Edit detail for SandBox2 revision 10 of 12
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Editor: test1
Time: 2013/04/30 17:19:44 GMT+0 |
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| Note: | ||
changed: -\begin{axiom} -A:=matrix[[cos(x)-y,-sin(x)],[sin(x),cos(x)-y]] Tere is no matrix solve: \begin{axiom} changed: -\end{axiom} B(1) \end{axiom} removed: -A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]] -B=solve(A(1,1)*A(2,2)-A(2,1)*A(1,2)=0,L) -B -\end{axiom} - -\begin{axiom} -A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]] -B:=solve(A(1,1)*A(2,2)-A(2,1)*A(1,2)=0,L) -B -\end{axiom} - -\begin{axiom} -A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]] -B:=solve(A(1,1)*A(2,2)-A(2,1)*A(1,2)=0,L) -B.1 -\end{axiom} - -\begin{axiom} -A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]] -B:=solve(A(1,1)*A(2,2)-A(2,1)*A(1,2)=0,L) removed: -\end{axiom} - -\begin{axiom} -A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]] -B:=solve(A(1,1)*A(2,2)-A(2,1)*A(1,2)=0,L) removed: -\end{axiom} - -\begin{axiom} -A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]] -[a,b]:=solve(A(1,1)*A(2,2)-A(2,1)*A(1,2)=0,L) -\end{axiom} - -\begin{axiom} -A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]] removed: -A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]] -[a,b]:=solve(A(1,1)*A(2,2)-A(2,1)*A(1,2)=0,L) -a -\end{axiom} - -\begin{axiom} -A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]] -B:=solve(A(1,1)*A(2,2)-A(2,1)*A(1,2)=0,L) changed: -A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]] -B:=solve(A(1,1)*A(2,2)-A(2,1)*A(1,2)=0,L) -LA1:=matrix[sqrt(-1)*sin(x)+cos(x),-sqrt(-1)*sin(x)+cos(x)] -\end{axiom} LA1:=matrix[[sqrt(-1)*sin(x)+cos(x),-sqrt(-1)*sin(x)+cos(x)]] \end{axiom} changed: -LA1:=matrix[sqrt(-1)*sin(x)] -\end{axiom} - -\begin{axiom} -A:=matrix[cos(x)-L] -\end{axiom} - LA1:=matrix[[sqrt(-1)*sin(x)]] \end{axiom} \begin{axiom} A:=matrix[[cos(x)-L]] \end{axiom} The following produces scripted symbol! added: Again, we get scripted symbol! removed: - -\begin{axiom} -L:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]] -\end{axiom} removed: -\end{axiom} - -\begin{axiom} -A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]] -D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]] -v:=matrix[[v11],[v12]] -\end{axiom} - -\begin{axiom} -A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]] -D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]] -v:=matrix[[v11],[v12]] -A*v -D(1)*v -\end{axiom} - -\begin{axiom} -A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]] -D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]] changed: -\end{axiom} - -\begin{axiom} -A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]] -D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]] -v:=matrix[[v11],[v12]] -A*v -D(1,1)*v -solve(A*v=D(1,1)3v,v11) -\end{axiom} - -\begin{axiom} -A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]] -D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]] -v:=matrix[[v11],[v12]] -A*v -D(1,1)*v -solve(A*v=D(1,1)*v,v11) -\end{axiom} - -\begin{axiom} -A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]] -D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]] -v:=matrix[[v11],[v12]] -A*v -D(1,1)*v -A*v=D(1,1)*v -\end{axiom} - -\begin{axiom} -A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]] -D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]] -v:=matrix[[v11],[v12]] -A*v -D(1,1)*v -solve(A*v=D(1,1)*v,v11) -\end{axiom} - -\begin{axiom} -A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]] -D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]] -v:=matrix[[v11],[v12]] -A*v -D(1,1)*v -solve(A*v=D(1,1)*v,v) -\end{axiom} - -\begin{axiom} -A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]] -D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]] -v:=matrix[[v11],[v12]] -A*v -D(1,1)*v -solve((A-D(1,1))v=0,v) -\end{axiom} - -\begin{axiom} -A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]] -D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]] -v:=matrix[[v11],[v12]] -A*v -D(1,1)*v -A*v-D(1,1)*v=0 -\end{axiom} - -\begin{axiom} -A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]] -D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]] -v:=matrix[[v11],[v12]] -A*v -D(1,1)*v -A*v-D(1,1)*v=0 -\end{axiom} - -\begin{axiom} -A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]] -D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]] -v:=matrix[[v11],[v12]] -A*v -D(1,1)*v -A*v-D(1,1)*v=0 -\end{axiom} - -\begin{axiom} -A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]] -D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]] -v:=matrix[[v11],[v12]] -A*v -D(1,1)*v -A*v-D(1,1)*v -\end{axiom} - solve([w = 0 for w in parts(A*v - D(1,1)*v)], [v11, v12]) \end{axiom} Note that the following does not work: \begin{axiom} solve(A*vA*v=D(1,1)*v,v) solve((A-D(1,1))*v=0,v) \end{axiom} despite possibility of creating matrix equations: \begin{axiom} A*vA*v=D(1,1)*v \end{axiom} Undetermined example: changed: -\end{axiom} - -\begin{axiom} -A:=matrix[[cos(x),-sin(x)],[sin(x),cos(x)]] -D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]] -v:=matrix[[v11],[v12]] -A*v -D(1,1)*v -solve(A*v-D(1,1)*v=0,v(1,1)) -\end{axiom} - -\begin{axiom} -A:=matrix[[cos(x),-sin(x)],[sin(x),cos(x)]] -D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]] -v:=matrix[[v11],[v12]] -A*v -D(1,1)*v -solve(A*v-D(1,1)*v=0,v11) -\end{axiom} - -\begin{axiom} -A:=matrix[[cos(x)-L,-sin(x)],[sin(x),cos(x)-L]] -D:=matrix[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]] -v:=matrix[[v11],[v12]] -A*v -D(1,1)*v -A*v-D(1,1)*v -\end{axiom} - -\begin{axiom} -A*v -\end{axiom} solve([w = 0 for w in parts(A*v-D(1,1)*v)], [v11, v12]) \end{axiom} changed: -\begin(axiom) \begin{axiom} )clear all y := operator 'y changed: -\end(axiom) - -\begin{axiom} -solve(D(y x, x)^2+y x=1,y,x) -\end{axiom} - -\begin{axiom} -deq := (x**2 + 1) * D(y x, x, 2) + 3 * x * D(y x, x) + y x = 0 \end{axiom} \begin{axiom} deq := (x^2 + 1) * D(y x, x, 2) + 3 * x * D(y x, x) + y x = 0 removed: -f(x)=x*2 -D(y,x) -(x**2 + 1) * D(y, x, 2) + 3 * x * D(y, x) + y = 0 -\end{axiom} - -\begin{axiom} -y := operator y
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)set output tex on
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)set output algebra off
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)set output mathml off
