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Editor: page Time: 2011/03/12 15:43:50 GMT-8
Note: test mathml

added:
\begin{axiom}
)set output tex off
)set output algebra off
)set output mathml on
\end{axiom}

axiom

)set output tex off

axiom

)set output algebra off

axiom

)set output mathml on

Indefinite intregral

arctan = atan

axiom

integrate(1/atan(x),x)

\int \frac{1}{arctan (x)} ⅆ x

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")

\frac{- \sqrt{3} log (3 a^{2} {\sqrt[3]{a^{2}}}^{2} + (- 2 a^{3} + a^{2}) \sqrt[3]{a^{2}} + a^{4} - 2 a^{3}) + 2 \sqrt{3} log ({\sqrt[3]{a^{2}}}^{2} + 2 a \sqrt[3]{a^{2}} + a^{2}) + 12 arctan (\frac{2 \sqrt{3} \sqrt[3]{a^{2}} - a \sqrt{3}}{3 a}) + 2 π}{12 \sqrt{3} \sqrt[3]{a^{2}}}

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

axiom

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

[\frac{- 2 a log (\sqrt{- b}) + a log (\frac{(- 4 b^{2} + 4 b) \sqrt{- b} - b^{3} + 6 b^{2} - b}{b^{2} + 2 b + 1})}{4 \sqrt{- b}}, \frac{a arctan (\frac{\sqrt{b}}{b})}{\sqrt{b}}]?

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

Solutions of Transcendental Equations

axiom

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

[x = 2 arctan (\frac{\sqrt{- y^{2} + 2} + 1}{y + 1}), x = - 2 arctan (\frac{\sqrt{- y^{2} + 2} - 1}{y + 1})]?

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

axiom

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

[y = sin (x) + cos (x)]?

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

axiom

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

[x = 2 arctan (\frac{\sqrt{- y^{2} + 2} + 1}{y + 1}), x = - 2 arctan (\frac{\sqrt{- y^{2} + 2} - 1}{y + 1})]?

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

axiom

solve(cos(x)=0,x)

[x = \frac{π}{2}]?

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

axiom

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

[]?

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

axiom

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

[t1 = 2 arctan (\frac{\sqrt{- c^{2} + b^{2} + a^{2}} + b}{c + a}), t1 = - 2 arctan (\frac{\sqrt{- c^{2} + b^{2} + a^{2}} - b}{c + a})]?

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

axiom

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

[x = 2 arctan (\frac{\sqrt{- y^{2} + 2} + 1}{y + 1}), x = - 2 arctan (\frac{\sqrt{- y^{2} + 2} - 1}{y + 1})]?

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

Matrices

axiom

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

[\begin{matrix} cos (x) - y & - sin (x) \\ sin (x) & cos (x) - y \end{matrix}]?

Type: Matrix(Expression(Integer))

axiom

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

[\begin{matrix} cos (x) - y & - sin (x) \\ sin (x) & cos (x) - y \end{matrix}]?

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]]

[\begin{matrix} cos (x) - L & - sin (x) \\ sin (x) & cos (x) - L \end{matrix}]?

Type: Matrix(Expression(Integer)) B:=solve(A(1,1)A(2,2)-A(2,1)A(1,2)=0,L)

$[L = \sqrt{- 1} sin (x) + cos (x), L = - \sqrt{- 1} sin (x) + cos (x)]?$

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

axiom

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

[\begin{matrix} cos (x) - L & - sin (x) \\ sin (x) & cos (x) - L \end{matrix}]?

Type: Matrix(Expression(Integer)) B=solve(A(1,1)A(2,2)-A(2,1)A(1,2)=0,L)

$[L = \sqrt{- 1} sin (x) + cos (x), L = - \sqrt{- 1} sin (x) + cos (x)]? = [L = \sqrt{- 1} sin (x) + cos (x), L = - \sqrt{- 1} sin (x) + cos (x)]?$

Type: Equation(List(Equation(Expression(Integer)))) B(1)

$L = \sqrt{- 1} sin (x) + cos (x)$

Type: Equation(Expression(Integer))

axiom

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

[\begin{matrix} cos (x) - L & - sin (x) \\ sin (x) & cos (x) - L \end{matrix}]?

