MathAction SandBox2

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  - SandBox2 <-- You are here.

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(1) -> )set output tex on

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)set output algebra off

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)set output mathml off

Indefinite intregral

arctan = atan

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integrate(1/atan(x),x)

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

(1)

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

Definite intregral

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

$\label{eq2}\frac{-{{\sqrt{3}}\ {\log \left({{3 \ {{a}^{2}}\ {{\root{3}\of{{a}^{2}}}^{2}}}+{{\left(-{2 \ {{a}^{3}}}+{{a}^{2}}\right)}\ {\root{3}\of{{a}^{2}}}}+{{a}^{4}}-{2 \ {{a}^{3}}}}\right)}}+{2 \ {\sqrt{3}}\ {\log \left({{{\root{3}\of{{a}^{2}}}^{2}}+{2 \ a \ {\root{3}\of{{a}^{2}}}}+{{a}^{2}}}\right)}}+{{12}\ {\arctan \left({\frac{{2 \ {\sqrt{3}}\ {\root{3}\of{{a}^{2}}}}-{a \ {\sqrt{3}}}}{3 \ a}}\right)}}+{{\sqrt{3}}\ {\log \left({{a}^{4}}\right)}}-{2 \ {\sqrt{3}}\ {\log \left({{a}^{2}}\right)}}+{2 \ \pi}}{{12}\ {\sqrt{3}}\ {\root{3}\of{{a}^{2}}}}$

(2)

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

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

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

(3)

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

Solutions of Transcendental Equations

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

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

(4)

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

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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)))

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

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

(6)

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

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solve(cos(x)=0,x)

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

(7)

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

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

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

(8)

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

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

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

(9)

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

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

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

(10)

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

Matrices

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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))

There is no matrix solve:

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solve(A=0,y)

   There are 20 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.

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

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

(12)

Type: Matrix(Expression(Integer))

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

$\label{eq13}\left[{L ={{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}, \:{L ={-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}\right]$

(13)

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

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B(1)

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

(14)

Type: Equation(Expression(Integer))

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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))

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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))))

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B(1)

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

(17)

Type: Equation(Expression(Integer))

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v:=vector[v11,v12]

$\label{eq18}\left[ v 11, \: v 12 \right]$

(18)

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

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

$\label{eq19}\left[ \begin{array}{c} {L ={{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}} \ {L ={-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}$

(19)

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

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

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

(20)

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

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$\label{eq21}L ={{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}$

(21)

Type: Equation(Expression(Integer))

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

(22)

Type: Equation(Expression(Integer))

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

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

(23)

Type: List(Expression(Integer))

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

$\label{eq24}\left[ \begin{array}{cc} {{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}&{-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}$

(24)

Type: Matrix(Expression(Integer))

Complex Values

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

$\label{eq25}\left[ \begin{array}{c} {{\sqrt{- 1}}\ {\sin \left({x}\right)}}$

(25)

Type: Matrix(Expression(Integer))

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

$\label{eq26}\left[ \begin{array}{c} {{\cos \left({x}\right)}- L}$

(26)

Type: Matrix(Expression(Integer))

Due to mismatched type the following produces scripted symbol!

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A:=matrix[a,b]

$\label{eq27}matrix_{{L ={{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}, \:{L ={-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}}$

(27)

Type: Symbol

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A:=matrix[[a,b]]

$\label{eq28}\left[ \begin{array}{cc} {L ={{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}&{L ={-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}$

(28)

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

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

$\label{eq29}\left[ \begin{array}{c} {L ={{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}} \ {L ={-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}$

(29)

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

Again, due to mismatched types we get scripted symbol!

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

$\label{eq30}matrix_{{\left[{{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}\right]}, \:{\left[{L ={-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}}\right]}}$

(30)

Type: Symbol

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

$\label{eq31}\left[ \begin{array}{c} {{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}} \ -{{\sqrt{- 1}}\ {\cos \left({x}\right)}\ {\sin \left({x}\right)}}$

(31)

Type: Matrix(Expression(Integer))

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

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

(32)

Type: Matrix(Expression(Integer))

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

$\label{eq33}\left[ \begin{array}{c} {{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}} \ {-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}$

(33)

Type: Matrix(Expression(Integer))

