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Editor: page Time: 2011/03/12 18:48:37 GMT-8
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changed:
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)set output tex on

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-)set output mathml on
-\end{axiom}
)set output mathml off
\end{axiom}

axiom

)set output tex on

axiom

)set output algebra off

axiom

)set output mathml off

Indefinite intregral

arctan = atan

axiom

integrate(1/atan(x),x)

$\label{eq1}\int^{ \displaystyle x}{{1 \over{\arctan \left({\%A}\right)}}\ {d \%A}}$

(1)

Type: Union(Expression(Integer),...)

Definite intregral

axiom

integrate(1/(a+z^3), z=0..1,"noPole");

Type: Union(f1: OrderedCompletion?(Expression(Integer)),...)

axiom

integrate(1/(a+z^3), z=0..1,"noPole")

$\label{eq2}{\left( \begin{array}{@{}l} \displaystyle -{{\sqrt{3}}\ {\log{\left({{3 \ {a^2}\ {{\root{3}\of{a^2}}^2}}+{{\left(-{2 \ {a^3}}+{a^2}\right)}\ {\root{3}\of{a^2}}}+{a^4}-{2 \ {a^3}}}\right)}}}+{2 \ {\sqrt{3}}\ {\log \left({{{\root{3}\of{a^2}}^2}+{2 \ a \ {\root{3}\of{a^2}}}+{a^2}}\right)}}+ \ \ \displaystyle {{12}\ {\arctan \left({{{2 \ {\sqrt{3}}\ {\root{3}\of{a^2}}}-{a \ {\sqrt{3}}}}\over{3 \ a}}\right)}}+{2 \ \pi}$

(2)

Type: Union(f1: OrderedCompletion?(Expression(Integer)),...)

axiom

integrate(a/(b+z^2),z=0..1,"noPole")

$\label{eq3}\begin{array}{@{}l} \displaystyle \left[{{\left( \begin{array}{@{}l} \displaystyle -{2 \ a \ {\log \left({\sqrt{- b}}\right)}}+ \ \ \displaystyle {a \ {\log \left({{{{\left(-{4 \ {b^2}}+{4 \ b}\right)}\ {\sqrt{- b}}}-{b^3}+{6 \ {b^2}}- b}\over{{b^2}+{2 \ b}+ 1}}\right)}}$

(3)

Type: Union(f2: List(OrderedCompletion?(Expression(Integer))),...)

Solutions of Transcendental Equations

axiom

solve(cos(x)-y=-sin(x),x)

$\label{eq4}\begin{array}{@{}l} \displaystyle \left[{x ={2 \ {\arctan \left({{{\sqrt{-{y^2}+ 2}}+ 1}\over{y + 1}}\right)}}}, \: \right. \ \ \displaystyle \left.{x = -{2 \ {\arctan \left({{{\sqrt{-{y^2}+ 2}}- 1}\over{y + 1}}\right)}}}\right]$

(4)

Type: List(Equation(Expression(Integer)))

axiom

solve(cos(x)-y=-sin(x),y)

$\label{eq5}\left[{y ={{\sin \left({x}\right)}+{\cos \left({x}\right)}}}\right]$

(5)

Type: List(Equation(Expression(Integer)))

axiom

solve(cos(x)-y=-sin(x),x)

$\label{eq6}\begin{array}{@{}l} \displaystyle \left[{x ={2 \ {\arctan \left({{{\sqrt{-{y^2}+ 2}}+ 1}\over{y + 1}}\right)}}}, \: \right. \ \ \displaystyle \left.{x = -{2 \ {\arctan \left({{{\sqrt{-{y^2}+ 2}}- 1}\over{y + 1}}\right)}}}\right]$

(6)

Type: List(Equation(Expression(Integer)))

axiom

solve(cos(x)=0,x)

$\label{eq7}\left[{x ={\pi \over 2}}\right]$

(7)

Type: List(Equation(Expression(Integer)))

axiom

solve(sin(e) - e = 0, e)

$\label{eq8}\left[ \right]$

(8)

Type: List(Equation(Expression(Integer)))

axiom

solve(a*cos(t1) + b*sin(t1) = c, t1)

$\label{eq9}\begin{array}{@{}l} \displaystyle \left[{t 1 ={2 \ {\arctan \left({{{\sqrt{-{c^2}+{b^2}+{a^2}}}+ b}\over{c + a}}\right)}}}, \: \right. \ \ \displaystyle \left.{t 1 = -{2 \ {\arctan \left({{{\sqrt{-{c^2}+{b^2}+{a^2}}}- b}\over{c + a}}\right)}}}\right]$

(9)

Type: List(Equation(Expression(Integer)))

axiom

solve(cos(x)-y=-sin(x),x)

