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|rB@[EXYE:;WO9_[@gj$o3B%c`fGIDtZ7IX]/jPHqX.(A+'Lghq2p?@t(g(R-| |&@h?+p\.(_==dd\Gt7?3Yp<1rpU/o\5(276jn''Z'LL_$`Pg2.^V%5+mbN2;| |I8-X+L(mlSk?O/qf%N74V3FDGTFIU0&CJD5_o'@oVP)NpmdBN*o=:)@cZCs">V=J^:"-JLWfTe?A;jr/UCISR| |:bi9._)kj<66[U9cBcX"C*?2iCJTuKr"%43c8ajC1]HS4$(LdN1'tkG-3+#G| |!(fUS7'8jaJs)7q| |9}| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 0 ~V?f0 (Row)~p0 1 ~V?f0 (RowOp)~p0 1 ~V?f0 (MakeSubMatrix)~p0 1 ~V?f0 (RowReduce)~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(?)):(0)~p0 4 ~Hs(sin(?n*?)):(0)~p0 4 ~Hs(cos(1/2*?)):(0)~p0 4 ~Hs(cos(?n/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$@ b%H b&P!WW}]|[~p1 1 ~V?c5 ('o)~p0 2 ~V?c1 ('p)~p0 2 ~V?c0 (c)~p0 2 ~V?c0 (b)~p0 2 ~V?c0 (a)~p0 2 ~V?c4 (i)~p0 2 ~V?c3 ('N)~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4" *~: ;bP7&c55*Variables| |}& b!( b"0 b#8 b$@ 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$@ b%H b&P!WW}]|[~p1 1 ~V?f132 (FromSpherical)~p0 2 ~V?f130 (FromCylindrical)~p0 2 ~V?f128 (FromPolar)~p0 2 ~V?f144 (RowsOf)~p0 2 ~V?f146 (ColsOf)~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})'# b'4" *~: ;bP7&c55*Names to the back| |}& b!( b"0 b#8 b$@ 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 ~Q ]|Expr|[#b @`bb#_b#_b#_})%# b'4" *~: ;bP7&c55*Row Operation Package| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})'# b'4" *~: ;bP7&c55*Base and Defined| | Names}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~Hs(RowAdd(?a,?b,?c,?o)):(RowAdd_1(RowsOf(?o),~ ?a,?b,?c,?o))~p0 2 ~V?f146 (ColumnsOf)~p0 2 ~V?m0 (A)~p0 2 ~V?f0 (RowAdd)~p0 2 ~V?m0 (B)~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})## b'4" *~: ;bP7&c55*RowReduction Package| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4" *~: ;bP7&c55*RowReduce| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Hs(RowReduce(?o)):(RowReduce_1(?o,RowsOf(?o),~ ColumnsOf(?o)))~p0 3 ~Hs(RowReduce(?o)):(RowReduce_1(?o,RowsOf(?o),~ ColumnsOf(?o)))~p0 3 ~Hs(RowReduce_1(?o,?a,?b)):(RowReduce_2(?o,(Conditional(~ ?a,(?a=0)))))~p0 3 ~Hs(RowReduce_2(?o,?a)):(RowReduce_3(?o,MakeSubMatrix(~ ?o,?a)))~p0 3 ~Hs(RowReduce_3(?o,?p)):(RowReduce_4(?p^(-1)*?o))~p0 3 ~Hs(RowReduce_4(?o)):(?o)~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4" *~: ;bP7&c55*MakeSubMatrix| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 2 ~Hs(MakeSubMatrix(?o,2)):(?o_(1,1),?o_(1,2);?o_~ (2,1),?o_(2,2))~p0 