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fricas
)set output tex on
 
fricas
)set output algebra off
 
fricas
)set output mathml off

Indefinite intregral

arctan = atan

fricas
integrate(1/atan(x),x)

\label{eq1}\int^{
\displaystyle
x}{{1 \over{\arctan \left({\%A}\right)}}\ {d \%A}}(1)
Type: Union(Expression(Integer),...)

Definite intregral

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

\label{eq2}{\left(
\begin{array}{@{}l}
\displaystyle
-{{\sqrt{3}}\ {\log{\left({{3 \ {{a}^{2}}\ {{\root{3}\of{{a}^{2}}}^{2}}}+{{\left(-{2 \ {{a}^{3}}}+{{a}^{2}}\right)}\ {\root{3}\of{{a}^{2}}}}+{{a}^{4}}-{2 \ {{a}^{3}}}}\right)}}}+{2 \ {\sqrt{3}}\ {\log \left({{{\root{3}\of{{a}^{2}}}^{2}}+{2 \  a \ {\root{3}\of{{a}^{2}}}}+{{a}^{2}}}\right)}}+ 
\
\
\displaystyle
{{12}\ {\arctan \left({{{2 \ {\sqrt{3}}\ {\root{3}\of{{a}^{2}}}}-{a \ {\sqrt{3}}}}\over{3 \  a}}\right)}}+{2 \  \pi}
(2)
Type: Union(f1: OrderedCompletion?(Expression(Integer)),...)

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

\label{eq3}\begin{array}{@{}l}
\displaystyle
\left[{{\left(
\begin{array}{@{}l}
\displaystyle
-{2 \  a \ {\log \left({\sqrt{- b}}\right)}}+ 
\
\
\displaystyle
{a \ {\log \left({{{{\left(-{4 \ {{b}^{2}}}+{4 \  b}\right)}\ {\sqrt{- b}}}-{{b}^{3}}+{6 \ {{b}^{2}}}- b}\over{{{b}^{2}}+{2 \  b}+ 1}}\right)}}
(3)
Type: Union(f2: List(OrderedCompletion?(Expression(Integer))),...)

Solutions of Transcendental Equations

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

\label{eq4}\begin{array}{@{}l}
\displaystyle
\left[{x ={2 \ {\arctan \left({{{\sqrt{-{{y}^{2}}+ 2}}+ 1}\over{y + 1}}\right)}}}, \: \right.
\
\
\displaystyle
\left.{x = -{2 \ {\arctan \left({{{\sqrt{-{{y}^{2}}+ 2}}- 1}\over{y + 1}}\right)}}}\right] 
(4)
Type: List(Equation(Expression(Integer)))

fricas
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)))

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

\label{eq6}\begin{array}{@{}l}
\displaystyle
\left[{x ={2 \ {\arctan \left({{{\sqrt{-{{y}^{2}}+ 2}}+ 1}\over{y + 1}}\right)}}}, \: \right.
\
\
\displaystyle
\left.{x = -{2 \ {\arctan \left({{{\sqrt{-{{y}^{2}}+ 2}}- 1}\over{y + 1}}\right)}}}\right] 
(6)
Type: List(Equation(Expression(Integer)))

fricas
solve(cos(x)=0,x)

\label{eq7}\left[{x ={\pi \over 2}}\right](7)
Type: List(Equation(Expression(Integer)))

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

\label{eq8}\left[ \right](8)
Type: List(Equation(Expression(Integer)))

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

\label{eq9}\begin{array}{@{}l}
\displaystyle
\left[{t 1 ={2 \ {\arctan \left({{{\sqrt{-{{c}^{2}}+{{b}^{2}}+{{a}^{2}}}}+ b}\over{c + a}}\right)}}}, \: \right.
\
\
\displaystyle
\left.{t 1 = -{2 \ {\arctan \left({{{\sqrt{-{{c}^{2}}+{{b}^{2}}+{{a}^{2}}}}- b}\over{c + a}}\right)}}}\right] 
(9)
Type: List(Equation(Expression(Integer)))