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

$\label{eq34}\left[ \begin{array}{cc} {{\cos \left({x}\right)}- L}& -{\sin \left({x}\right)} \ {\sin \left({x}\right)}&{{\cos \left({x}\right)}- L}$

(34)

Type: Matrix(Expression(Integer))

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

$\label{eq35}\left[ \begin{array}{c} {{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}} \ {-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}$

(35)

Type: Matrix(Expression(Integer))

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A*D

$\label{eq36}\left[ \begin{array}{c} {{{\sqrt{- 1}}\ {{\sin \left({x}\right)}^{2}}}+{{\left({{\left({\sqrt{- 1}}- 1 \right)}\ {\cos \left({x}\right)}}-{L \ {\sqrt{- 1}}}\right)}\ {\sin \left({x}\right)}}+{{\cos \left({x}\right)}^{2}}-{L \ {\cos \left({x}\right)}}} \ {{{\sqrt{- 1}}\ {{\sin \left({x}\right)}^{2}}}+{{\left({{\left(-{\sqrt{- 1}}+ 1 \right)}\ {\cos \left({x}\right)}}+{L \ {\sqrt{- 1}}}\right)}\ {\sin \left({x}\right)}}+{{\cos \left({x}\right)}^{2}}-{L \ {\cos \left({x}\right)}}}$

(36)

Type: Matrix(Expression(Integer))

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

$\label{eq37}\left[ \begin{array}{c} v 11 \ v 12$

(37)

Type: Matrix(Polynomial(Integer))

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A*v

$\label{eq38}\left[ \begin{array}{c} {-{v 12 \ {\sin \left({x}\right)}}+{v 11 \ {\cos \left({x}\right)}}-{L \ v 11}} \ {{v 11 \ {\sin \left({x}\right)}}+{v 12 \ {\cos \left({x}\right)}}-{L \ v 12}}$

(38)

Type: Matrix(Expression(Integer))

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D(1,1)*v

$\label{eq39}\left[ \begin{array}{c} {{v 11 \ {\sqrt{- 1}}\ {\sin \left({x}\right)}}+{v 11 \ {\cos \left({x}\right)}}} \ {{v 12 \ {\sqrt{- 1}}\ {\sin \left({x}\right)}}+{v 12 \ {\cos \left({x}\right)}}}$

(39)

Type: Matrix(Expression(Integer))

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solve([w = 0 for w in parts(A*v - D(1,1)*v)], [v11, v12])

$\label{eq40}\left[{\left[{v 11 = 0}, \:{v 12 = 0}\right]}\right]$

(40)

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

Note that the following does not work:

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solve(A*vA*v=D(1,1)*v,v)

   There are 20 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(Matrix(Expression(Integer)))
                         Matrix(Polynomial(Integer))

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

despite possibility of creating matrix equations:

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A*vA*v=D(1,1)*v

$\label{eq41}\begin{array}{@{}l} \displaystyle {\left[ \begin{array}{c} {-{v 12 \ vA \ {\sin \left({x}\right)}}+{v 11 \ vA \ {\cos \left({x}\right)}}-{L \ v 11 \ vA}} \ {{v 11 \ vA \ {\sin \left({x}\right)}}+{v 12 \ vA \ {\cos \left({x}\right)}}-{L \ v 12 \ vA}}$

(41)

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

Undetermined example:

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

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

(42)

Type: Matrix(Expression(Integer))

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

$\label{eq43}\left[ \begin{array}{c} {{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}} \ {-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}$

(43)

Type: Matrix(Expression(Integer))

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

$\label{eq44}\left[ \begin{array}{c} v 11 \ v 12$

(44)

Type: Matrix(Polynomial(Integer))

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A*v

$\label{eq45}\left[ \begin{array}{c} {-{v 12 \ {\sin \left({x}\right)}}+{v 11 \ {\cos \left({x}\right)}}} \ {{v 11 \ {\sin \left({x}\right)}}+{v 12 \ {\cos \left({x}\right)}}}$

(45)

Type: Matrix(Expression(Integer))

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D(1,1)*v

$\label{eq46}\left[ \begin{array}{c} {{v 11 \ {\sqrt{- 1}}\ {\sin \left({x}\right)}}+{v 11 \ {\cos \left({x}\right)}}} \ {{v 12 \ {\sqrt{- 1}}\ {\sin \left({x}\right)}}+{v 12 \ {\cos \left({x}\right)}}}$

