login  home  contents  what's new  discussion  bug reports     help  links  subscribe  changes  refresh  edit

fricas
jb := JBUNDLE(['x,'y,'z],['u]);
Type: Type
fricas
jbx := JBX jb;
Type: Type
fricas
jbl := JBLF(jb,jbx);
Type: Type
fricas
de := JDE(jb,jbl);
Type: Type
fricas
ck := CKP(jb,jbl);
Type: Type

fricas
eq1:jbl := D('u,['z,'z]) + 'y * D('u,['x,'x])

\label{eq1}{u_{z , \: z}}+{y \ {u_{x , \: x}}}(1)
Type: JetBundleLinearFunction?(JetBundle?([x,y,z],[u]),JetBundleXExpression?(JetBundle?([x,y,z],[u])))

fricas
eq2:jbl := D('u,['y,'y])

\label{eq2}u_{y , \: y}(2)
Type: JetBundleLinearFunction?(JetBundle?([x,y,z],[u]),JetBundleXExpression?(JetBundle?([x,y,z],[u])))

fricas
printSys([eq1,eq2])$de

\label{eq3}\begin{array}{c}
{\ }
\
{{{u_{z , \: z}}+{y \ {u_{x , \: x}}}}= 0}
\
{\ }
\
{{u_{y , \: y}}= 0}
\
(3)

fricas
janet:de := makeSystem([eq1,eq2])$de

\label{eq4}\begin{array}{c}
{\ }
\
{{{u_{z , \: z}}+{y \ {u_{x , \: x}}}}= 0}
\
{\ }
\
{{u_{y , \: y}}= 0}
\
(4)
Type: JetDifferentialEquation?(JetBundle?([x,y,z],[u]),JetBundleLinearFunction?(JetBundle?([x,y,z],[u]),JetBundleXExpression?(JetBundle?([x,y,z],[u]))))

fricas
setOutMode(14)$ck

\label{eq5}0(5)
fricas
setRedMode(1)$ck

\label{eq6}0(6)

fricas
complete(janet)$ck

\label{eq7}\ (7)

\label{eq8}\mbox{\rm \hbox{\axiomType{Symbol}\ }}{M_{2}}\mbox{\rm not involutive !}\mbox{\rm \hbox{\axiomType{Dimension}\ } :}4(8)

\label{eq9}\ (9)

\label{eq10}\mbox{\rm \hbox{\axiomType{Symbol}\ }}{M_{3}}\mbox{\rm involutive !}\mbox{\rm \hbox{\axiomType{Dimension}\ } :}4(10)

\label{eq11}\ (11)

\label{eq12}\mbox{\rm \hbox{\axiomType{Equation}\ }}{R_{3}}\mbox{\rm not involutive !}\mbox{\rm \hbox{\axiomType{Dimension}\ } :}{12}(12)

\label{eq13}\ (13)

\label{eq14}\mbox{\rm = = = = = = =}1 \mbox{\rm.\hbox{\axiomType{Projection}\ } = = = = = = =}(14)

\label{eq15}\mbox{\rm \hbox{\axiomType{Integrability}\ } condition (s)}(15)

\label{eq16}\begin{array}{c}
{\ }
\
{{u_{y , \: x , \: x}}= 0}
\
(16)

\label{eq17}\begin{array}{@{}l}
\displaystyle
= = = = = = = = = = = = = = = = = = = 
\
\
\displaystyle
= = = = = = = = = = 
(17)

\label{eq18}\ (18)

\label{eq19}\mbox{\rm \hbox{\axiomType{Symbol}\ }}{\hbox{\axiomType{ALTSUPERSUB}\ } \left({M , \: 3, \:{\left(1 \right)}}\right)}\mbox{\rm not involutive !}\mbox{\rm \hbox{\axiomType{Dimension}\ } :}3(19)

\label{eq20}\ (20)

\label{eq21}\mbox{\rm \hbox{\axiomType{Symbol}\ }}{\hbox{\axiomType{ALTSUPERSUB}\ } \left({M , \: 4, \:{\left(1 \right)}}\right)}\mbox{\rm involutive !}\mbox{\rm \hbox{\axiomType{Dimension}\ } :}2(21)

\label{eq22}\ (22)

\label{eq23}\mbox{\rm \hbox{\axiomType{Equation}\ }}{\hbox{\axiomType{ALTSUPERSUB}\ } \left({R , \: 4, \:{\left(1 \right)}}\right)}\mbox{\rm not involutive !}\mbox{\rm \hbox{\axiomType{Dimension}\ } :}{13}(23)

\label{eq24}\ (24)

\label{eq25}\mbox{\rm = = = = = = =}2 \mbox{\rm.\hbox{\axiomType{Projection}\ } = = = = = = =}(25)

\label{eq26}\mbox{\rm \hbox{\axiomType{Integrability}\ } condition (s)}(26)

\label{eq27}\begin{array}{c}
{\ }
\
{{u_{x , \: x , \: x , \: x}}= 0}
\
(27)

\label{eq28}\begin{array}{@{}l}
\displaystyle
= = = = = = = = = = = = = = = = = = = 
\
\
\displaystyle
= = = = = = = = = = 
(28)

\label{eq29}\ (29)

\label{eq30}\mbox{\rm \hbox{\axiomType{Symbol}\ }}{\hbox{\axiomType{ALTSUPERSUB}\ } \left({M , \: 4, \:{\left(2 \right)}}\right)}\mbox{\rm not involutive !}\mbox{\rm \hbox{\axiomType{Dimension}\ } :}1(30)

\label{eq31}\ (31)

\label{eq32}\mbox{\rm \hbox{\axiomType{Symbol}\ }}{\hbox{\axiomType{ALTSUPERSUB}\ } \left({M , \: 5, \:{\left(2 \right)}}\right)}\mbox{\rm involutive !}\mbox{\rm \hbox{\axiomType{Dimension}\ } :}0(32)

\label{eq33}\ (33)

\label{eq34}\mbox{\rm <em> </em> <em> </em> <em> </em> <em> </em> <em> </em> <em> </em> <em> </em> <em> \hbox{\axiomType{Final}\ } \hbox{\axiomType{Result}\ } </em> <em> </em> <em> </em> <em> </em> <em> </em> <em> </em> <em> </em> <em> </em>}(34)

\label{eq35}\ (35)

\label{eq36}\mbox{\rm \hbox{\axiomType{Equation}\ }}{\hbox{\axiomType{ALTSUPERSUB}\ } \left({R , \: 5, \:{\left(2 \right)}}\right)}\mbox{\rm involutive !}(36)

\label{eq37}\mbox{\rm \hbox{\axiomType{System}\ } without prolonged equations.\hbox{\axiomType{Dimension}\ } :}{12}(37)

\label{eq38}\begin{array}{c}
{\ }
\
{{u_{x , \: x , \: x , \: x}}= 0}
\
{\ }
\
{{u_{y , \: x , \: x}}= 0}
\
{\ }
\
{{{u_{z , \: z}}+{y \ {u_{x , \: x}}}}= 0}
\
{\ }
\
{{u_{y , \: y}}= 0}
\
(38)

\label{eq39}\ (39)

\label{eq40}\mbox{\rm \hbox{\axiomType{System}\ } of finite type.}(40)
Type: Void




  Subject:   Be Bold !!
  ( 13 subscribers )  
Please rate this page: