~v353 200 yz#gVWi]bWbTbWk\hDamjD]] yzwx$NeS^TcUdVmOPVWYTRMUPT_UhVQWfXc ~w294 56 258 551 0 0 0 0 ~f? 14 12 10 ? 3 1 1 0 ? ? ? "Times" ? ? ? 0 ? 1 1 "Times" 12 ? ? 5 0 c n 1 1 0 0 k 468 m"?n page ?p?a" ? 1 26177 26178 26115 26178 1 1 1 1 0 0 8405120 0 -1 1 0 -1 -1 -1 -1 -1 1 1 0 0 2 0 0 ? ? ? ? ? ? ? ? ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4`fb#_}" *~: ;bP8&c55*`g| |pc! Bc SF| |%-@Ni!!!!.!6>-P!riZ/s8H+3!([(i!([(i!!!!!!"AqL%%1Z$!20C'!"QJ_| |E,kpY!!!!!!!!!!!$2+@!"&]+!!!!.!6>//!!!$!K-1-o!!!!.!6>-?!!E9%| |!!!!i!!!!i!!!!1!$D7D!!iQ)!!!Fa[o`V1!!!!!!!!!.!6>-?!!!!.!6>-?| |!"+8WJH16$JH2YL!#4Joir=Q0fDsq2JH4=&ir=Q0o`+um"98H#rI4_G$pX^h| |:]:6@!!)urNdgp)'>=GHs#g>^YQ$0S!5JQ[!!$@*4o>9cIQ[Zos*aqJs+(1A| |!!**$qu?j#!<<-$rW)ou!!)ls&c_q34TGJcs"+3N^]2U[!+,[gqu@"O4TIYF| |IK0BJJH59A!dcs3CZF?N31d| |!!n$:!'U@2!!*%M!;-s*k$`rrBh4rtnT4Ipi:a| |J,`=F!.Y#u!5JO6&:a0KY7Ntsrr@QIrrIV!rr3_j:]Nbqs5.2a&:a0KY7L^6| |rrCCF@/^-3^]-P!!'pS!J,K5QCdLs1a']rr@QIrr>=N!!1UQ!!)urIf9APO.ZFp!!%NKs"M4f!0@/`O8ls;| |J%u#uIpi<&5X6HAs.<-f^EE"6J'\-[O8lDEs1\R6s.B=!r;[MGs$-Pa5l\Sa| |J)C9uIt.Kj5X5nG!!**$qu@0,!<<*#!<<*#!<<*#!W)j#s#g>^4g4hb!l+ae| |rW!JDcbD%3?GGA\!%krl!!*&b!(_V>s"M4f!5JPQ5X6IlT9'#5TDp#6!.Y%K| |0YdVfO8lDEs1]\+^]2&u@/nP<5TkRVT2>R&+RecKci67ks0%L`^B"<6TDr>!,hi:4TKs2s#p5Z!<;?b'7^&^cbKJ[^]0pU| |5QK]V^]2'`hu3U,J,fPp^]+<&rt#1Vru_;ks*k#6s5/]!,hc9%_qH4!%e1gs8P4^IfKF2qZ$WrlMqTJs8UE[| |rrBh6T79*+hnQr+^VA\*!%`X"s3JI[!:Tq!!71Zf!.Y#u!'pSAIt%HJs1aW`| |:iQGq!)W]fn,Eq!ci5-errCsS!#!'H5QCdLs1\O6^]-P!J,d95@-IXl!>!,hi:4TKs2s#p5Z!<;?b| |'7^&^cbKJ[^]0pU5QK]V^]2'`hu3U,J,fPp^]+<&rt#1Vru_;ks*k#6s5/h>IfKF2!'U@2!!*&b!#'k^5d14f!5JPQ5X5lgs8P@as'Yg+| |14TQk+RecKci67ks0%L`^B"<6| |+Rf=QrW!VHs):4W5l\S!!5JP!!.Y$@5X6IW!!**$qu?`u!WE)t!WE'"!!.OtJ4TIYFIK0BJlMqTJs$3dfrrBh6E'QZ"| |@/p6ls8QL+!&B'(5d14f!0@/`O8lrp!.Y#u!'pS15X7#Qs.<-fY9<<&J'\-[| |O8lDEs1\R6ruge1+T;?S^]/7<0L5ZQ!!'e65QH<6T0PXal2Uhc!W2ou!OQd5VPJ'^An8Ks$-R6s.;PA+RB(/| |^B=N:rVbRO^'-b"rBC8nrr!"\!!%KHrVaG=!!*$^!,_c:IK0A_%K$29NrM6B| |IfKF2!'U@2!!*&b!!e#R5S3Da!5JL4#='F3mf;hV+T;?SJ,_bFn,EA!J+*E0| |&-)][s*k#6rVlo5J,]H_h_5$q^]31f!"aYKs.9i&s8N(Ks1eO5!5JO5$GSk+| |^An8Ks$-R6rVlkIl2^\^!WW6%rW)ltrW)fr$ig;-4TK@"!.FnJ^CC)@%Z^QP| |!.OtJ4TIYFIK0BJlMq0>s$..arrBh4rs(e3s6fsVruh:@'7^$I&F]W!