Edit detail for SandBox2 revision 7 of 12

Indefinite intregral

arctan = atan

integrate(1/atan(x),x)

(1)

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

Definite intregral

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

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

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

(2)

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

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

(3)

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

Solutions of Transcendental Equations

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

(4)

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

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

(5)

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

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

(6)

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

solve(cos(x)=0,x)

(7)

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

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

(8)

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

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

(9)

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

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

(10)

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

Matrices

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

(11)

Type: Matrix(Expression(Integer))

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

(12)

Type: Matrix(Expression(Integer))

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.

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

(13)

Type: Matrix(Expression(Integer))

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

(14)

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

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

(15)

Type: Matrix(Expression(Integer))

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

(16)

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

B(1)

(17)

Type: Equation(Expression(Integer))

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

(18)

Type: Matrix(Expression(Integer))

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

(19)

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

B

(20)

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

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

(21)

Type: Matrix(Expression(Integer))

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

(22)

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

B

(23)

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

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

(24)

Type: Matrix(Expression(Integer))

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

(25)

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

B.1

(26)

Type: Equation(Expression(Integer))

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

(27)

Type: Matrix(Expression(Integer))

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

(28)

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

v:=vector[v11,v12]

(29)

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

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

(30)

Type: Matrix(Expression(Integer))

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

(31)

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

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

(32)

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

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

(33)

Type: Matrix(Expression(Integer))

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

(34)

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

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

(35)

Type: Matrix(Expression(Integer))

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

(36)

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

a

(37)

Type: Equation(Expression(Integer))

b

(38)

Type: Equation(Expression(Integer))

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

(39)

Type: Matrix(Expression(Integer))

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

(40)

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

a

(41)

Type: Equation(Expression(Integer))

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

(42)

Type: Matrix(Expression(Integer))

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

(43)

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

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

(44)

Type: List(Expression(Integer))

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

(45)

Type: Matrix(Expression(Integer))

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

(46)

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

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

(47)

Type: Symbol

Complex Values

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

(48)

Type: Symbol

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

(49)

Type: Symbol

A:=matrix[a,b]

(50)

Type: Symbol

A:=matrix[[a,b]]

(51)

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

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

(52)

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

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

(53)

Type: Symbol

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

(54)

Type: Matrix(Expression(Integer))

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

(55)

Type: Matrix(Expression(Integer))

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

(56)

Type: Matrix(Expression(Integer))

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

(57)

Type: Matrix(Expression(Integer))

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

   There are 8 exposed and 3 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)]]

(58)

Type: Matrix(Expression(Integer))

A*D

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

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

   There are 8 exposed and 3 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)]]

(59)

Type: Matrix(Expression(Integer))

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

(60)

Type: Matrix(Polynomial(Integer))

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

   There are 8 exposed and 3 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)]]

(61)

Type: Matrix(Expression(Integer))

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

(62)

Type: Matrix(Polynomial(Integer))

A*v

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

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

   There are 8 exposed and 3 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)]]

(63)

Type: Matrix(Expression(Integer))

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

(64)

Type: Matrix(Polynomial(Integer))

A*v

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

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

   There are 8 exposed and 3 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)]]

(65)

Type: Matrix(Expression(Integer))

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

(66)

Type: Matrix(Polynomial(Integer))

A*v

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

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

   There are 8 exposed and 3 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)]]

(67)

Type: Matrix(Expression(Integer))

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

(68)

Type: Matrix(Polynomial(Integer))

A*v

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

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

   There are 8 exposed and 3 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)]]

(69)

Type: Matrix(Expression(Integer))

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

(70)

Type: Matrix(Polynomial(Integer))

A*v

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

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

   There are 8 exposed and 3 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)]]

(71)

Type: Matrix(Expression(Integer))

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

(72)

Type: Matrix(Polynomial(Integer))

A*v

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

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

   There are 8 exposed and 3 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)]]

(73)

Type: Matrix(Expression(Integer))

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

(74)

Type: Matrix(Polynomial(Integer))

A*v

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

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

   There are 8 exposed and 3 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)]]

(75)

Type: Matrix(Expression(Integer))

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

(76)

Type: Matrix(Polynomial(Integer))

A*v

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

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

   There are 8 exposed and 3 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)]]

(77)

Type: Matrix(Expression(Integer))

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

(78)

Type: Matrix(Polynomial(Integer))

A*v

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

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

   There are 8 exposed and 3 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)]]

(79)

Type: Matrix(Expression(Integer))

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

(80)

Type: Matrix(Polynomial(Integer))

A*v

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

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

   There are 8 exposed and 3 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)]]

(81)

Type: Matrix(Expression(Integer))

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

(82)

Type: Matrix(Polynomial(Integer))

A*v

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

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

   There are 8 exposed and 3 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)]]

(83)

Type: Matrix(Expression(Integer))

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

(84)

Type: Matrix(Polynomial(Integer))

A*v

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

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

(85)

Type: Matrix(Expression(Integer))

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

(86)

Type: Matrix(Expression(Integer))

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

(87)

Type: Matrix(Polynomial(Integer))

A*v

(88)

Type: Matrix(Expression(Integer))

D(1,1)*v

(89)

Type: Matrix(Expression(Integer))

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

(90)

Type: Matrix(Expression(Integer))

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

(91)

Type: Matrix(Expression(Integer))

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

(92)

Type: Matrix(Expression(Integer))

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

(93)

Type: Matrix(Polynomial(Integer))

A*v

(94)

Type: Matrix(Expression(Integer))

D(1,1)*v

(95)

Type: Matrix(Expression(Integer))

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.

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

(96)

Type: Matrix(Expression(Integer))

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

(97)

Type: Matrix(Expression(Integer))

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

(98)

Type: Matrix(Polynomial(Integer))

A*v

(99)

Type: Matrix(Expression(Integer))

D(1,1)*v

(100)

Type: Matrix(Expression(Integer))

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.

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

   There are 8 exposed and 3 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)]]

(101)

Type: Matrix(Expression(Integer))

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

(102)

Type: Matrix(Polynomial(Integer))

A*v

(103)

Type: Matrix(Expression(Integer))

D(1,1)*v

(104)

Type: Matrix(Expression(Integer))

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

(105)

Type: Matrix(Expression(Integer))

A*v

(106)

Type: Matrix(Expression(Integer))

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

(107)

Type: Matrix(Expression(Integer))

Differential Equations

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

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.

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.

y := operator y

(108)

Type: BasicOperator

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

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

(109)

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

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.

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.

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.

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

(110)

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

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

(111)

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

Solutions in Expression domain

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

(112)

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

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