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" #"} ^ _~A(~ x=3)~p0 2 ~sb/_! } !& c#T"!c"\"_c/__c/__} ^ _~A(x=(~ -b-sqrt(b^2-4*a*c))/(2*a))~p0 0 ~A(x=(-(-4)-sqrt((-4)^2-4*1*3))/(2*1))~p0 1 ~sb/_! } b00* c#T"_c/__c/__! " #"} ^ _~A(~ x=1)~p0 2 ~sb/_! } !& c#T"!c"\"_c/__c/__} ^ _~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4[(! ) # b'4| |}& b!( b"0 b#8 b$@ b%H b&P!WW}) # b'4}& b!( b"0 b#8 b$@ b%H b&P!WW}| |) # b'4}& b!( b"0 b#8 b$@ b%H b&P!WW}) # b'4| |}& b!( b"0 b#8 b$@ b%H b&P!WW}) # b'4}& b!( b"0 b#8 b$@ b%H b&P!WW}| |) # b'4}& b!( b"0 b#8 b$@ b%H b&P!WW}) # b'4| |}& b!( b"0 b#8 b$@ b%H b&P!WW}) # b'4}& b!( b"0 b#8 b$@ b%H b&P!WW}}| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p3 0 ~Q ]|Expr|[#b @`bb#_b#_b#_}) # b'4}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p3 1 ~V?c3 ('N)~p0 2 ~V?f277 (arcsec)~p0 2 ~V?f276 (arccsc)~p0 2 ~V?f278 (arccot)~p0 2 ~V?f310 (arccoth)~p0 2 ~V?f308 (arccsch)~p0 2 ~V?f309 (arcsech)~p0 2 ~V?f306 (arctanh)~p0 2 ~V?f305 (arccosh)~p0 2 ~V?f304 (arcsinh)~p0 2 ~V?f292 (csch)~p0 2 ~V?f294 (coth)~p0 2 ~V?f293 (sech)~p0 2 ~V?f290 (tanh)~p0 2 ~V?f289 (cosh)~p0 2 ~V?f288 (sinh)~p0 2 ~V?v0 (outputMAX)~p0 2 ~V?v0 (inputMAX)~p0 2 ~V?v0 (outputMIN)~p0 2 ~V?v0 (inputMIN)~p0 2 ~V?f0 (g)~p0 2 ~V?f0 (f)~p0 2 ~V?v0 (yMax)~p0 2 ~V?v0 (yMin)~p0 2 ~V?v0 (xMax)~p0 2 ~V?v0 (xMin)~p0 2 ~Hs((tan(x))/(sin(x))):(1/(cos(x)))~p0 2 ~Hs((cot(x))/(cos(x))):(1/(sin(x)))~p0 2 ~Hs((sin(x))/(tan(x))):(cos(x))~p0 2 ~Hs((cos(x))/(cot(x))):(sin(x))~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b$L" SGSB^: ;bP8&c0!*Trigonometry| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~V?c1 ('p)~p0 3 ~V?f256 (sin)~p0 3 ~V?f257 (cos)~p0 3 ~V?f258 (tan)~p0 3 ~V?f261 (sec)~p0 3 ~V?f260 (csc)~p0 3 ~V?f262 (cot)~p0 3 ~V?f272 (arcsin)~p0 3 ~V?f273 (arccos)~p0 3 ~V?f274 (arctan)~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b$L" SGSB^: ;bP8&c0!*Logarithms ,F| | Powers}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~V?f32 (log)~p0 3 ~V?f307 (ln)~p0 3 ~V?f291 (exp)~p0 3 ~V?c2 (e)~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b$L" SGSB^: ;bP8&c0!*Standard Rules| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b$L" *|: ;bP8&c0!