&:a0K| |T+Cu&J,auu5lL]`^OQ7_(#L\F5em?V:]M&Vn,K!k!<<'!J,d:_!!'e5rsHM+| |s1\O6^]-P!J,TBIJ*I%2!?| |5l\S!!5JP!!.XtI!.X>8!2BPp!;l^'5Q1OF!!'2#r@e3OIf''d!!*$^!.HL"| |^An7O!!(pV9`R?V4TKs2s#g?Fs*aqJs+(1A!;ccu!!*-"!<*#t!;cd>!!*$^| |!.HL"^An7O!!(pV9`R?V4TKs2s#g?Fs*aqJs+(1A!;ccu!!*-"!<*#t!;cd>| |!!*$^!.HL"^An7O!!(pV9`R?V4TKs2s#g?Fs*aqJs+(1C!!!_o!94$0!8%;2| |s+(1&!94$0!;-rb=5u`*!m9!)#lS]:q(#9)Q"Tn/pL?/LS4RXUEOt!R)bRJ6bi;n4AZ#jMgM\qEP>IOSnl4| |S/D[,7>it;3"rK[nk@7-?l8'qG)L:YRpirIL8RTIQ#PBS`T"R>GZA(Ha6LaB| |Pl6%Qo1>*9.6F(1(:,QU;JnB3/<31E]s31PGpr%Rqbg&4o+^f*0>GK8j-L9\| |#_3Th!%c"fJ3bL]>s$uW9%u]A=dB@;MP@$U0pNoOM#gU<0)&41d%hs^;;as9Oa+dQ]]++YI*U+Rn<&r3\B$Ydei| |F<'Hd3<3G?!8)*G3)?qUlu#rA(3([(QIR>/S)C$| |/Bb=9@uR\KDML?\faJ*(O2h53a)RQF8Wqlbh/0W*]Q-:LfX;eh&a+O$*7i37| |YHQK*R\o>\DB-\=/j.JO+:&t-Tp3Q:XS+Q4j4.np>iQW>RUT9b!Pm&9F:$s/| |npiYsk)Je):J\Z1:R4_cm@Lc| |p[[l1cZ@AlkF>G-EmliG!/3p6csXAd.tg0!!e;s5!<f$$$NO'R!T4Ff.R0ll7S6?K"0/)94Zl5/&ji6YI!Kutiot3oq_o]ne+J#m| |'g563KTICmY:h]c,u>iWBILcG29],Am,^OhY7?Ol(HDFmUkA/Ie=dGuhHLQqi| |n0#7KhN:4>MJ=ZaZ:kGjH7bT0k'Q+N2]8:YfANd)=9.h\tSpsJ>>+?Q!&(24F>-qu55KD[Hn!=BN*oU`3!!!!j| |78?7R6=>EF| |9}| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 0 ~V?f169 (SolveNewton)~p0 1 ~V?v0 (NewtonVar)~p0 1 ~V?v0 (NewtonSeed)~p0 1 ~V?v0 ('l)~p0 1 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b$L" *~: ;bP7&c55*Trigonometry| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~V?f276 (arccsc)~p0 2 ~V?f278 (arccot)~p0 2 ~V?f256 (sin)~p0 2 ~V?f257 (cos)~p0 2 ~V?f258 (tan)~p0 2 ~V?f261 (sec)~p0 2 ~V?f260 (csc)~p0 2 ~V?f262 (cot)~p0 2 ~V?f272 (arcsin)~p0 2 ~V?f273 (arccos)~p0 2 ~V?f274 (arctan)~p0 2 ~V?f277 (arcsec)~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b$L" *~: ;bP7&c55*Hyperbolic| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~V?f309 (arcsech)~p0 2 ~V?f304 (arcsinh)~p0 2 ~V?f294 (coth)~p0 2 ~V?f310 (arccoth)~p0 2 ~V?f306 (arctanh)~p0 2 ~V?f293 (sech)~p0 2 ~V?f288 (sinh)~p0 2 ~V?f289 (cosh)~p0 2 ~V?f290 (tanh)~p0 2 ~V?f305 (arccosh)~p0 2 ~V?f308 (arccsch)~p0 2 ~V?f292 (csch)~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b$L" *~: ;bP7&c55*Logarithms ,F Powers| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~V?f32 (log)~p0 2 ~V?f307 (ln)~p0 