6™-‘f6‘-•p Av6•-‘m"‹8•,!@6ž-•" A€r‹8Š,"@$|N6›-›%@6‘-Š*6Œ-‘&‹8‘,&@mdata„UUü0Œ!™>6-™%@H A€N6‘-Œ† 6Œ-š A@ A`(”A pš_  6”-”$‹8,6–-–$‹8œ,%6ƒ-”+6‚-–5 odata„UUü@@=6”-”'‚E6–-–'‚Q” X -_6”-6”¤0 6ƒ-”'– Aƒ"P:ƒ,$6”-ƒ06–-@®8 AP8–"@*—Ådata„UUü*‹8Œ,"@A!¸4 A@6”-–6—-6— 6ž-Œ* AP4 A!Â4 6-‹8ž,6˜-@ 6-ž&,—!46-%—data„UUüÌ9Ÿ-ž&@!6-&@,6œ-”$‹8Ÿ,9(œAÖœ"@A`àœ"6@A0ê˜Aô"œ!odata„UUü  + " Aþ  - 6œ-6œ œ(A x"@A ^ A&(Aëdata„UUü0(˜  -  A: - AD(˜  + NAX Ab6˜-l  Ÿ $xI6Ðdata„UUü…-D™™™™6‰-?'6‡-C56¦-@'‡=6†-‰$¦I6§-@&y"6¨-I:,'@&A`9@™,‹9¨,¤;A ¾data„UUü, ;@,¡;@€,©;@,o6‹8,-§}Ž-@§Œ6‹8Ž,- Žz  A {=Ž-@£   Ždata„UUü# ý^: ÅÒÒÏÒ, expected ¡= €D Enter a problem, orD $enter another question mark for helpŠI 6Œ-§6£- " Édata„UUüB, A#0¤: A 0I 4A0” 4?A" ž 6ª-£ 0XA€¨I A 0 4=?6¡.#assignee ot¤data„UUüher than X. See topic 3.I A²"6£-ª&@6©." A ¼ 2A) 3ZApÆ: 6©.  A 0 0=)6£-ª&data„UUü@06©.: A Ð? ©4X56¡.#assignee other than X. See topic 3.? AÚ(6€-68€,-@( A î^data„UUü ý 4;A!ø 4?A" 4&A€ l  0b6¡.QÒÅÔÕÒÎ, semicolon, ampersand, operator, digit,pdata„UUü decimal point, variable or (l @& A`  (” ”& A!P#’"@*"@*–@' ”B ----¬data„UUü------------ =”'–F –P A! 5 A05–"@*—*’"@A!** A@6”-–6—-6— 6ž-Œ* A03data„UUü4 >©4A!€H6ž-@:©,&@d6œ-‹8ž,R 6‹8ž,-Œ(œA!p\J6-‹8œ,%@6’-œ&,-œ%@Œ:6’-’%5data„UUü@F6‹8’,-‹8,J f1-@‹8,#‹8,!œ16‹8,-‹8,&p   6Œ-’z 6§-Œ„ A 0 4A0Ž ·data„UUüA@˜l A`K’@)@)—)–@)” @)”!@b6¡.existing topic #l A¢L >:A%data„UUü,L”A"@A"pA#A# A#0A#@A#`¬S& >:A%,The help topics are) S %1: Expressions Èdata„UUü 5: Compound lines¯Q+ #2: Factored display 6: SubstitutionQ !3: Assignments 7: Derivative±@ 4: Non-display @ odata„UUü"Enter a topic number followed by a¶C  question mark. @ !Study topics in order first time!C ¹6, $See ALGICALC manuadata„UUül for more detail.6 A0À\\ >:A%,IAfter each question-mark prompt, enteran expression using digits, decimalÃPP HÙdata„UUüpoints, parentheses and the letter x together with operators +, -, /, *ÆQQ Iand ^. The latter means raising to a power. *,Kdata„UUü meaning multiply, can beÊ= omitted. = %An equivalent expression is displayedÌ** "expanded and reduced over a common×data„UUüÎOO Gdenominator, provided the input and each of its subexpressions can beÔP% represented as a ratio of twoM #polynomdata„UUüials in x. For example, typeP ÖM& 1 + (x^2 - 1) / (x^2 + 2x + 1); 1.5*10^2/(x+1)^6C 4/6M A#€Þ22 >:A%,E“data„UUünd an input expression with anàNN Fampersand (&) to display an equivalentfactored expression in which theâRR Jletter i repÈdata„UUüresents the square root of-1. (To remember '&', think of it asèY- %suggesting a 'plurality' of factors).0 Y $Although expa,data„UUünsion is limited by theêNN Ffinite accuracy and magnitude of BASICarithmetic, factoring is furtherìTT Llimited by its iterªdata„UUüative search. Thus,factoring is slower, less accurate andò+(  more likely to cause 'overflow'.+ ô\! As factoring exampleùdata„UUüs try$ ; x^3 - x^2 + x - 1&R 1 / (x^5 + x + 1)&\ A#€üI' >:A%,An entry of the form* F  variable = expr^data„UUüessionI ÿP) !causes the resulting value of theP "expression to be 'assigned' to the :& variable for use in subsequent¬data„UUü7  expressions.:  S) !x cannot be assigned a value, andS %every other variable must be assigned ^' a value before bei‡data„UUüng used in an7  expression.: ^ As an example, try the sequence <  r = (x^3-1)/(x^2-1)2 r*x + r^2 + 1/r< A#€Õdata„UUü ^P HFollow an assignment with a semicolon to suppress display of an assigned[ value.^  C For example, enter -  îdata„UUü p = x + 1;0 9  p^3C A#€ S* "Several assignments can precede anS $assignment or expression in a single Z' entr data„UUüy, separated by semicolons.* ? For example, tryB Z p=x+1; q=p^2; p+q+x A#€$ \\ >:A%,ITo substitute a nudata„UUümeric value for x inan expression, enter the expression' U. &then the numeric value, separated by @1 U This 'at' operator data„UUühas the same* .. &'precedence' as addition & subtraction. @  For example, try /  p = (x+1)^22 =  p @ 1@ 1 & Ëdata„UUü p @ 2   p@1/2& A#€8 Q2 >:A%,This topic is for those who areN familiar with calculus.Q ; R+ #To diff–data„UUüerentiate an expression withR "respect to x, enter the expression> O(  followed by %, which is named toO "suggest a ratio *data„UUüof infinitesimals.B L 1 &% has the same precedence as addition.4 I As examples, tryL E A  x^2/(x+1) % '  x^2/(x+Udata„UUü1) %&* A 9 + (x^5 + x^3 %%)L W . #After trying several such examples,W $enter a question mark to display theN " he data„UUúlp topic menu." A0V %6¡.easier problem'% A€4examples,W $enter a question mark to display theN " hDudata„UUþ©