$\label{eq10}\begin{array}{@{}l} \displaystyle \left[{x ={2 \ {\arctan \left({{{\sqrt{-{y^2}+ 2}}+ 1}\over{y + 1}}\right)}}}, \: \right. \ \ \displaystyle \left.{x = -{2 \ {\arctan \left({{{\sqrt{-{y^2}+ 2}}- 1}\over{y + 1}}\right)}}}\right]$

(10)

Type: List(Equation(Expression(Integer)))

Matrices

axiom

A:=matrix[[cos(x)-y,-sin(x)],[sin(x),cos(x)-y]]

$\label{eq11}\left[ \begin{array}{cc} {{\cos \left({x}\right)}- y}& -{\sin \left({x}\right)} \ {\sin \left({x}\right)}&{{\cos \left({x}\right)}- y}$

(11)

Type: Matrix(Expression(Integer))

axiom

A:=matrix[[cos(x)-y,-sin(x)],[sin(x),cos(x)-y]]

$\label{eq12}\left[ \begin{array}{cc} {{\cos \left({x}\right)}- y}& -{\sin \left({x}\right)} \ {\sin \left({x}\right)}&{{\cos \left({x}\right)}- y}$

(12)

Type: Matrix(Expression(Integer))

axiom

solve(A=0,y)

   There are 18 exposed and 3 unexposed library operations named solve 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                              )display op solve
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named solve
      with argument type(s) 
                Equation(SquareMatrix(2,Expression(Integer)))
                                 Variable(y)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

axiom

A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]

$\label{eq13}\left[ \begin{array}{cc} {{\cos \left({x}\right)}- L}& -{\sin \left({x}\right)} \ {\sin \left({x}\right)}&{{\cos \left({x}\right)}- L}$

(13)

Type: Matrix(Expression(Integer))

axiom

B:=solve(A(1,1)*A(2,2)-A(2,1)*A(1,2)=0,L)

$\label{eq14}\left[{L ={{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}, \:{L ={-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}\right]$

(14)

Type: List(Equation(Expression(Integer)))

axiom

A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]

$\label{eq15}\left[ \begin{array}{cc} {{\cos \left({x}\right)}- L}& -{\sin \left({x}\right)} \ {\sin \left({x}\right)}&{{\cos \left({x}\right)}- L}$

(15)

Type: Matrix(Expression(Integer))

axiom

B=solve(A(1,1)*A(2,2)-A(2,1)*A(1,2)=0,L)

$\label{eq16}\begin{array}{@{}l} \displaystyle {\left[{L ={{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}, \:{L ={-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}\right]}= \ \ \displaystyle {\left[{L ={{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}, \:{L ={-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}\right]}$

(16)

Type: Equation(List(Equation(Expression(Integer))))

axiom

B(1)

$\label{eq17}L ={{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}$

(17)

Type: Equation(Expression(Integer))

axiom

A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]

$\label{eq18}\left[ \begin{array}{cc} {{\cos \left({x}\right)}- L}& -{\sin \left({x}\right)} \ {\sin \left({x}\right)}&{{\cos \left({x}\right)}- L}$

(18)

Type: Matrix(Expression(Integer))

axiom

B=solve(A(1,1)*A(2,2)-A(2,1)*A(1,2)=0,L)

$\label{eq19}\begin{array}{@{}l} \displaystyle {\left[{L ={{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}, \:{L ={-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}\right]}= \ \ \displaystyle {\left[{L ={{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}, \:{L ={-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}\right]}$

(19)

Type: Equation(List(Equation(Expression(Integer))))

axiom

$\label{eq20}\left[{L ={{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}, \:{L ={-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}\right]$

(20)

Type: List(Equation(Expression(Integer)))

axiom

A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]

$\label{eq21}\left[ \begin{array}{cc} {{\cos \left({x}\right)}- L}& -{\sin \left({x}\right)} \ {\sin \left({x}\right)}&{{\cos \left({x}\right)}- L}$

(21)

Type: Matrix(Expression(Integer))

axiom

B:=solve(A(1,1)*A(2,2)-A(2,1)*A(1,2)=0,L)

$\label{eq22}\left[{L ={{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}, \:{L ={-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}\right]$

(22)

Type: List(Equation(Expression(Integer)))

axiom

$\label{eq23}\left[{L ={{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}, \:{L ={-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}\right]$

(23)

Type: List(Equation(Expression(Integer)))

axiom

A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]

$\label{eq24}\left[ \begin{array}{cc} {{\cos \left({x}\right)}- L}& -{\sin \left({x}\right)} \ {\sin \left({x}\right)}&{{\cos \left({x}\right)}- L}$

(24)

Type: Matrix(Expression(Integer))

axiom

B:=solve(A(1,1)*A(2,2)-A(2,1)*A(1,2)=0,L)