2 ~V?f291 (exp)~p0 2 ~V?c2 (e)~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b$L" *~: ;bP7&c55*Standard Rules| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b$L" *~: ;bP7&c55*Logarithms ,F Powers| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Ht(?x^(-?y)):(1/?x^?y)~p0 3 ~Hs(exp(?z)):(e^?z)~p0 3 ~Hs(e^(ln(?x))):(?x)~p0 3 ~Hs(10^(log(?x))):(?x)~p0 3 ~Hs(?y^(log_?y(?x))):(?x)~p0 3 ~Hs(ln(e^?x)):(?x)~p0 3 ~Hs(log(10^?x)):(?x)~p0 3 ~Hs(log_?y(?y^?x)):(?x)~p0 3 ~He(ln(?u*?v)):(ln(?u)+ln(?v))~p0 3 ~He(log(?u*?v)):(log(?u)+log(?v))~p0 3 ~He(log_?y(?u*?v)):(log_?y(?u)+log_?y(?v))~p0 3 ~He(ln(?u/?v)):(ln(?u)-ln(?v))~p0 3 ~He(log(?u/?v)):(log(?u)-log(?v))~p0 3 ~He(log_?y(?u/?v)):(log_?y(?u)-log_?y(?v))~p0 3 ~He(ln(?u^?v)):(?v*ln(?u))~p0 3 ~He(log(?u^?v)):(?v*log(?u))~p0 3 ~He(log_?y(?u^?v)):(?v*log_?y(?u))~p0 3 ~He(ln(sqrt(?u))):(1/2*ln(?u))~p0 3 ~He(log(sqrt(?u))):(1/2*log(?u))~p0 3 ~He(log_?y(sqrt(?u))):(1/2*log_?y(?u))~p0 3 ~He(?z^(?x+?y)):(?z^?x*?z^?y)~p0 3 ~He(?z^(?x-?y)):(?z^?x*?z^(-?y))~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b$L" *~: ;bP7&c55*Trigonometry| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})+# b$L" *~: ;bP7&c55*Simplify ,M negation| | and common zeros}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Hs(sin(-?x)):(-sin(?x))~p0 4 ~Hs(cos(-?x)):(cos(?x))~p0 4 ~Hs(tan(-?x)):(-tan(?x))~p0 4 ~Hs(sin('p)):(0)~p0 4 ~Hs(sin(?n*'p)):(0)~p0 4 ~Hs(cos(1/2*'p)):(0)~p0 4 ~Hs(cos(?n/2*'p)):(0)~p0 4 ~Hs(-(cos(?x))^2-(sin(?x))^2):(-1)~p0 4 ~Hs(cos('p/2)):(0)~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})'# b$L" *~: ;bP7&c55*Transform to basic| | types}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Ht(tan(?x)):((sin(?x))/(cos(?x)))~p0 4 ~Ht(csc(?x)):(1/(sin(?x)))~p0 4 ~Ht(sin(?x)):(1/(csc(?x)))~p0 4 ~Ht(sec(?x)):(1/(cos(?x)))~p0 4 ~Ht(cos(?x)):(1/(sec(?x)))~p0 4 ~Ht(cot(?x)):((cos(?x))/(sin(?x)))~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b$L" *~: ;bP7&c55*Trig Addition| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Ht(cos(?x+?y)):(cos(?x)*cos(?y)-sin(?x)*sin(?y))~p0 4 ~Ht(sin(?x+?y)):(cos(?x)*sin(?y)+sin(?x)*cos(?y))~p0 4 ~Ht(cos(2*?x)):(2*(cos(?x))^2-1)~p0 4 ~Ht(sin(2*?x)):(2*cos(?x)*sin(?x))~p0 