3 ~Hs(MakeSubMatrix(?o,3)):(?o_(1,1),?o_(1,2),?o_~ (1,3);?o_(2,1),?o_(2,2),?o_(2,3);?o_(3,1),?o_(~ 3,2),?o_(3,3))~p0 3 ~Hs(MakeSubMatrix(?o,4)):(?o_(1,1),?o_(1,2),?o_~ (1,3),?o_(1,4);?o_(2,1),?o_(2,2),?o_(2,3),?o_(~ 2,4);?o_(3,1),?o_(3,2),?o_(3,3),?o_(3,4);?o_(4,~ 1),?o_(4,2),?o_(4,3),?o_(4,4))~p0 3 ~Hs(MakeSubMatrix(?o,5)):(?o_(1,1),?o_(1,2),?o_~ (1,3),?o_(1,4),?o_(1,5);?o_(2,1),?o_(2,2),?o_(~ 2,3),?o_(2,4),?o_(2,5);?o_(3,1),?o_(3,2),?o_(3,~ 3),?o_(3,4),?o_(3,5);?o_(4,1),?o_(4,2),?o_(4,3),~ ?o_(4,4),?o_(4,5);?o_(5,1),?o_(5,2),?o_(5,3),?o_~ (5,4),?o_(5,5))~p0 3 ~Hs(MakeSubMatrix(?o,6)):(?o_(1,1),?o_(1,2),?o_~ (1,3),?o_(1,4),?o_(1,5),?o_(1,6);?o_(2,1),?o_(~ 2,2),?o_(2,3),?o_(2,4),?o_(2,5),?o_(2,6);?o_(3,~ 1),?o_(3,2),?o_(3,3),?o_(3,4),?o_(3,5),?o_(3,6);~ ?o_(4,1),?o_(4,2),?o_(4,3),?o_(4,4),?o_(4,5),?o_~ (4,6);?o_(5,1),?o_(5,2),?o_(5,3),?o_(5,4),?o_(~ 5,5),?o_(5,6);?o_(6,1),?o_(6,2),?o_(6,3),?o_(6,~ 4),?o_(6,5),?o_(6,6))~p0 3 ~Hs(MakeSubMatrix(?o,7)):(?o_(1,1),?o_(1,2),?o_~ (1,3),?o_(1,4),?o_(1,5),?o_(1,6),?o_(1,7);?o_(~ 2,1),?o_(2,2),?o_(2,3),?o_(2,4),?o_(2,5),?o_(2,~ 6),?o_(2,7);?o_(3,1),?o_(3,2),?o_(3,3),?o_(3,4),~ ?o_(3,5),?o_(3,6),?o_(3,7);?o_(4,1),?o_(4,2),?o_~ (4,3),?o_(4,4),?o_(4,5),?o_(4,6),?o_(4,7);?o_(~ 5,1),?o_(5,2),?o_(5,3),?o_(5,4),?o_(5,5),?o_(5,~ 6),?o_(5,7);?o_(6,1),?o_(6,2),?o_(6,3),?o_(6,4),~ ?o_(6,5),?o_(6,6),?o_(6,7);?o_(7,1),?o_(7,2),?o_~ (7,3),?o_(7,4),?o_(7,5),?o_(7,6),?o_(7,7))~p0 3 ~Hs(MakeSubMatrix(?o,8)):(?o_(1,1),?o_(1,2),?o_~ (1,3),?o_(1,4),?o_(1,5),?o_(1,6),?o_(1,7),?o_(~ 1,8);?o_(2,1),?o_(2,2),?o_(2,3),?o_(2,4),?o_(2,~ 5),?o_(2,6),?o_(2,7),?o_(2,8);?o_(3,1),?o_(3,2),~ ?o_(3,3),?o_(3,4),?o_(3,5),?o_(3,6),?o_(3,7),?o_~ (3,8);?o_(4,1),?o_(4,2),?o_(4,3),?o_(4,4),?o_(~ 4,5),?o_(4,6),?o_(4,7),?o_(4,8);?o_(5,1),?o_(5,~ 2),?o_(5,3),?o_(5,4),?o_(5,5),?o_(5,6),?o_(5,7),~ ?o_(5,8);?o_(6,1),?o_(6,2),?o_(6,3),?o_(6,4),?o_~ (6,5),?o_(6,6),?o_(6,7),?o_(6,8);?o_(7,1),?o_(~ 7,2),?o_(7,3),?o_(7,4),?o_(7,5),?o_(7,6),?o_(7,~ 7),?o_(7,8);?o_(8,1),?o_(8,2),?o_(8,3),?o_(8,4),~ ?o_(8,5),?o_(8,6),?o_(8,7),?o_(8,8))~p0 3 ~Q ]|Expr|[#b @`bb#_b#_b#_})'# b'4" *~: ;bP6&c55*dim ,] 2 rules| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~Hs(RowAdd_1(2,1,2,?c,?o)):(RowAdd(?,?,?,(1,0;~ ?c,1)*?o))~p0 2 ~Hs(RowAdd_1(2,1,1,?c,?o)):(RowAdd(?,?,?,(?c,0;~ 0,1)*?o))~p0 2 ~Hs(RowAdd_1(2,2,2,?c,?o)):(RowAdd(?,?,?,(1,0;~ 0,?c)*?o))~p0 2 ~Hs(RowAdd_1(2,2,1,?c,?o)):(RowAdd(?,?,?,(1,?c;~ 