$\label{eq25}\left[{L ={{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}, \:{L ={-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}\right]$

(25)

Type: List(Equation(Expression(Integer)))

axiom

B.1

$\label{eq26}L ={{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}$

(26)

Type: Equation(Expression(Integer))

axiom

A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]

$\label{eq27}\left[ \begin{array}{cc} {{\cos \left({x}\right)}- L}& -{\sin \left({x}\right)} \ {\sin \left({x}\right)}&{{\cos \left({x}\right)}- L}$

(27)

Type: Matrix(Expression(Integer))

axiom

B:=solve(A(1,1)*A(2,2)-A(2,1)*A(1,2)=0,L)

$\label{eq28}\left[{L ={{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}, \:{L ={-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}\right]$

(28)

Type: List(Equation(Expression(Integer)))

axiom

v:=vector[v11,v12]

$\label{eq29}\left[ v 11, \: v 12 \right]$

(29)

Type: Vector(OrderedVariableList?([v11,v12]))

axiom

A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]

$\label{eq30}\left[ \begin{array}{cc} {{\cos \left({x}\right)}- L}& -{\sin \left({x}\right)} \ {\sin \left({x}\right)}&{{\cos \left({x}\right)}- L}$

(30)

Type: Matrix(Expression(Integer))

axiom

B:=solve(A(1,1)*A(2,2)-A(2,1)*A(1,2)=0,L)

$\label{eq31}\left[{L ={{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}, \:{L ={-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}\right]$

(31)

Type: List(Equation(Expression(Integer)))

axiom

v:=matrix[[B.1],[B.2]]

$\label{eq32}\left[ \begin{array}{c} {L ={{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}} \ {L ={-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}$

(32)

Type: Matrix(Equation(Expression(Integer)))

axiom

A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]

$\label{eq33}\left[ \begin{array}{cc} {{\cos \left({x}\right)}- L}& -{\sin \left({x}\right)} \ {\sin \left({x}\right)}&{{\cos \left({x}\right)}- L}$

(33)

Type: Matrix(Expression(Integer))

axiom

[a,b]:=solve(A(1,1)*A(2,2)-A(2,1)*A(1,2)=0,L)

$\label{eq34}\left[{L ={{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}, \:{L ={-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}\right]$

(34)

Type: List(Equation(Expression(Integer)))

axiom

A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]

$\label{eq35}\left[ \begin{array}{cc} {{\cos \left({x}\right)}- L}& -{\sin \left({x}\right)} \ {\sin \left({x}\right)}&{{\cos \left({x}\right)}- L}$

(35)

Type: Matrix(Expression(Integer))

axiom

[a,b]:=solve(A(1,1)*A(2,2)-A(2,1)*A(1,2)=0,L)

$\label{eq36}\left[{L ={{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}, \:{L ={-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}\right]$

(36)

Type: List(Equation(Expression(Integer)))

axiom

$\label{eq37}L ={{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}$

(37)

Type: Equation(Expression(Integer))

axiom

$\label{eq38}L ={-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}$

(38)

Type: Equation(Expression(Integer))

axiom

A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]

$\label{eq39}\left[ \begin{array}{cc} {{\cos \left({x}\right)}- L}& -{\sin \left({x}\right)} \ {\sin \left({x}\right)}&{{\cos \left({x}\right)}- L}$

(39)

Type: Matrix(Expression(Integer))

axiom

[a,b]:=solve(A(1,1)*A(2,2)-A(2,1)*A(1,2)=0,L)

$\label{eq40}\left[{L ={{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}, \:{L ={-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}\right]$

(40)

Type: List(Equation(Expression(Integer)))

axiom

$\label{eq41}L ={{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}$

(41)

Type: Equation(Expression(Integer))

axiom

A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]

$\label{eq42}\left[ \begin{array}{cc} {{\cos \left({x}\right)}- L}& -{\sin \left({x}\right)} \ {\sin \left({x}\right)}&{{\cos \left({x}\right)}- L}$

(42)

Type: Matrix(Expression(Integer))

axiom

B:=solve(A(1,1)*A(2,2)-A(2,1)*A(1,2)=0,L)

$\label{eq43}\left[{L ={{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}, \:{L ={-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}\right]$

(43)

Type: List(Equation(Expression(Integer)))

axiom

LA1:=[sqrt(-1)*sin(x)+cos(x),-sqrt(-1)*sin(x)+cos(x)]

$\label{eq44}\left[{{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}, \:{-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}\right]$

(44)

Type: List(Expression(Integer))

axiom

A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]

$\label{eq45}\left[ \begin{array}{cc} {{\cos \left({x}\right)}- L}& -{\sin \left({x}\right)} \ {\sin \left({x}\right)}&{{\cos \left({x}\right)}- L}$

(45)