(46)

Type: Matrix(Expression(Integer))

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

$\label{eq47}\left[ \begin{array}{c} {{\left(-{v 11 \ {\sqrt{- 1}}}- v 12 \right)}\ {\sin \left({x}\right)}} \ {{\left(-{v 12 \ {\sqrt{- 1}}}+ v 11 \right)}\ {\sin \left({x}\right)}}$

(47)

Type: Matrix(Expression(Integer))

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solve([w = 0 for w in parts(A*v-D(1,1)*v)], [v11, v12])

$\label{eq48}\left[{\left[{v 11 = -{\frac{\%BP}{\sqrt{- 1}}}}, \:{v 12 = \%BP}\right]}\right]$

(48)

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

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

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

$\label{eq49}\left[ \begin{array}{cc} {\cos \left({x}\right)}& -{\sin \left({x}\right)} \ {\sin \left({x}\right)}&{\cos \left({x}\right)}$

(49)

Type: Matrix(Expression(Integer))

Differential Equations

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)clear all

   All user variables and function definitions have been cleared.
y := operator 'y

$\label{eq50}y$

(50)

Type: BasicOperator?

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

   >> Error detected within library code:
   getlincoeff: not an appropriate ordinary differential equation

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

$\label{eq51}{{{\left({{x}^{2}}+ 1 \right)}\ {{y^{\prime \prime}}\left({x}\right)}}+{3 \ x \ {{y^{\prime}}\left({x}\right)}}+{y \left({x}\right)}}= 0$

(51)

Type: Equation(Expression(Integer))

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solve(deq, y, x)

$\label{eq52}\begin{array}{@{}l} \displaystyle \left[{particular = 0}, \: \right. \ \ \displaystyle \left.{basis ={\left[{\frac{1}{\sqrt{{{x}^{2}}+ 1}}}, \:{\frac{\log \left({{\sqrt{{{x}^{2}}+ 1}}- x}\right)}{\sqrt{{{x}^{2}}+ 1}}}\right]}}\right]$

(52)

Type: Union(Record(particular: Expression(Integer),basis: List(Expression(Integer))),...)

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

$\label{eq53}{\arctan \left({y \left({x}\right)}\right)}- x$

(53)

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

Just trying to understand the syntax

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

$\label{eq54}\left[{{{a \ {{x}^{2}}}+{b \ x}+ c}= 0}\right]$

(54)

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

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

$\label{eq55}\left[{{{a \ {{x}^{2}}}+{b \ x}+ c}= 0}\right]$

(55)

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

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

$\label{eq56}\left[{\frac{{\sqrt{-{4 \ a \ c}+{{b}^{2}}}}- b}{2 \ a}}, \:{\frac{-{\sqrt{-{4 \ a \ c}+{{b}^{2}}}}- b}{2 \ a}}\right]$

(56)

Type: List(Expression(Integer))

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

   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(a)

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

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

$\label{eq57}\left[{{{{x}^{2}}+ x -{97}}= 0}\right]$

(57)

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

fricas

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

$\label{eq58}\left[{x = - 1}\right]$

(58)

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

Solutions in Expression domain

fricas

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

$\label{eq59}\left[{x ={\frac{{\sqrt{389}}- 1}{2}}}, \:{x ={\frac{-{\sqrt{3 89}}- 1}{2}}}\right]$

(59)

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

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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)

$\label{eq60}\begin{array}{@{}l} \displaystyle \left[{x = \%x 19}, \: \right. \ \ \displaystyle \left.{ \begin{array}{@{}l} \displaystyle x = \ \ \displaystyle {\frac{{\sqrt{-{3 \ {{b}^{2}}\ {{\%x 19}^{2}}}+{{\left(-{2 \ {{b}^{2}}\ d}+{2 \ {{b}^{2}}}-{2 \ b}\right)}\ \%x 19}+{{{b}^{2}}\ {{d}^{2}}}+{{\left({2 \ {{b}^{2}}}-{{10}\ b}\right)}\ d}+{{b}^{2}}+{2 \ b}+ 1}}-{b \ \%x 19}-{b \ d}+ b - 1}{2 \ b}}$

(60)

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