4 ~Ht(sin(?n*?x)):(cos((?n-1)*?x)*sin(?x)+cos(?x)*~ sin((?n-1)*?x))~p0 4 ~Ht(cos(?n*?x)):(cos(?x)*cos((?n-1)*?x)-sin(?x)*~ sin((?n-1)*?x))~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})/# b$L" *~: ;bP7&c55*Transform ,M into| | another flavor of trig function}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Ht((sin(?x))^2):(1-(cos(?x))^2)~p0 4 ~Ht((cos(?x))^2):(1-(sin(?x))^2)~p0 4 ~Ht((tan(?x))^2):((sec(?x))^2-1)~p0 4 ~Ht((sec(?x))^2):((tan(?x))^2+1)~p0 4 ~Ht((csc(?x))^2):((cot(?x))^2+1)~p0 4 ~Ht((cot(?x))^2):((csc(?x))^2-1)~p0 4 ~Hs((sin(?x))^2+(cos(?x))^2):(1)~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})b @# b%4" *~: ;bP7&c55*substituting | |z,]tan,Hx,O2,I into a rational function in sin,Hx,I and cos,H| |x,I}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Hs(cos(2*arctan(?z))):((1-?z^2)/(1+?z^2))~p0 4 ~Hs(sin(2*arctan(?z))):(2*?z/(1+?z^2))~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b$L" *~: ;bP7&c55*Other rules| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Ht((cos(?x))^2):(1/2*(cos(2*?x)+1))~p0 4 ~Ht((sin(?x))^2):(1/2*(-cos(2*?x)+1))~p0 4 ~Ht(cos(?x)*sin(?x)):(1/2*sin(2*?x))~p0 4 ~Hs(sin(arccos(?x))):(sqrt(-?x^2+1))~p0 4 ~Hs(cos(arcsin(?x))):(sqrt(-?x^2+1))~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b!T" *~: ;bP7&c55*Hyperbolic| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})+# b$L" *~: ;bP7&c55*Simplify ,M negation| | and common zeros}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Hs(sinh(-?x)):(-sinh(?x))~p0 4 ~Hs(cosh(-?x)):(cosh(?x))~p0 4 ~Hs(tanh(-?x)):(-tanh(?x))~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})'# b$L" *~: ;bP7&c55*Transform into | |other types}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Ht((sinh(?x))^2):((cosh(?x))^2-1)~p0 4 ~Ht((cosh(?x))^2):(1+(sinh(?x))^2)~p0 4 ~Ht((tanh(?x))^2):(1-(sech(?x))^2)~p0 4 ~Ht(sinh(?x)):((e^?x-e^(-?x))/2)~p0 4 ~Ht(cosh(?x)):((e^?x+e^(-?x))/2)~p0 4 ~Ht(tanh(?x)):((e^?x-e^(-?x))/(e^?x+e^(-?x)))~p0 4 ~Ht(tanh(?x)):((sinh(?x))/(cosh(?x)))~p0 4 ~Hs((cosh(?x))^2-(sinh(?x))^2):(1)~p0 4 ~Hs(-(cosh(?x))^2+(sinh(?x))^2):(-1)~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b$L" *~: ;bP7&c55*Other