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(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$L" *|: ;bP7&c0!*Logarithms ,F Powers| |}& b!( b"0 b#8 b$@ 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$L" *|: ;bP7&c0!*Standard Rules| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b$L" *|: ;bP7&c0!*Logarithms ,F Powers| |}& b!( b"0 b#8 b$@ 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$L" *|: ;bP7&c0!*Trigonometry| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})+# b$L" *|: ;bP7&c0!*Simplify ,M negation| | and common zeros}& b!( b"0 b#8 b$@ 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$L" *|: ;bP7&c0!*Transform to basic| | types}& b!( b"0 b#8 b$@ 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$L" *|: ;bP7&c0!*Trig Addition| |}& b!( b"0 b#8 b$@ 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$L" *|: ;bP7&c0!*Transform ,M into| | another flavor of trig function}& b!( b"0 b#8 b$@ 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&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$@ b%H b&P!WW}]|[~p1 3 ~Hs(cos(2*arctan(?z))):((1-?z^2)/(1+?z^2))~p0 4 ~Hs(sin(2*arctan(?z))):(2*?z/(1+?z^2))~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b$L" *|: ;bP7&c0!*Other rules| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 3 ~Ht((cos(?x))^2):(1/2*(cos(2*?x)+1))~p0 4 ~Ht((sin(?x))^2):(1/2*(-cos(2*?x)+1))~p0 4 ~Ht(cos(?x)*sin(?x)):(1/2*sin(2*?x))~p0 4 ~Hs(sin(arccos(?x))):(sqrt(-?x^2+1))~p0 4 ~Hs(cos(arcsin(?x))):(sqrt(-?x^2+1))~p0 4 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b!T" *|: ;bP7&c0!*Hyperbolic| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})+# b$L" *|: ;bP7&c0!*Simplify ,M negation| | and common zeros}& b!( b"0 b#8 b$@ 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$L" *|: ;bP7&c0!*Transform into | |other types}& b!( b"0 b#8 b$@ 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$L" *|: ;bP7&c0!*Other hyperbolic| | rules}& b!( b"0 b#8 b$@ 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&c0!*Constants| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~V?c6 (C)~p0 2 ~V?c5 ('o)~p0 2 ~V?c1 ('p)~p0 2 ~V?c0 (c)~p0 2 ~V?c0 (b)~p0 2 ~V?c0 (a)~p0 2 ~V?c4 (i)~p0 2 ~V?c3 ('N)~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4" *|: ;bP7&c0!*Variables| |}& b!( b"0 b#8 b$@ 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&c0!*Functions| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~V?f162 (max)~p0 2 ~V?f161 (min)~p0 2 ~V?f132 (FromSpherical)~p0 2 ~V?f130 (FromCylindrical)~p0 2 ~V?f128 (FromPolar)~p0 2 ~V?f144 (RowsOf)~p0 2 ~V?f146 (ColsOf)~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})'# b'4" *|: ;bP7&c0!*Names to the back| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~V?f0 (dlim)~p0 3 ~V?f0 (SAEQN)~p0 3 ~V?f0 (SA)~p0 3 ~V?f0 (D)~p0 3 ~V?f0 (N)~p0 3 ~V?v0 (xSV)~p0 3 ~V?d16 (d)~p0 1 ~Ie(x,y)~p0 0 ~A(f(x,y)=x^2+y^2*sin(x*y))~p0 0 ~A(Diff(x)*f(x,y))~p0 0 ~A(Diff(x)*f(x,y)=y^3*cos(x*y)+2*x)~p0 1 ~sb/^!!! } b00*!! c#T"!c"H"!c#L"_c/__c/__!" } ^ _~ ~A(Diff(y)*f(x,y))~p0 0 ~A(Diff(y)*f(x,y)=x*y^2*cos(x*y)+2*y*sin(x*y))~p0 1 ~sb/^!!! } b00*!! c#T"!c"H"!c#L"_c/__c/__!" } ^ _~c2 162 -1 161 -1 160 -1 ~c2 164 -1 163 -1 160 -1 ~e