Type: Matrix(Expression(Integer)) B=solve(A(1,1)A(2,2)-A(2,1)A(1,2)=0,L)

$[L = \sqrt{- 1} sin (x) + cos (x), L = - \sqrt{- 1} sin (x) + cos (x)]? = [L = \sqrt{- 1} sin (x) + cos (x), L = - \sqrt{- 1} sin (x) + cos (x)]?$

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

$[L = \sqrt{- 1} sin (x) + cos (x), L = - \sqrt{- 1} sin (x) + cos (x)]?$

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

axiom

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

[\begin{matrix} cos (x) - L & - sin (x) \\ sin (x) & cos (x) - L \end{matrix}]?

Type: Matrix(Expression(Integer)) B:=solve(A(1,1)A(2,2)-A(2,1)A(1,2)=0,L)

$[L = \sqrt{- 1} sin (x) + cos (x), L = - \sqrt{- 1} sin (x) + cos (x)]?$

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

$[L = \sqrt{- 1} sin (x) + cos (x), L = - \sqrt{- 1} sin (x) + cos (x)]?$

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

axiom

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

[\begin{matrix} cos (x) - L & - sin (x) \\ sin (x) & cos (x) - L \end{matrix}]?

Type: Matrix(Expression(Integer)) B:=solve(A(1,1)A(2,2)-A(2,1)A(1,2)=0,L)

$[L = \sqrt{- 1} sin (x) + cos (x), L = - \sqrt{- 1} sin (x) + cos (x)]?$

Type: List(Equation(Expression(Integer))) B.1

$L = \sqrt{- 1} sin (x) + cos (x)$

Type: Equation(Expression(Integer))

axiom

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

[\begin{matrix} cos (x) - L & - sin (x) \\ sin (x) & cos (x) - L \end{matrix}]?

Type: Matrix(Expression(Integer)) B:=solve(A(1,1)A(2,2)-A(2,1)A(1,2)=0,L)

$[L = \sqrt{- 1} sin (x) + cos (x), L = - \sqrt{- 1} sin (x) + cos (x)]?$

Type: List(Equation(Expression(Integer))) v:=vector[v11,v12]?

$[v11, v12]?$

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

axiom

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

[\begin{matrix} cos (x) - L & - sin (x) \\ sin (x) & cos (x) - L \end{matrix}]?

Type: Matrix(Expression(Integer)) B:=solve(A(1,1)A(2,2)-A(2,1)A(1,2)=0,L)

$[L = \sqrt{- 1} sin (x) + cos (x), L = - \sqrt{- 1} sin (x) + cos (x)]?$

Type: List(Equation(Expression(Integer))) v:=matrix[[B.1],[B.2]]?

$[\begin{matrix} L = \sqrt{- 1} sin (x) + cos (x) \\ L = - \sqrt{- 1} sin (x) + cos (x) \end{matrix}]?$

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

axiom

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

[\begin{matrix} cos (x) - L & - sin (x) \\ sin (x) & cos (x) - L \end{matrix}]?

Type: Matrix(Expression(Integer)) [a,b]:=solve(A(1,1)A(2,2)-A(2,1)A(1,2)=0,L)

$[L = \sqrt{- 1} sin (x) + cos (x), L = - \sqrt{- 1} sin (x) + cos (x)]?$

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

axiom

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

[\begin{matrix} cos (x) - L & - sin (x) \\ sin (x) & cos (x) - L \end{matrix}]?

Type: Matrix(Expression(Integer)) [a,b]:=solve(A(1,1)A(2,2)-A(2,1)A(1,2)=0,L)

$[L = \sqrt{- 1} sin (x) + cos (x), L = - \sqrt{- 1} sin (x) + cos (x)]?$

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

$L = \sqrt{- 1} sin (x) + cos (x)$

Type: Equation(Expression(Integer)) b

$L = - \sqrt{- 1} sin (x) + cos (x)$

Type: Equation(Expression(Integer))

axiom

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

[\begin{matrix} cos (x) - L & - sin (x) \\ sin (x) & cos (x) - L \end{matrix}]?