*Logarithms ,F Powers| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Ht(?x^(-?y)):(1/?x^?y)~p0 4 ~Hs(exp(?z)):(e^?z)~p0 4 ~Hs(e^(ln(?x))):(?x)~p0 4 ~Hs(10^(log(?x))):(?x)~p0 4 ~Hs(?y^(log_?y(?x))):(?x)~p0 4 ~Hs(ln(e^?x)):(?x)~p0 4 ~Hs(log(10^?x)):(?x)~p0 4 ~Hs(log_?y(?y^?x)):(?x)~p0 4 ~He(ln(?u*?v)):(ln(?u)+ln(?v))~p0 4 ~He(log(?u*?v)):(log(?u)+log(?v))~p0 4 ~He(log_?y(?u*?v)):(log_?y(?u)+log_?y(?v))~p0 4 ~He(ln(?u/?v)):(ln(?u)-ln(?v))~p0 4 ~He(log(?u/?v)):(log(?u)-log(?v))~p0 4 ~He(log_?y(?u/?v)):(log_?y(?u)-log_?y(?v))~p0 4 ~He(ln(?u^?v)):(?v*ln(?u))~p0 4 ~He(log(?u^?v)):(?v*log(?u))~p0 4 ~He(log_?y(?u^?v)):(?v*log_?y(?u))~p0 4 ~He(ln(sqrt(?u))):(1/2*ln(?u))~p0 4 ~He(log(sqrt(?u))):(1/2*log(?u))~p0 4 ~He(log_?y(sqrt(?u))):(1/2*log_?y(?u))~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b$L" *|: ;bP8&c0!*Trigonometry| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})+# b$L" *|: ;bP8&c0!*Simplify ,M negation| | and common zeros}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~Hs(sin(-?x)):(-sin(?x))~p0 5 ~Hs(cos(-?x)):(cos(?x))~p0 5 ~Hs(tan(-?x)):(-tan(?x))~p0 5 ~Hs(sin('p)):(0)~p0 5 ~Hs(sin(?n*'p)):(0)~p0 5 ~Hs(cos(1/2*'p)):(0)~p0 5 ~Hs(cos(?n/2*'p)):(0)~p0 5 ~Q ]|Expr|[#b @`bb#_b#_b#_})'# b$L" *|: ;bP8&c0!*Transform to basic| | types}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~Ht(tan(?x)):((sin(?x))/(cos(?x)))~p0 5 ~Ht(csc(?x)):(1/(sin(?x)))~p0 5 ~Ht(sin(?x)):(1/(csc(?x)))~p0 5 ~Ht(sec(?x)):(1/(cos(?x)))~p0 5 ~Ht(cos(?x)):(1/(sec(?x)))~p0 5 ~Ht(cot(?x)):((cos(?x))/(sin(?x)))~p0 5 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b$L" *|: ;bP8&c0!*Trig Addition| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~Ht(cos(?x+?y)):(cos(?x)*cos(?y)-sin(?x)*sin(?y))~p0 5 ~Ht(sin(?x+?y)):(cos(?x)*sin(?y)+sin(?x)*cos(?y))~p0 5 ~Ht(cos(2*?x)):(2*(cos(?x))^2-1)~p0 5 ~Ht(sin(2*?x)):(2*cos(?x)*sin(?x))~p0 5 ~Ht(sin(?n*?x)):(cos((?n-1)*?x)*sin(?x)+cos(?x)*~ sin((?n-1)*?x))~p0 5 ~Ht(cos(?n*?x)):(cos(?x)*cos((?n-1)*?x)-sin(?x)*~ sin((?n-1)*?x))~p0 5 ~Q ]|Expr|[#b @`bb#_b#_b#_})/# b$L" *|: ;bP8&c0!*Transform ,M into| | another flavor of trig function}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~Ht((sin(?x))^2):(1-(cos(?x))^2)~p0 5 ~Ht((cos(?x))^2):(1-(sin(?x))^2)~p0 5 ~Ht((tan(?x))^2):((sec(?x))^2-1)~p0 5 ~Ht((sec(?x))^2):((tan(?x))^2+1)~p0 5 ~Ht((csc(?x))^2):((cot(?x))^2+1)~p0 5 ~Ht((cot(?x))^2):((csc(?x))^2-1)~p0 5 ~Hs((sin(?x))^2+(cos(?x))^2):(1)~p0 5 ~Q ]|Expr|[#b @`bb#_b#_b#_})b @# b%4" SGSB^: ;bP8&c0!