0,1)*?o))~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})'# b'4" *~: ;bP6&c55*dim ,] 3 rules| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~Hs(RowAdd_1(3,1,2,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0;?c,1,0;0,0,1)*?o))~p0 2 ~Hs(RowAdd_1(3,1,3,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0;0,1,0;?c,0,1)*?o))~p0 2 ~Hs(RowAdd_1(3,2,3,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0;0,1,0;0,?c,1)*?o))~p0 2 ~Hs(RowAdd_1(3,1,1,?c,?o)):(RowAdd(?,?,?,(?c,0,~ 0;0,1,0;0,0,1)*?o))~p0 2 ~Hs(RowAdd_1(3,2,2,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0;0,?c,0;0,0,1)*?o))~p0 2 ~Hs(RowAdd_1(3,3,3,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0;0,1,0;0,0,?c)*?o))~p0 2 ~Hs(RowAdd_1(3,3,2,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0;0,1,?c;0,0,1)*?o))~p0 2 ~Hs(RowAdd_1(3,3,1,?c,?o)):(RowAdd(?,?,?,(1,0,~ ?c;0,1,0;0,0,1)*?o))~p0 2 ~Hs(RowAdd_1(3,2,1,?c,?o)):(RowAdd(?,?,?,(1,?c,~ 0;0,1,0;0,0,1)*?o))~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})'# b'4" *~: ;bP6&c55*dim ,] 4 rules| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~Hs(RowAdd_1(4,1,2,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0;?c,1,0,0;0,0,1,0;0,0,0,1)*?o))~p0 2 ~Hs(RowAdd_1(4,1,3,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0;0,1,0,0;?c,0,1,0;0,0,0,1)*?o))~p0 2 ~Hs(RowAdd_1(4,1,4,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0;0,1,0,0;0,0,1,0;?c,0,0,1)*?o))~p0 2 ~Hs(RowAdd_1(4,2,3,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0;0,1,0,0;0,?c,1,0;0,0,0,1)*?o))~p0 2 ~Hs(RowAdd_1(4,2,4,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0;0,1,0,0;0,0,1,0;0,?c,0,1)*?o))~p0 2 ~Hs(RowAdd_1(4,3,4,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0;0,1,0,0;0,0,1,0;0,0,?c,1)*?o))~p0 2 ~Hs(RowAdd_1(4,1,1,?c,?o)):(RowAdd(?,?,?,(?c,0,~ 0,0;0,1,0,0;0,0,1,0;0,0,0,1)*?o))~p0 2 ~Hs(RowAdd_1(4,2,2,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0;0,?c,0,0;0,0,1,0;0,0,0,1)*?o))~p0 2 ~Hs(RowAdd_1(4,3,3,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0;0,1,0,0;0,0,?c,0;0,0,0,1)*?o))~p0 2 ~Hs(RowAdd_1(4,4,4,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0;0,1,0,0;0,0,1,0;0,0,0,?c)*?o))~p0 2 ~Hs(RowAdd_1(4,4,1,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,?c;0,1,0,0;0,0,1,0;0,0,0,1)*?o))~p0 2 ~Hs(RowAdd_1(4,4,2,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0;0,1,0,?c;0,0,1,0;0,0,0,1)*?o))~p0 2 ~Hs(RowAdd_1(4,4,3,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0;0,1,0,0;0,0,1,?c;0,0,0,1)*?o))~p0 2 ~Hs(RowAdd_1(4,3,2,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0;0,1,?c,0;0,0,1,0;0,0,0,1)*?o))~p0 2 ~Hs(RowAdd_1(4,3,1,?c,?o)):(RowAdd(?,?,?,(1,0,~ ?c,0;0,1,0,0;0,0,1,0;0,0,0,1)*?o))~p0 2 ~Hs(RowAdd_1(4,2,1,?c,?o)):(RowAdd(?,?,?,(1,?c,~ 0,0;0,1,0,0;0,0,1,0;0,0,0,1)*?o))~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_})'# b'4" *~: ;bP6&c55*dim ,] 5 rules| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~Hs(RowAdd_1(5,1,1,?c,?o)):(RowAdd(?,?,?,(?c,0,~ 0,0,0;0,1,0,0,0;0,0,1,0,0;0,0,0,1,0;0,0,0,0,1)*~ ?o))~p0 2 ~Hs(RowAdd_1(5,2,2,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,?c,0,0,0;0,0,1,0,0;0,0,0,1,0;0,0,0,0,1)*~ ?o))~p0 2 ~Hs(RowAdd_1(5,3,3,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,0,0,0;0,0,?c,0,0;0,0,0,1,0;0,0,0,0,1)*~ ?o))~p0 2 ~Hs(RowAdd_1(5,4,4,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,0,0,0;0,0,1,0,0;0,0,0,?c,0;0,0,0,0,1)*~ ?o))~p0 2 ~Hs(RowAdd_1(5,5,5,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,0,0,0;0,0,1,0,0;0,0,0,1,0;0,0,0,0,?c)*~ ?o))~p0 2 ~Hs(RowAdd_1(5,1,2,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;?c,1,0,0,0;0,0,1,0,0;0,0,0,1,0;0,0,0,0,1)*~ ?o))~p0 2 ~Hs(RowAdd_1(5,1,3,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,0,0,0;?c,0,1,0,0;0,0,0,1,0;0,0,0,0,1)*~ ?o))~p0 2 ~Hs(RowAdd_1(5,1,4,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,0,0,0;0,0,1,0,0;?c,0,0,1,0;0,0,0,0,1)*~ ?o))~p0 2 ~Hs(RowAdd_1(5,1,5,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,0,0,0;0,0,1,0,0;0,0,0,1,0;?c,0,0,0,1)*~ ?o))~p0 2 ~Hs(RowAdd_1(5,2,3,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,0,0,0;0,?c,1,0,0;0,0,0,1,0;0,0,0,0,1)*~ ?o))~p0 2 ~Hs(RowAdd_1(5,2,4,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,0,0,0;0,0,1,0,0;0,?c,0,1,0;0,0,0,0,1)*~ ?o))~p0 2 ~Hs(RowAdd_1(5,2,5,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,0,0,0;0,0,1,0,0;0,0,0,1,0;0,?c,0,0,1)*~ ?o))~p0 2 ~Hs(RowAdd_1(5,3,4,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,0,0,0;0,0,1,0,0;0,0,?c,1,0;0,0,0,0,1)*~ ?o))~p0 2 ~Hs(RowAdd_1(5,3,5,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,0,0,0;0,0,1,0,0;0,0,0,1,0;0,0,?c,0,1)*~ ?o))~p0 2 ~Hs(RowAdd_1(5,4,5,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,0,0,0;0,0,1,0,0;0,0,0,1,0;0,0,0,?c,1)*~ ?o))~p0 2 ~Hs(RowAdd_1(5,5,1,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,?c;0,1,0,0,0;0,0,1,0,0;0,0,0,1,0;0,0,0,0,1)*~ ?o))~p0 2 ~Hs(RowAdd_1(5,5,2,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,0,0,?c;0,0,1,0,0;0,0,0,1,0;0,0,0,0,1)*~ ?o))~p0 2 ~Hs(RowAdd_1(5,5,3,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,0,0,0;0,0,1,0,?c;0,0,0,1,0;0,0,0,0,1)*~ ?o))~p0 2 ~Hs(RowAdd_1(5,5,4,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,0,0,0;0,0,1,0,0;0,0,0,1,?c;0,0,0,0,1)*~ ?o))~p0 2 ~Hs(RowAdd_1(5,4,1,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,?c,0;0,1,0,0,0;0,0,1,0,0;0,0,0,1,0;0,0,0,0,1)*~ ?o))~p0 2 ~Hs(RowAdd_1(5,4,2,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,0,?c,0;0,0,1,0,0;0,0,0,1,0;0,0,0,0,1)*~ ?o))~p0 2 ~Hs(RowAdd_1(5,4,3,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,0,0,0;0,0,1,?c,0;0,0,0,1,0;0,0,0,0,1)*~ ?o))~p0 2 ~Hs(RowAdd_1(5,3,1,?c,?o)):(RowAdd(?,?,?,(1,0,~ ?c,0,0;0,1,0,0,0;0,0,1,0,0;0,0,0,1,0;0,0,0,0,1)*~ ?o))~p0 2 ~Hs(RowAdd_1(5,3,2,?c,?o)):(RowAdd(?,?,?,(1,0,~ 0,0,0;0,1,?c,0,0;0,0,1,0,0;0,0,0,1,0;0,0,0,0,1)*~ ?o))~p0 2 ~Hs(RowAdd_1(5,2,1,?c,?o)):(RowAdd(?,?,?,(1,?c,~ 0,0,0;0,1,0,0,0;0,0,1,0,0;0,0,0,1,0;0,0,0,0,1)*~ ?o))~p0 2 ~Q ]|Expr|[#b @`bb#_b#_b#_}`fb"#})!# b'4`f }[$! `fb"#}) # b'4| |}& b!( b"0 b#8 b$@ b%H b&P!WW})(# b'4" *~: ;bP9&c55)Gaussin ja| | Jordanin menetelm.*}& b!( b"0 b#8 b$@ b%H b&P!WW})## b'4Manuaalinen| | versio}& 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$@ b%H b&P!WW}]|[~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4" *~: ;bP7&c55*Instructions| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4[%! `fb#@})%# b'4" *~: ;bP7&c54IIn| |,MPlace Calculations}& b!( b"0 b#8 b$@ b%H b&P!WW}`f })<# b'4| |&c54JMAC&c55*,Z Use `f#}&c55)CTRL,MApple ,M1`f }&c55* on the| | right,Mhand,Mside to keep the}& b!( b"0 b#8 b$@ b%H b&P!WW})3# b'4| |calculations in place,N Do each `f#}&c55)CTRL,MApple,M1`f }&c55* | |Twice}& b!( b"0 b#8 b$@ b%H b&P!WW})b A# b'4&c54JWIN&c55*,Z | |Use `fb"#}&c55)CTRL,MALT,MOPT,M1`f }&c55* on the right ,M hand| | ,M side to keep the}& b!( b"0 b#8 b$@ b%H b&P!WW})6# b'4calculations| | in place,N Do each `fb"#}&c55)CTRL,MALT,MOPT,M1 `f }&c55*Twice| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 1 ~A(A=RowAdd(?,?,?,(3,2,1,4;3,-3,2,-4;7,0,-2,4)))~p0 1 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4[(! ) # b'4| |}& b!( b"0 b#8 b$@ b%H b&P!WW})*# b'4" *~: ;bP8&c54JHow to Use| | RowAdd Function,Z}& b!( b"0 b#8 b$@ b%H b&P!WW}) # b'4| |}& b!