Type: Matrix(Expression(Integer)) [a,b]:=solve(A(1,1)A(2,2)-A(2,1)A(1,2)=0,L)

$[L = \sqrt{- 1} sin (x) + cos (x), L = - \sqrt{- 1} sin (x) + cos (x)]?$

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

$L = \sqrt{- 1} sin (x) + cos (x)$

Type: Equation(Expression(Integer))

axiom

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

[\begin{matrix} cos (x) - L & - sin (x) \\ sin (x) & cos (x) - L \end{matrix}]?

Type: Matrix(Expression(Integer)) B:=solve(A(1,1)A(2,2)-A(2,1)A(1,2)=0,L)

$[L = \sqrt{- 1} sin (x) + cos (x), L = - \sqrt{- 1} sin (x) + cos (x)]?$

Type: List(Equation(Expression(Integer))) LA1:=[sqrt(-1)sin(x)+cos(x),-sqrt(-1)sin(x)+cos(x)]?

$[\sqrt{- 1} sin (x) + cos (x), - \sqrt{- 1} sin (x) + cos (x)]?$

Type: List(Expression(Integer))

axiom

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

[\begin{matrix} cos (x) - L & - sin (x) \\ sin (x) & cos (x) - L \end{matrix}]?

Type: Matrix(Expression(Integer)) B:=solve(A(1,1)A(2,2)-A(2,1)A(1,2)=0,L)

$[L = \sqrt{- 1} sin (x) + cos (x), L = - \sqrt{- 1} sin (x) + cos (x)]?$

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

axiom

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

   >> System error:
   Cannot take first of an empty list

Complex Values

axiom

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

   >> System error:
   Cannot take first of an empty list

axiom

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

   >> System error:
   Cannot take first of an empty list

axiom

A:=matrix[a,b]

   >> System error:
   Cannot take first of an empty list

axiom

A:=matrix[[a,b]]

[\begin{matrix} L = \sqrt{- 1} sin (x) + cos (x) & L = - \sqrt{- 1} sin (x) + cos (x) \end{matrix}]?

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

axiom

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

[\begin{matrix} L = \sqrt{- 1} sin (x) + cos (x) \\ L = - \sqrt{- 1} sin (x) + cos (x) \end{matrix}]?

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

axiom

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

   >> System error:
   Cannot take first of an empty list

axiom

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

[\begin{matrix} \sqrt{- 1} sin (x) + cos (x) \\ - \sqrt{- 1} cos (x) sin (x) \end{matrix}]?

Type: Matrix(Expression(Integer))

axiom

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

[\begin{matrix} \sqrt{- 1} sin (x) + cos (x) \\ - \sqrt{- 1} sin (x) + cos (x) \end{matrix}]?

Type: Matrix(Expression(Integer))

axiom

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

[\begin{matrix} \sqrt{- 1} sin (x) + cos (x) \\ - \sqrt{- 1} sin (x) + cos (x) \end{matrix}]?

Type: Matrix(Expression(Integer))

axiom

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

[\begin{matrix} \sqrt{- 1} sin (x) + cos (x) \\ - \sqrt{- 1} sin (x) + cos (x) \end{matrix}]?

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)]]

[\begin{matrix} \sqrt{- 1} sin (x) + cos (x) \\ - \sqrt{- 1} sin (x) + cos (x) \end{matrix}]?

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)]]

[\begin{matrix} \sqrt{- 1} sin (x) + cos (x) \\ - \sqrt{- 1} sin (x) + cos (x) \end{matrix}]?

Type: Matrix(Expression(Integer)) v:=matrix[[v11],[v12]]?

$[\begin{matrix} v11 \\ v12 \end{matrix}]?$

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)]]

[\begin{matrix} \sqrt{- 1} sin (x) + cos (x) \\ - \sqrt{- 1} sin (x) + cos (x) \end{matrix}]?

Type: Matrix(Expression(Integer)) v:=matrix[[v11],[v12]]?

$[\begin{matrix} v11 \\ v12 \end{matrix}]?$

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)]]

[\begin{matrix} \sqrt{- 1} sin (x) + cos (x) \\ - \sqrt{- 1} sin (x) + cos (x) \end{matrix}]?

Type: Matrix(Expression(Integer)) v:=matrix[[v11],[v12]]?