Type: Matrix(Expression(Integer))

axiom

B:=solve(A(1,1)*A(2,2)-A(2,1)*A(1,2)=0,L)

$\label{eq46}\left[{L ={{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}, \:{L ={-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}\right]$

(46)

Type: List(Equation(Expression(Integer)))

axiom

LA1:=matrix[sqrt(-1)*sin(x)+cos(x),-sqrt(-1)*sin(x)+cos(x)]

$\label{eq47}matrix_{{{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}, \:{-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}$

(47)

Type: Symbol

Complex Values

axiom

LA1:=matrix[sqrt(-1)*sin(x)]

$\label{eq48}matrix_{{\sqrt{- 1}}\ {\sin \left({x}\right)}}$

(48)

Type: Symbol

axiom

A:=matrix[cos(x)-L]

$\label{eq49}matrix_{{\cos \left({x}\right)}- L}$

(49)

Type: Symbol

axiom

A:=matrix[a,b]

$\label{eq50}matrix_{{L ={{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}, \:{L ={-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}}$

(50)

Type: Symbol

axiom

A:=matrix[[a,b]]

$\label{eq51}\left[ \begin{array}{cc} {L ={{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}&{L ={-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}$

(51)

Type: Matrix(Equation(Expression(Integer)))

axiom

A:=matrix[[a],[b]]

$\label{eq52}\left[ \begin{array}{c} {L ={{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}} \ {L ={-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}$

(52)

Type: Matrix(Equation(Expression(Integer)))

axiom

A:=matrix[[sqrt(-1)*sin(x)+cos(x)],[b]]

$\label{eq53}matrix_{{\left[{{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}\right]}, \:{\left[{L ={-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}\right]}}$

(53)

Type: Symbol

axiom

A:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)*cos(x)]]

$\label{eq54}\left[ \begin{array}{c} {{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}} \ -{{\sqrt{- 1}}\ {\cos \left({x}\right)}\ {\sin \left({x}\right)}}$

(54)

Type: Matrix(Expression(Integer))

axiom

LA1:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]

$\label{eq55}\left[ \begin{array}{c} {{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}} \ {-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}$

(55)

Type: Matrix(Expression(Integer))

axiom

LAM:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]

$\label{eq56}\left[ \begin{array}{c} {{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}} \ {-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}$

(56)

Type: Matrix(Expression(Integer))

axiom

L:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]

$\label{eq57}\left[ \begin{array}{c} {{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}} \ {-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}$

(57)

Type: Matrix(Expression(Integer))

axiom

A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]

   There are 8 exposed and 4 unexposed library operations named - 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                                )display op -
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named - 
      with argument type(s) 
                             Expression(Integer)
                         Matrix(Expression(Integer))

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]

$\label{eq58}\left[ \begin{array}{c} {{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}} \ {-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}$

(58)

Type: Matrix(Expression(Integer))

axiom

A*D

   >> Error detected within library code:
   can't multiply matrices of incompatible dimensions

axiom

A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]

   There are 8 exposed and 4 unexposed library operations named - 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                                )display op -
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named - 
      with argument type(s) 
                             Expression(Integer)
                         Matrix(Expression(Integer))

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]

$\label{eq59}\left[ \begin{array}{c} {{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}} \ {-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}$

(59)

Type: Matrix(Expression(Integer))

axiom

v:=matrix[[v11],[v12]]

$\label{eq60}\left[ \begin{array}{c} v 11 \ v 12$

(60)

Type: Matrix(Polynomial(Integer))

axiom

A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]

   There are 8 exposed and 4 unexposed library operations named - 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                                )display op -
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named - 
      with argument type(s) 
                             Expression(Integer)
                         Matrix(Expression(Integer))

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]

$\label{eq61}\left[ \begin{array}{c} {{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}} \ {-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}$

(61)

Type: Matrix(Expression(Integer))

axiom

v:=matrix[[v11],[v12]]

$\label{eq62}\left[ \begin{array}{c} v 11 \ v 12$

(62)

Type: Matrix(Polynomial(Integer))

axiom

A*v

   >> Error detected within library code:
   can't multiply matrices of incompatible dimensions

axiom

A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]

   There are 8 exposed and 4 unexposed library operations named - 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                                )display op -
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named - 
      with argument type(s) 
                             Expression(Integer)
                         Matrix(Expression(Integer))

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]

$\label{eq63}\left[ \begin{array}{c} {{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}} \ {-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}$

(63)

Type: Matrix(Expression(Integer))

axiom

v:=matrix[[v11],[v12]]

$\label{eq64}\left[ \begin{array}{c} v 11 \ v 12$

(64)

Type: Matrix(Polynomial(Integer))

axiom

A*v

   >> Error detected within library code:
   can't multiply matrices of incompatible dimensions

axiom

A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]