*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$@ b%H b&P!WW}]|[~p1 4 ~Hs(cos(2*arctan(?z))):((1-?z^2)/(1+?z^2))~p0 5 ~Hs(sin(2*arctan(?z))):(2*?z/(1+?z^2))~p0 5 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b$L" *|: ;bP8&c0!*Other rules| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 4 ~Ht((cos(?x))^2):(1/2*(cos(2*?x)+1))~p0 5 ~Ht((sin(?x))^2):(1/2*(-cos(2*?x)+1))~p0 5 ~Ht(cos(?x)*sin(?x)):(1/2*sin(2*?x))~p0 5 ~Hs(sin(arccos(?x))):(sqrt(-?x^2+1))~p0 5 ~Hs(cos(arcsin(?x))):(sqrt(-?x^2+1))~p0 5 ~V?c4 (i)~p0 2 ~V?d16 (d)~p0 2 ~V?v0 (k)~p0 2 ~V?c0 (n)~p0 2 ~V?c0 (c)~p0 2 ~V?c0 (b)~p0 2 ~V?c0 (a)~p0 2 ~V?v0 (z)~p0 2 ~V?v0 (y)~p0 2 ~V?v0 (x)~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_}) # b'4}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p3 1 ~A(a*x^2+b*x+c=0)~p0 2 ~A(1*x^2+(-4)*x+3=0)~p0 3 ~sb/_! } b00* c#T"_c/__c/__! " #"} ^ _~A(~ (x-4)*(2*1/(x-4)+x)=0)~p0 2 ~A(3*x^2-5*x+1=0)~p0 2 ~G1 1 183 242 0 1 3 4 10 (xMin...xMax):(yMin...~ yMax):(?=0...2*'p):('p/5):(10)~Q ]|Expr|[#b @`bb#_b#_b#_})!# b"@" *|: ;bP8&c0!*Declarations| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 0 ~R11184810 ? (x,y):(y=bottom...top):(x=left...~ right):(0)~p0 1 ~gc1 2 ? 0 -32768 -4096 0 65535 -2731 4096 0 ~gc1 2 ? 0 -32768 -4096 0 65535 0 4096 0 ~gc1 2 ? 0 -32768 -4096 0 65535 2731 4096 0 ~ ~R11184810 ? (x,y):(x=left...right):(y=bottom...~ top):(0)~p0 1 ~gc1 2 ? 0 -32768 -2048 0 65535 4096 -2048 0 ~gc1 2 ? 0 -32768 0 0 65535 4096 0 0 ~gc1 2 ? 0 -32768 2048 0 65535 4096 2048 0 ~ ~X2 11184810 ((Conditional(0,(left<0)*(right>0);~ left,(right<1000000000))),y):(y=bottom-(top-bottom)/~ 100...top+(top-bottom)/100):(y)~p0 1 ~gc0 2 ? 0 -32768 -4178 0 65535 0 4178 0 ~X1 11184810 (~ x,(Conditional(0,(bottom<0)*(top>0);bottom,(top<~ 1000000000)))):(x=left-(right-left)/100...right+~ (right-left)/100):(x)~p0 1 ~gc0 2 ? 0 -32768 0 0 65535 4178 0 0 ~V?c64 (left)~p0 1 ~V?c65 (right)~p0 1 ~V?c66 (bottom)~p0 1 ~V?c67 (top)~p0 1 ~Q ]|Expr|[#b @`bb#_b#_b#_}) # b'4}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 0 ~L1 0 ? (?,?):(x=left...right)~p0 1 ~gc0 2 ? 0 -32768 -32768 0 65535 -32768 -32768 0 ~ ~S4 ? 255 ? ? (?,?):(?):(4)~p0 1 ~gc-1 1 ? 0 -32768 -32768 0 ~t~p0 2 ~A(xMin=-3)~p0 2 ~d~A(xMax=3)~p0 255 ~d~A(yMin=-4)~p0 2 ~d~A(yMax=4)~p0 255 ~d~A(f(x)=x)~p0 2 ~A(g(x)=x)~p0 2 ~c1 13 -1 143 -1 ~c4 16 -1 15 -1 3 -1 6 -1 9 -1 ~c1 17 -1 16 -1 ~c4 19 -1 18 -1 9 -1 6 -1 3 -1 ~c1 20 -1 19 -1 ~c4 143 -1 142 -1 9 -1 6 -1 3 -1 ~e