$[\begin{matrix} v11 \\ v12 \end{matrix}]?$

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)]]

[\begin{matrix} \sqrt{- 1} sin (x) + cos (x) \\ - \sqrt{- 1} sin (x) + cos (x) \end{matrix}]?

Type: Matrix(Expression(Integer)) v:=matrix[[v11],[v12]]?

$[\begin{matrix} v11 \\ v12 \end{matrix}]?$

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)]]

[\begin{matrix} \sqrt{- 1} sin (x) + cos (x) \\ - \sqrt{- 1} sin (x) + cos (x) \end{matrix}]?

Type: Matrix(Expression(Integer)) v:=matrix[[v11],[v12]]?

$[\begin{matrix} v11 \\ v12 \end{matrix}]?$

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)]]

[\begin{matrix} \sqrt{- 1} sin (x) + cos (x) \\ - \sqrt{- 1} sin (x) + cos (x) \end{matrix}]?

Type: Matrix(Expression(Integer)) v:=matrix[[v11],[v12]]?

$[\begin{matrix} v11 \\ v12 \end{matrix}]?$

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)]]

[\begin{matrix} \sqrt{- 1} sin (x) + cos (x) \\ - \sqrt{- 1} sin (x) + cos (x) \end{matrix}]?

Type: Matrix(Expression(Integer)) v:=matrix[[v11],[v12]]?

$[\begin{matrix} v11 \\ v12 \end{matrix}]?$

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)]]

[\begin{matrix} \sqrt{- 1} sin (x) + cos (x) \\ - \sqrt{- 1} sin (x) + cos (x) \end{matrix}]?

Type: Matrix(Expression(Integer)) v:=matrix[[v11],[v12]]?

$[\begin{matrix} v11 \\ v12 \end{matrix}]?$

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)]]

[\begin{matrix} \sqrt{- 1} sin (x) + cos (x) \\ - \sqrt{- 1} sin (x) + cos (x) \end{matrix}]?

Type: Matrix(Expression(Integer)) v:=matrix[[v11],[v12]]?

$[\begin{matrix} v11 \\ v12 \end{matrix}]?$

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)]]

[\begin{matrix} \sqrt{- 1} sin (x) + cos (x) \\ - \sqrt{- 1} sin (x) + cos (x) \end{matrix}]?

Type: Matrix(Expression(Integer)) v:=matrix[[v11],[v12]]?

$[\begin{matrix} v11 \\ v12 \end{matrix}]?$

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)]]

[\begin{matrix} \sqrt{- 1} sin (x) + cos (x) \\ - \sqrt{- 1} sin (x) + cos (x) \end{matrix}]?

Type: Matrix(Expression(Integer)) v:=matrix[[v11],[v12]]?

$[\begin{matrix} v11 \\ v12 \end{matrix}]?$

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)]]

[\begin{matrix} \sqrt{- 1} sin (x) + cos (x) \\ - \sqrt{- 1} sin (x) + cos (x) \end{matrix}]?

Type: Matrix(Expression(Integer)) v:=matrix[[v11],[v12]]?

$[\begin{matrix} v11 \\ v12 \end{matrix}]?$

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)]]

[\begin{matrix} \sqrt{- 1} sin (x) + cos (x) \\ - \sqrt{- 1} sin (x) + cos (x) \end{matrix}]?

Type: Matrix(Expression(Integer)) v:=matrix[[v11],[v12]]?

$[\begin{matrix} v11 \\ v12 \end{matrix}]?$

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)]]

[\begin{matrix} cos (x) & - sin (x) \\ sin (x) & cos (x) \end{matrix}]?

Type: Matrix(Expression(Integer)) D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]?

$[\begin{matrix} \sqrt{- 1} sin (x) + cos (x) \\ - \sqrt{- 1} sin (x) + cos (x) \end{matrix}]?$

Type: Matrix(Expression(Integer)) v:=matrix[[v11],[v12]]?

$[\begin{matrix} v11 \\ v12 \end{matrix}]?$

Type: Matrix(Polynomial(Integer)) A*v

$[\begin{matrix} - v12 sin (x) + v11 cos (x) \\ v11 sin (x) + v12 cos (x) \end{matrix}]?$

Type: Matrix(Expression(Integer)) D(1,1)*v

$[\begin{matrix} v11 \sqrt{- 1} sin (x) + v11 cos (x) \\ v12 \sqrt{- 1} sin (x) + v12 cos (x) \end{matrix}]?$

Type: Matrix(Expression(Integer)) Av-D(1,1)v

$[\begin{matrix} (- v11 \sqrt{- 1} - v12) sin (x) \\ (- v12 \sqrt{- 1} + v11) sin (x) \end{matrix}]?$

Type: Matrix(Expression(Integer))

axiom

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

[\begin{matrix} cos (x) & - sin (x) \\ sin (x) & cos (x) \end{matrix}]?

Type: Matrix(Expression(Integer)) D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]?

$[\begin{matrix} \sqrt{- 1} sin (x) + cos (x) \\ - \sqrt{- 1} sin (x) + cos (x) \end{matrix}]?$

Type: Matrix(Expression(Integer)) v:=matrix[[v11],[v12]]?

$[\begin{matrix} v11 \\ v12 \end{matrix}]?$

Type: Matrix(Polynomial(Integer)) A*v

$[\begin{matrix} - v12 sin (x) + v11 cos (x) \\ v11 sin (x) + v12 cos (x) \end{matrix}]?$

Type: Matrix(Expression(Integer)) D(1,1)*v

$[\begin{matrix} v11 \sqrt{- 1} sin (x) + v11 cos (x) \\ v12 \sqrt{- 1} sin (x) + v12 cos (x) \end{matrix}]?$

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)]]

[\begin{matrix} cos (x) & - sin (x) \\ sin (x) & cos (x) \end{matrix}]?

Type: Matrix(Expression(Integer)) D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]?

$[\begin{matrix} \sqrt{- 1} sin (x) + cos (x) \\ - \sqrt{- 1} sin (x) + cos (x) \end{matrix}]?$

Type: Matrix(Expression(Integer)) v:=matrix[[v11],[v12]]?

$[\begin{matrix} v11 \\ v12 \end{matrix}]?$

Type: Matrix(Polynomial(Integer)) A*v

$[\begin{matrix} - v12 sin (x) + v11 cos (x) \\ v11 sin (x) + v12 cos (x) \end{matrix}]?$

Type: Matrix(Expression(Integer)) D(1,1)*v

$[\begin{matrix} v11 \sqrt{- 1} sin (x) + v11 cos (x) \\ v12 \sqrt{- 1} sin (x) + v12 cos (x) \end{matrix}]?$

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)]]

[\begin{matrix} \sqrt{- 1} sin (x) + cos (x) \\ - \sqrt{- 1} sin (x) + cos (x) \end{matrix}]?

Type: Matrix(Expression(Integer)) v:=matrix[[v11],[v12]]?

$[\begin{matrix} v11 \\ v12 \end{matrix}]?$

Type: Matrix(Polynomial(Integer)) A*v

$[\begin{matrix} - v12 sin (x) + v11 cos (x) \\ v11 sin (x) + v12 cos (x) \end{matrix}]?$

Type: Matrix(Expression(Integer)) D(1,1)*v

$[\begin{matrix} v11 \sqrt{- 1} sin (x) + v11 cos (x) \\ v12 \sqrt{- 1} sin (x) + v12 cos (x) \end{matrix}]?$

Type: Matrix(Expression(Integer)) Av-D(1,1)v

$[\begin{matrix} (- v11 \sqrt{- 1} - v12) sin (x) \\ (- v12 \sqrt{- 1} + v11) sin (x) \end{matrix}]?$

Type: Matrix(Expression(Integer))

axiom

A*v

[\begin{matrix} - v12 sin (x) + v11 cos (x) \\ v11 sin (x) + v12 cos (x) \end{matrix}]?

Type: Matrix(Expression(Integer))

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

axiom

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

[\begin{matrix} cos (x) & - sin (x) \\ sin (x) & cos (x) \end{matrix}]?

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

y

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)

[x = 0]?

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)

[x^{2} + x - 97 = 0]?

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

axiom

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

[x = - 1]?

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

Solutions in Expression domain

axiom

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

[x = \frac{\sqrt{389} - 1}{2}, x = \frac{- \sqrt{389} - 1}{2}]?

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