( b"0 b#8 b$@ b%H b&P!WW})/# b'4&c55*RowAdd,H X,L Y,L Z,L| | Matrix ,I}& b!( b"0 b#8 b$@ b%H b&P!WW}) # b'4| |}& b!( b"0 b#8 b$@ b%H b&P!WW})5# b'4`fb"#}&c55)Add`f } `f#},H| |Z times Row X,I`f } to `fb!D}Row Y`f,} in Matrix| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`f }) # b'4| |}& b!( b"0 b#8 b$@ b%H b&P!WW}`fb!D})5# b'4if X ,] Y,L then | |multiply Row X by Z}& b!( b"0 b#8 b$@ b%H b&P!WW}}| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 1 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4" *~: ;bP7&c55*Example| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 0 ~A(A=(3,2,1,4;3,-3,2,-4;7,0,-2,4))~p0 1 ~d~A(B=RowAdd(1,2,-1,A))~p0 1 ~A(B=RowAdd(?,?,?,(1,0,0;-1,1,0;0,0,1)*(3,2,1,~ 4;3,-3,2,-4;7,0,-2,4)))~p0 2 ~sb/_!! } $&! c#T"!c#L"_c/__c/__} ^ _~A(B=RowAdd(~ ?,?,?,(3,2,1,4;0,-5,1,-8;7,0,-2,4)))~p0 3 ~sb/_!! } $&! c#T"!c#L"_c/__c/__} ^ _~A(B=RowAdd(~ 1,1,1/3,(3,2,1,4;0,-5,1,-8;7,0,-2,4)))~p0 3 ~A(B=RowAdd(?,?,?,(0.33333333333333331,0,0;0,1,~ 0;0,0,1)*(3,2,1,4;0,-5,1,-8;7,0,-2,4)))~p0 4 ~sb/_!! } $&! c#T"!c#L"_c/__c/__} ^ _~A(B=RowAdd(~ ?,?,?,(1,0.66666666666666663,0.33333333333333331,~ 1.3333333333333333;0,-5,1,-8;7,0,-2,4)))~p0 5 ~sb/_!! } $&! c#T"!c#L"_c/__c/__} ^ _~A(B=RowAdd(~ 1,3,-7,(1,0.66666666666666663,0.33333333333333331,~ 1.3333333333333333;0,-5,1,-8;7,0,-2,4)))~p0 5 ~A(B=RowAdd(?,?,?,(1,0,0;0,1,0;-7,0,1)*(1,0.66666666666666663,~ 0.33333333333333331,1.3333333333333333;0,-5,1,~ -8;7,0,-2,4)))~p0 6 ~sb/_!! } $&! c#T"!c#L"_c/__c/__} ^ _~A(B=RowAdd(~ ?,?,?,(1,0.66666666666666663,0.33333333333333331,~ 1.3333333333333333;0,-5,1,-8;0,-4.6666666666666661,~ -4.333333333333333,-5.3333333333333321)))~p0 7 ~sb/_!! } $&! c#T"!c#L"_c/__c/__} ^ _~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4["! ),# b'4" *~: ;bP8&c55)Matriisin| | muuttaminen &c55*,Havaa ohje tuplaklikkaamalla,I| |}& b!( b"0 b#8 b$@ 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}]|[~p1 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})b!%# b'4" *~: ;bP8&c55*Valitsemalla | |hiirell.* koko rivin tai sarakkeen,L voit poistaa sen del,Mn.*| |pp.*imell.*,N Uuden sarakkeen,Orivin taas saa pilkku,Opuolipiste| |,Mn.*pp.*imell.*,N Osoittimen on oltava silloin viimeisell.* | |sarakkeella,Orivill.*,N }& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 1 ~A(A=(3,2,1,4;3,-3,2,-4;5,0,-2,4))~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4["! ) # b'4| |}& b!