hyperbolic| | rules}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Ht((cosh(?x))^2):(1/2*(cosh(2*?x)+1))~p0 4 ~Ht((sinh(?x))^2):(1/2*(cosh(2*?x)-1))~p0 4 ~Ht(sinh(2*?x)):(2*cosh(?x)*sinh(?x))~p0 4 ~Ht(cosh(2*?x)):(2*(cosh(?x))^2-1)~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4" *~: ;bP7&c55*Constants| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~V?c0 (C)~p0 2 ~V?c5 ('o)~p0 2 ~V?c1 ('p)~p0 2 ~V?c0 (c)~p0 2 ~V?c0 (b)~p0 2 ~V?c0 (a)~p0 2 ~V?c4 (i)~p0 2 ~V?c3 ('N)~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4" *~: ;bP7&c55*Variables| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~V?v0 (n)~p0 2 ~V?v0 (h)~p0 2 ~V?v0 (v)~p0 2 ~V?v0 (u)~p0 2 ~V?v0 (w)~p0 2 ~V?v0 ('f)~p0 2 ~V?v0 ('r)~p0 2 ~V?v0 ('q)~p0 2 ~V?v0 (r)~p0 2 ~V?v0 (t)~p0 2 ~V?v0 (z)~p0 2 ~V?v0 (y)~p0 2 ~V?v0 (x)~p0 2 ~V?v0 (k)~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4" *~: ;bP7&c55*Functions| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~V?f162 (max)~p0 2 ~V?f161 (min)~p0 2 ~V?f132 (FromSpherical)~p0 2 ~V?f130 (FromCylindrical)~p0 2 ~V?f128 (FromPolar)~p0 2 ~V?f144 (RowsOf)~p0 2 ~V?f146 (ColsOf)~p0 2 ~V?d16 (d)~p0 1 ~Q ]|Expr|[#b @`bb#_b#_b#_}`fb#C})!# b'4`f }[#! `fb#C}) # b'4| |}& b!( b"0 b#8 b$@ b%H b&P!WW})+# b'4`f#}" *~: ;bP9&c55)Toisen| | asteen polynomin juuret ,H2,I}& b!( b"0 b#8 b$@ b%H b&P!WW}`fb#C}) # b'4| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})+# b'4" *~: ;bP8&c55*Muuta polynomin| | kertoimet ,Hja merkit,I}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~A(21*x^2-24*x-5789=0)~p0 0 ~T~A(x=1/42*(sqrt(486852)+24))~p0 0 ~sb/_!!! } )=!! c#T" c"L# c"H"!c%X" c'8 _c/__c/__"c#T" c"L#!c"T! c"H"!c'8 _c/__c/__ " !} ^ _~ ~A(x=1/21*sqrt(121713)+4/7)~p0 1 ~sb/_!!! } "$!! c#T"_c/__c/__} ^ _~A(x=17.184471558157753)~p0 2 ~sb/_!!! } $&!! c#T"!c"L"_c/__c/__} ^ _~t~p0 1 ~T~A(x=1/42*(-sqrt(486852)+24))~p0 0 ~sb/_!!! } )=!! c#T" c"L# c"H"!c%X" c'8 _c/__c/__"c#T" c"L#!c"T! c"H"!c'8 _c/__c/__!" !} ^ _~ ~A(x=-1/21*sqrt(121713)+4/7)~p0 1 ~sb/_!!! } "$!! c#T"_c/__c/__} ^ _~A(x=-16.041614415300607)~p0 2 ~sb/_!!! } $&!! c#T"!c"L"_c/__c/__} ^ _~t~p0 255 ~c1 0 158 -1 157 -1 ~c1 1 158 -1 0 158 -1 ~c1 2 158 -1 1 158 -1 ~c1 0 159 -1 157 -1 ~c1 1 159 -1 0 159 -1 ~c1 2 159 -1 1 159 -1 ~e