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

\label{eq10}\begin{array}{@{}l}
\displaystyle
\left[{x ={2 \ {\arctan \left({{{\sqrt{-{{y}^{2}}+ 2}}+ 1}\over{y + 1}}\right)}}}, \: \right.
\
\
\displaystyle
\left.{x = -{2 \ {\arctan \left({{{\sqrt{-{{y}^{2}}+ 2}}- 1}\over{y + 1}}\right)}}}\right] 
(10)
Type: List(Equation(Expression(Integer)))

Matrices

fricas
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:

fricas
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.

fricas
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))
fricas
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)))
fricas
B(1)

\label{eq14}L ={{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}(14)
Type: Equation(Expression(Integer))

fricas
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))
fricas
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))))
fricas
B(1)

\label{eq17}L ={{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}(17)
Type: Equation(Expression(Integer))

fricas
v:=vector[v11,v12]

\label{eq18}\left[ v 11, \: v 12 \right](18)
Type: Vector(OrderedVariableList([v11,v12]))
fricas
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)))
fricas
[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)))
fricas
a

\label{eq21}L ={{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}(21)
Type: Equation(Expression(Integer))
fricas
b

\label{eq22}L ={-{{\sqrt{- 1}}\ {\sin \left({x}\right)}}+{\cos \left({x}\right)}}(22)
Type: Equation(Expression(Integer))

fricas
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))

fricas
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

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

\label{eq25}\left[ 
\begin{array}{c}
{{\sqrt{- 1}}\ {\sin \left({x}\right)}}
(25)
Type: Matrix(Expression(Integer))

fricas
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!

fricas
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

fricas
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)))

fricas
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!

fricas
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

fricas
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))

fricas
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))

fricas
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))

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

\label{eq37}\left[ 
\begin{array}{c}
v 11 
\
v 12 
(37)
Type: Matrix(Polynomial(Integer))
fricas
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))
fricas
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))
fricas
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:

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

fricas
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:

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

\label{eq44}\left[ 
\begin{array}{c}
v 11 
\
v 12 
(44)
Type: Matrix(Polynomial(Integer))
fricas
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))
fricas
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))
fricas
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))
fricas
solve([w = 0 for w in parts(A*v-D(1,1)*v)], [v11, v12])

\label{eq48}\left[{\left[{v 11 = -{\%CI \over{\sqrt{- 1}}}}, \:{v 12 = \%CI}\right]}\right](48)
Type: List(List(Equation(Expression(Integer))))


e^{i\ \pi}=-1
 

fricas
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

fricas
)clear all
All user variables and function definitions have been cleared. y := operator 'y

\label{eq50}y(50)
fricas
solve(D(y x, x)^2+y x=1,y,x)
>> Error detected within library code: getlincoeff: not an appropriate ordinary differential equation

fricas
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_{\verb#" "#}^{, ,}}\left({x}\right)}}+{3 \  x \ {{y_{\verb#" "#}^{,}}\left({x}\right)}}+{y \left({x}\right)}}= 0(51)
Type: Equation(Expression(Integer))
fricas
solve(deq, y, x)

\label{eq52}\left[{particular = 0}, \:{basis ={\left[{1 \over{\sqrt{{{x}^{2}}+ 1}}}, \:{{\log \left({{\sqrt{{{x}^{2}}+ 1}}- x}\right)}\over{\sqrt{{{x}^{2}}+ 1}}}\right]}}\right](52)
Type: Union(Record(particular: Expression(Integer),basis: List(Expression(Integer))),...)

fricas
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

fricas
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))))

fricas
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))))

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

\label{eq56}\left[{{{\sqrt{-{4 \  a \  c}+{{b}^{2}}}}- b}\over{2 \  a}}, \:{{-{\sqrt{-{4 \  a \  c}+{{b}^{2}}}}- b}\over{2 \  a}}\right](56)
Type: List(Expression(Integer))

fricas
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.

fricas
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 ={{{\sqrt{389}}- 1}\over 2}}, \:{x ={{-{\sqrt{389}}- 1}\over 2}}\right](59)
Type: List(Equation(Expression(Integer)))

fricas
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 ={{\left(
\begin{array}{@{}l}
\displaystyle
{\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}}- 
\
\
\displaystyle
{b \  \%x 19}-{b \  d}+ b - 1 
(60)
Type: List(Equation(Expression(Integer)))




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