   There are 8 exposed and 4 unexposed library operations named - 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                                )display op -
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named - 
      with argument type(s) 
                             Expression(Integer)
                         Matrix(Expression(Integer))

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]

$\label{eq65}\left[ \begin{array}{c} {{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}} \ {-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}$

(65)

Type: Matrix(Expression(Integer))

axiom

v:=matrix[[v11],[v12]]

$\label{eq66}\left[ \begin{array}{c} v 11 \ v 12$

(66)

Type: Matrix(Polynomial(Integer))

axiom

A*v

   >> Error detected within library code:
   can't multiply matrices of incompatible dimensions

axiom

A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]

   There are 8 exposed and 4 unexposed library operations named - 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                                )display op -
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named - 
      with argument type(s) 
                             Expression(Integer)
                         Matrix(Expression(Integer))

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]

$\label{eq67}\left[ \begin{array}{c} {{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}} \ {-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}$

(67)

Type: Matrix(Expression(Integer))

axiom

v:=matrix[[v11],[v12]]

$\label{eq68}\left[ \begin{array}{c} v 11 \ v 12$

(68)

Type: Matrix(Polynomial(Integer))

axiom

A*v

   >> Error detected within library code:
   can't multiply matrices of incompatible dimensions

axiom

A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]

   There are 8 exposed and 4 unexposed library operations named - 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                                )display op -
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named - 
      with argument type(s) 
                             Expression(Integer)
                         Matrix(Expression(Integer))

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]

$\label{eq69}\left[ \begin{array}{c} {{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}} \ {-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}$

(69)

Type: Matrix(Expression(Integer))

axiom

v:=matrix[[v11],[v12]]

$\label{eq70}\left[ \begin{array}{c} v 11 \ v 12$

(70)

Type: Matrix(Polynomial(Integer))

axiom

A*v

   >> Error detected within library code:
   can't multiply matrices of incompatible dimensions

axiom

A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]

   There are 8 exposed and 4 unexposed library operations named - 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                                )display op -
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named - 
      with argument type(s) 
                             Expression(Integer)
                         Matrix(Expression(Integer))

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]

$\label{eq71}\left[ \begin{array}{c} {{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}} \ {-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}$

(71)

Type: Matrix(Expression(Integer))

axiom

v:=matrix[[v11],[v12]]

$\label{eq72}\left[ \begin{array}{c} v 11 \ v 12$

(72)

Type: Matrix(Polynomial(Integer))

axiom

A*v

   >> Error detected within library code:
   can't multiply matrices of incompatible dimensions

axiom

A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]

   There are 8 exposed and 4 unexposed library operations named - 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                                )display op -
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named - 
      with argument type(s) 
                             Expression(Integer)
                         Matrix(Expression(Integer))

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]

$\label{eq73}\left[ \begin{array}{c} {{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}} \ {-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}$

(73)

Type: Matrix(Expression(Integer))

axiom

v:=matrix[[v11],[v12]]

$\label{eq74}\left[ \begin{array}{c} v 11 \ v 12$

(74)

Type: Matrix(Polynomial(Integer))

axiom

A*v

   >> Error detected within library code:
   can't multiply matrices of incompatible dimensions

axiom

A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]

   There are 8 exposed and 4 unexposed library operations named - 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                                )display op -
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named - 
      with argument type(s) 
                             Expression(Integer)
                         Matrix(Expression(Integer))

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]

$\label{eq75}\left[ \begin{array}{c} {{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}} \ {-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}$

(75)

Type: Matrix(Expression(Integer))

axiom

v:=matrix[[v11],[v12]]

$\label{eq76}\left[ \begin{array}{c} v 11 \ v 12$

(76)

Type: Matrix(Polynomial(Integer))

axiom

A*v

   >> Error detected within library code:
   can't multiply matrices of incompatible dimensions

axiom

A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]

   There are 8 exposed and 4 unexposed library operations named - 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                                )display op -
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named - 
      with argument type(s) 
                             Expression(Integer)
                         Matrix(Expression(Integer))

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]

$\label{eq77}\left[ \begin{array}{c} {{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}} \ {-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}$

(77)

Type: Matrix(Expression(Integer))

axiom

v:=matrix[[v11],[v12]]

$\label{eq78}\left[ \begin{array}{c} v 11 \ v 12$

(78)

Type: Matrix(Polynomial(Integer))

axiom

A*v

   >> Error detected within library code:
   can't multiply matrices of incompatible dimensions

axiom

A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]

   There are 8 exposed and 4 unexposed library operations named - 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                                )display op -
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named - 
      with argument type(s) 
                             Expression(Integer)
                         Matrix(Expression(Integer))

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]

$\label{eq79}\left[ \begin{array}{c} {{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}} \ {-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}$

(79)

Type: Matrix(Expression(Integer))

axiom

v:=matrix[[v11],[v12]]

$\label{eq80}\left[ \begin{array}{c} v 11 \ v 12$

(80)

Type: Matrix(Polynomial(Integer))

axiom

A*v

   >> Error detected within library code:
   can't multiply matrices of incompatible dimensions

axiom

A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]

   There are 8 exposed and 4 unexposed library operations named - 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                                )display op -
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named - 
      with argument type(s) 
                             Expression(Integer)
                         Matrix(Expression(Integer))

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]

$\label{eq81}\left[ \begin{array}{c} {{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}} \ {-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}$

(81)

Type: Matrix(Expression(Integer))

axiom

v:=matrix[[v11],[v12]]

$\label{eq82}\left[ \begin{array}{c} v 11 \ v 12$

(82)

Type: Matrix(Polynomial(Integer))

axiom

A*v

   >> Error detected within library code:
   can't multiply matrices of incompatible dimensions

axiom

A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]

   There are 8 exposed and 4 unexposed library operations named - 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                                )display op -
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named - 
      with argument type(s) 
                             Expression(Integer)
                         Matrix(Expression(Integer))

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]

$\label{eq83}\left[ \begin{array}{c} {{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}} \ {-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}$

(83)

Type: Matrix(Expression(Integer))

axiom

v:=matrix[[v11],[v12]]

$\label{eq84}\left[ \begin{array}{c} v 11 \ v 12$

(84)

Type: Matrix(Polynomial(Integer))

axiom

A*v

   >> Error detected within library code:
   can't multiply matrices of incompatible dimensions

axiom

A:=matrix[[cos(x),-sin(x)],[sin(x),cos(x)]]

$\label{eq85}\left[ \begin{array}{cc} {\cos \left({x}\right)}& -{\sin \left({x}\right)} \ {\sin \left({x}\right)}&{\cos \left({x}\right)}$

(85)

Type: Matrix(Expression(Integer))

axiom

D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]

$\label{eq86}\left[ \begin{array}{c} {{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}} \ {-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}$

(86)

Type: Matrix(Expression(Integer))

axiom

v:=matrix[[v11],[v12]]

$\label{eq87}\left[ \begin{array}{c} v 11 \ v 12$

(87)

Type: Matrix(Polynomial(Integer))

axiom

A*v

$\label{eq88}\left[ \begin{array}{c} {-{v 12 \ {\sin \left({x}\right)}}+{v 11 \ {\cos \left({x}\right)}}} \ {{v 11 \ {\sin \left({x}\right)}}+{v 12 \ {\cos \left({x}\right)}}}$

(88)

Type: Matrix(Expression(Integer))

axiom

D(1,1)*v

$\label{eq89}\left[ \begin{array}{c} {{v 11 \ {\sqrt{- 1}}\ {\sin \left({x}\right)}}+{v 11 \ {\cos \left({x}\right)}}} \ {{v 12 \ {\sqrt{- 1}}\ {\sin \left({x}\right)}}+{v 12 \ {\cos \left({x}\right)}}}$

(89)

Type: Matrix(Expression(Integer))

axiom

A*v-D(1,1)*v

$\label{eq90}\left[ \begin{array}{c} {{\left(-{v 11 \ {\sqrt{- 1}}}- v 12 \right)}\ {\sin \left({x}\right)}} \ {{\left(-{v 12 \ {\sqrt{- 1}}}+ v 11 \right)}\ {\sin \left({x}\right)}}$

(90)

Type: Matrix(Expression(Integer))

axiom

A:=matrix[[cos(x),-sin(x)],[sin(x),cos(x)]]

$\label{eq91}\left[ \begin{array}{cc} {\cos \left({x}\right)}& -{\sin \left({x}\right)} \ {\sin \left({x}\right)}&{\cos \left({x}\right)}$

(91)

Type: Matrix(Expression(Integer))

axiom

D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]

$\label{eq92}\left[ \begin{array}{c} {{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}} \ {-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}$

(92)

Type: Matrix(Expression(Integer))

axiom

v:=matrix[[v11],[v12]]

$\label{eq93}\left[ \begin{array}{c} v 11 \ v 12$

(93)

Type: Matrix(Polynomial(Integer))

axiom

A*v

$\label{eq94}\left[ \begin{array}{c} {-{v 12 \ {\sin \left({x}\right)}}+{v 11 \ {\cos \left({x}\right)}}} \ {{v 11 \ {\sin \left({x}\right)}}+{v 12 \ {\cos \left({x}\right)}}}$

(94)

Type: Matrix(Expression(Integer))

axiom

D(1,1)*v

$\label{eq95}\left[ \begin{array}{c} {{v 11 \ {\sqrt{- 1}}\ {\sin \left({x}\right)}}+{v 11 \ {\cos \left({x}\right)}}} \ {{v 12 \ {\sqrt{- 1}}\ {\sin \left({x}\right)}}+{v 12 \ {\cos \left({x}\right)}}}$

(95)

Type: Matrix(Expression(Integer))

axiom

solve(A*v-D(1,1)*v=0,v(1,1))

   There are 3 exposed and 0 unexposed library operations named 
      equation having 2 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                            )display op equation
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named 
      equation with argument type(s) 
                         Matrix(Expression(Integer))
                             NonNegativeInteger

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

axiom

A:=matrix[[cos(x),-sin(x)],[sin(x),cos(x)]]

$\label{eq96}\left[ \begin{array}{cc} {\cos \left({x}\right)}& -{\sin \left({x}\right)} \ {\sin \left({x}\right)}&{\cos \left({x}\right)}$

(96)

Type: Matrix(Expression(Integer))

axiom

D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]

$\label{eq97}\left[ \begin{array}{c} {{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}} \ {-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}$

(97)

Type: Matrix(Expression(Integer))

axiom

v:=matrix[[v11],[v12]]

$\label{eq98}\left[ \begin{array}{c} v 11 \ v 12$

(98)

Type: Matrix(Polynomial(Integer))

axiom

A*v

$\label{eq99}\left[ \begin{array}{c} {-{v 12 \ {\sin \left({x}\right)}}+{v 11 \ {\cos \left({x}\right)}}} \ {{v 11 \ {\sin \left({x}\right)}}+{v 12 \ {\cos \left({x}\right)}}}$

(99)

Type: Matrix(Expression(Integer))

axiom

D(1,1)*v

$\label{eq100}\left[ \begin{array}{c} {{v 11 \ {\sqrt{- 1}}\ {\sin \left({x}\right)}}+{v 11 \ {\cos \left({x}\right)}}} \ {{v 12 \ {\sqrt{- 1}}\ {\sin \left({x}\right)}}+{v 12 \ {\cos \left({x}\right)}}}$

(100)

Type: Matrix(Expression(Integer))

axiom

solve(A*v-D(1,1)*v=0,v11)

   There are 3 exposed and 0 unexposed library operations named 
      equation having 2 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                            )display op equation
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named 
      equation with argument type(s) 
                         Matrix(Expression(Integer))
                             NonNegativeInteger

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

axiom

A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]]

   There are 8 exposed and 4 unexposed library operations named - 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                                )display op -
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named - 
      with argument type(s) 
                             Expression(Integer)
                         Matrix(Expression(Integer))

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]

$\label{eq101}\left[ \begin{array}{c} {{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}} \ {-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}$

(101)

Type: Matrix(Expression(Integer))

axiom

v:=matrix[[v11],[v12]]

$\label{eq102}\left[ \begin{array}{c} v 11 \ v 12$

(102)

Type: Matrix(Polynomial(Integer))

axiom

A*v

$\label{eq103}\left[ \begin{array}{c} {-{v 12 \ {\sin \left({x}\right)}}+{v 11 \ {\cos \left({x}\right)}}} \ {{v 11 \ {\sin \left({x}\right)}}+{v 12 \ {\cos \left({x}\right)}}}$

(103)

Type: Matrix(Expression(Integer))

axiom

D(1,1)*v

$\label{eq104}\left[ \begin{array}{c} {{v 11 \ {\sqrt{- 1}}\ {\sin \left({x}\right)}}+{v 11 \ {\cos \left({x}\right)}}} \ {{v 12 \ {\sqrt{- 1}}\ {\sin \left({x}\right)}}+{v 12 \ {\cos \left({x}\right)}}}$

(104)

Type: Matrix(Expression(Integer))

axiom

A*v-D(1,1)*v

$\label{eq105}\left[ \begin{array}{c} {{\left(-{v 11 \ {\sqrt{- 1}}}- v 12 \right)}\ {\sin \left({x}\right)}} \ {{\left(-{v 12 \ {\sqrt{- 1}}}+ v 11 \right)}\ {\sin \left({x}\right)}}$

(105)

Type: Matrix(Expression(Integer))

axiom

A*v

$\label{eq106}\left[ \begin{array}{c} {-{v 12 \ {\sin \left({x}\right)}}+{v 11 \ {\cos \left({x}\right)}}} \ {{v 11 \ {\sin \left({x}\right)}}+{v 12 \ {\cos \left({x}\right)}}}$

(106)

Type: Matrix(Expression(Integer))

$e^{i\ \pi}=-1$

axiom

A:=matrix[[cos(x),-sin(x)],[sin(x),cos(x)]]

$\label{eq107}\left[ \begin{array}{cc} {\cos \left({x}\right)}& -{\sin \left({x}\right)} \ {\sin \left({x}\right)}&{\cos \left({x}\right)}$

(107)

Type: Matrix(Expression(Integer))

Differential Equations

\begin(axiom) solve(D(y x, x)^2+y x=1,y,x) \end(axiom)

axiom

solve(D(y x, x)^2+y x=1,y,x)

   There are no library operations named y 
      Use HyperDoc Browse or issue
                                 )what op y
      to learn if there is any operation containing " y " in its name.