( b"0 b#8 b$@ b%H b&P!WW})/# b'4" *~: ;bP8&c55)Laskimen | |k.*ytt.: &c55*,Havaa ohje tuplaklikkaamalla,I| |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4[(! )(# b'4" *~: ;bP8&c55*Muuta| | matriisi A haluamaksesi,N}& b!( b"0 b#8 b$@ b%H b&P!WW})2# b'4| |Kopioi matriisi A 1,N rivin RowAdd,Mkomennon matriisiksi,N | |}& b!( b"0 b#8 b$@ b%H b&P!WW})*# b'4Muuta RowAdd,Mkomennon lukuarvo| |,Mparametrit }& b!( b"0 b#8 b$@ b%H b&P!WW})2# b'4 ,Hmuuntava| | rivi,L muunnettava rivi,L muuntokerroin,I,N| |}& b!( b"0 b#8 b$@ b%H b&P!WW}).# b'4Klikkaa alempia rivej.*,L| | jolloin komentosi suoritetaan,N}& b!( b"0 b#8 b$@ b%H b&P!WW}| |)5# b'4Kopioi 3,N rivin tuloksesta matriisi 1,N rivin RowAdd| |,Mkomentoon,N}& b!( b"0 b#8 b$@ b%H b&P!WW})&# b'4Anna uudet | |parametrit,N}& b!( b"0 b#8 b$@ b%H b&P!WW}).# b'4Jatka kunnes| | matriisi on halutussa muodossa,N }& b!( b"0 b#8 b$@ b%H b&P!WW}}| |}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 1 ~A(A=RowAdd(1,2,-1,(3,2,1,4;3,-3,2,-4;5,0,-2,4)))~p0 0 ~Q ]|Expr|[#b @`bb#_b#_b#_})$# b'4" *~: ;bP8&c55*Piilotettua apulaskentaa| |,A}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p1 1 ~A(A=RowAdd_1(RowsOf(3,2,1,4;3,-3,2,-4;5,0,-2,~ 4),1,2,-1,(3,2,1,4;3,-3,2,-4;5,0,-2,4)))~p0 2 ~sb/_! } !& c#T"!c#L"_c/__c/__} ^ _~A(A=RowAdd(~ ?,?,?,(1,0,0;-1,1,0;0,0,1)*(3,2,1,4;3,-3,2,-4;~ 5,0,-2,4)))~p0 3 ~sb/_! } !& c#T"!c#L"_c/__c/__} ^ _~A(A=RowAdd(~ ?,?,?,(1*3+0*3+0*5,1*2+0*(-3)+0*0,1*1+0*2+0*(-~ 2),1*4+0*(-4)+0*4;(-1)*3+1*3+0*5,(-1)*2+1*(-3)+~ 0*0,(-1)*1+1*2+0*(-2),(-1)*4+1*(-4)+0*4;0*3+0*~ 3+1*5,0*2+0*(-3)+1*0,0*1+0*2+1*(-2),0*4+0*(-4)+~ 1*4)))~p0 4 ~sb/_! } "& c#T"!c#L"_c/__c/__} ^ _~A(A=RowAdd(~ ?,?,?,(3,2,1,4;-3+3,-3-2,-1+2,2*(-4);5,0,-2,4)))~p0 1 ~sb/_! } !& c#T"!c#L"_c/__c/__} ^ _~A(A=RowAdd(~ ?,?,?,(3,2,1,4;0,-5,1,-8;5,0,-2,4)))~p0 1 ~sb/_! } !& c#T"!c#L"_c/__c/__} ^ _~Q ]|Expr|[#b @`bb#_b#_b#_})!# b'4["! )4# b'4" *~: ;bP8&c55*Kopioi| | alimman rivin tuloksesta matriisi 1,N rivin RowAdd,Mkomentoon| |,N}& b!( b"0 b#8 b$@ b%H b&P!WW})7# b'4Anna 1,Nrivill.* uudet| | parametrit ja klikkaa sitten alinta laskentarivi.*,N | |}& b!( b"0 b#8 b$@ b%H b&P!WW}}}& b!( b"0 b#8 b$@ b%H b&P!WW}]|[~p0 1 ~c5 246 -1 245 -1 244 -1 161 -1 159 -1 186 -1 ~c1 247 -1 246 -1 ~c3 249 -1 248 -1 159 -1 189 -1 ~c1 250 -1 249 -1 ~c3 252 -1 251 -1 159 -1 187 -1 ~c1 253 -1 252 -1 ~c2 261 -1 259 -1 159 -1 ~c2 262 -1 261 -1 186 -1 ~c1 263 -1 262 -1 ~c1 264 -1 263 -1 ~c1 265 -1 264 -1 ~e