Indefinite intregral
arctan = atan
fricas
integrate(1/atan(x),x)
 | (1) |
Type: Union(Expression(Integer),
Definite intregral
fricas
integrate(1/(a+z^3),z=0..1, "noPole");
Type: Union(f1: OrderedCompletion?(Expression(Integer)),
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}](images/1235263094229162541-16.0px.png "\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)}}](images/7839913523987526616-16.0px.png "\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]](images/3896584577681173115-16.0px.png "\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]](images/712053455446202497-16.0px.png "\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]](images/7079529620546141649-16.0px.png "\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]](images/3443005033297865073-16.0px.png "\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]](images/1204202700703939827-16.0px.png "\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]](images/8146113657743882150-16.0px.png "\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]](images/2337382471770170389-16.0px.png "\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}](images/6357058329757158999-16.0px.png "\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))
Tere 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}](images/3509563691394374086-16.0px.png "\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]](images/4338133582744262913-16.0px.png "\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)
 | (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}](images/2540560158200750531-16.0px.png "\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]}](images/2051760077061943340-16.0px.png "\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)
 | (17) |
Type: Equation(Expression(Integer))
fricas
v:=vector[v11,v12]
![\label{eq18}\left[ v 11, \: v 12 \right]](images/1166423591014029648-16.0px.png "\label{eq18}\left[ v 11, \: v 12 \right]") | (18) |
Type: Vector(OrderedVariableList?([v11,
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)}}}](images/8592109025960101252-16.0px.png "\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]](images/1961149360139209143-16.0px.png "\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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a
 | (21) |
Type: Equation(Expression(Integer))
fricas
b
 | (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]](images/4574934365963804880-16.0px.png "\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)]]
 | (24) |
Type: Matrix(Expression(Integer))
Complex Values
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LA1:=matrix[[sqrt(-1)*sin(x)]]
 | (25) |
Type: Matrix(Expression(Integer))
fricas
A:=matrix[[cos(x)-L]]
 | (26) |
Type: Matrix(Expression(Integer))
The following produces scripted symbol!
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A:=matrix[a,b]
 | (27) |
Type: Symbol
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A:=matrix[[a,b]]
 | (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)}}}](images/2324616538299440009-16.0px.png "\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, 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]}}](images/883829150546726707-16.0px.png "\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)}}](images/2314376156294358796-16.0px.png "\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)}}](images/2775233438833337329-16.0px.png "\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)}}](images/2335846422878572098-16.0px.png "\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}](images/4160332173086292538-16.0px.png "\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)}}](images/8691905769578920516-16.0px.png "\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)}}}](images/3373935171433110109-16.0px.png "\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](images/8032623634602769361-16.0px.png "\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}}](images/8010977258720415888-16.0px.png "\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)}}}](images/4012272025110716234-16.0px.png "\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]](images/167884235143421358-16.0px.png "\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}}](images/6346601403476306040-16.0px.png "\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)}](images/1675095808569929097-16.0px.png "\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)}}](images/2274297281452073345-16.0px.png "\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](images/2924055931946994807-16.0px.png "\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)}}}](images/7134834849701038029-16.0px.png "\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)}}}](images/1035793518426463520-16.0px.png "\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)}}](images/8774662521800305447-16.0px.png "\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 = -{\%CJ \over{\sqrt{- 1}}}}, \:{v 12 = \%CJ}\right]}\right]](images/1081290530103900356-16.0px.png "\label{eq48}\left[{\left[{v 11 = -{\%CJ \over{\sqrt{- 1}}}}, \:{v 12 = \%CJ}\right]}\right]") | (48) |
Type: List(List(Equation(Expression(Integer))))
 |
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)}](images/8375172082474433868-16.0px.png "\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
 | (50) |
Type: BasicOperator?
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
 | (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]](images/1873955015756959080-16.0px.png "\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),
fricas
solve(D(y(x),x)-y(x)^2=1, y, 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]](images/6905881175199368787-16.0px.png "\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]](images/8698693565472638508-16.0px.png "\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]](images/5647263545147453480-16.0px.png "\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]](images/3511736337951170681-16.0px.png "\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]](images/322754845702652664-16.0px.png "\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]](images/892410864054569521-16.0px.png "\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](images/2988882434564000323-16.0px.png "\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)))