   Cannot find a definition or applicable library operation named y 
      with argument type(s) 
                                 Variable(x)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

axiom

deq := (x**2 + 1) * D(y x, x, 2) + 3 * x * D(y x, x) + y x = 0

   There are no library operations named y 
      Use HyperDoc Browse or issue
                                 )what op y
      to learn if there is any operation containing " y " in its name.

   Cannot find a definition or applicable library operation named y 
      with argument type(s) 
                                 Variable(x)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
solve(deq, y, x)

   There are 6 exposed and 1 unexposed library operations named solve 
      having 3 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                              )display op solve
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named solve
      with argument type(s) 
                                Variable(deq)
                                 Variable(y)
                                 Variable(x)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

axiom

f(x)=x*2

   There are no library operations named f 
      Use HyperDoc Browse or issue
                                 )what op f
      to learn if there is any operation containing " f " in its name.

   Cannot find a definition or applicable library operation named f 
      with argument type(s) 
                                 Variable(x)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
D(y,x)

   There are 5 exposed and 0 unexposed library operations named D 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                                )display op D
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named D 
      with argument type(s) 
                                 Variable(y)
                                 Variable(x)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
(x**2 + 1) * D(y, x, 2) + 3 * x * D(y, x) + y = 0

   There are 3 exposed and 0 unexposed library operations named D 
      having 3 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                                )display op D
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named D 
      with argument type(s) 
                                 Variable(y)
                                 Variable(x)
                               PositiveInteger

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

axiom

y := operator y

$\label{eq108}y$

(108)

Type: BasicOperator?

axiom

solve(D(y(x),x)-y(x)^2=1,y,x)

   There are 5 exposed and 0 unexposed library operations named D 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                                )display op D
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named D 
      with argument type(s) 
                             Expression(Integer)
                                 Variable(x)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

Just trying to understand the syntax

axiom

solve(a*x^2+b*x+c,x)

$\label{eq109}\left[{x = 0}\right]$

(109)

Type: List(Equation(Expression(Integer)))

axiom

solve(a*x^2+b*x+c=0,x)

   There are 18 exposed and 3 unexposed library operations named solve 
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                              )display op solve
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named solve
      with argument type(s) 
                   Equation(Equation(Expression(Integer)))
                                 Variable(x)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

axiom

zerosOf(a*x^2+b*x+c,x)

   There are 2 exposed and 0 unexposed library operations named zerosOf
      having 2 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                             )display op zerosOf
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named 
      zerosOf with argument type(s) 
                        Equation(Expression(Integer))
                                 Variable(x)

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

axiom

zerosOf(sqrt(h^2+a^2)-a=d,a)

   There are 4 exposed and 1 unexposed library operations named sqrt 
      having 1 argument(s) but none was determined to be applicable. 
      Use HyperDoc Browse, or issue
                              )display op sqrt
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named sqrt 
      with argument type(s) 
                        Equation(Expression(Integer))

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

axiom

solve(x^2+x+1=98,x)

$\label{eq110}\left[{{{x^2}+ x -{97}}= 0}\right]$

(110)

Type: List(Equation(Fraction(Polynomial(Integer))))

axiom

solve(x^2+2*x+1=0,x)

$\label{eq111}\left[{x = - 1}\right]$

(111)

Type: List(Equation(Fraction(Polynomial(Integer))))

Solutions in Expression domain

axiom

solve((x^2+x+1=98)::Equation Expression Integer,x)

$\label{eq112}\left[{x ={{{\sqrt{389}}- 1}\over 2}}, \:{x ={{-{\sqrt{389}}- 1}\over 2}}\right]$

(112)

Type: List(Equation(Expression(Integer)))

axiom

solve((x^3 * b + x^2*(b*d - b + 1) + x*(3*d - b*d - 1) + 2*d^2 - 2*d = 0)::Equation Expression Integer, x)

   Cannot convert from type Equation(Equation(Expression(Integer))) to 
      Equation(Expression(Integer)) for value
      3                 2                         2
   L x  + (L d - L + 1)x  + ((- L + 3)d - 1)x + 2d  - 2d =
           3             2        +---+           3           2
       (- x  + (- d + 1)x  + d x)\|- 1 sin(x) + (x  + (d - 1)x  - d x)cos(x)
     + 
        2                 2
       x  + (3d - 1)x + 2d  - 2d
     =
     0= 0