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

fricas
jb := IJB('x,'u,'p,4,3);
Type: Type
fricas
jbe := JBE jb;
Type: Type
fricas
de := JDE(jb,jbe);
Type: Type
fricas
ck := CKP(jb,jbe);
Type: Type

fricas
eq1:jbe := P(1,[4]) + U(1)*P(1,[1]) + U(2)*P(1,[2]) + U(3)*P(1,[3])

\label{eq1}{p_{4}^{1}}+{{u^{3}}\ {p_{3}^{1}}}+{{u^{2}}\ {p_{2}^{1}}}+{{u^{1}}\ {p_{1}^{1}}}(1)
Type: JetBundleExpression?(IndexedJetBundle?(x,u,p,4,3))
fricas
eq2:jbe := P(2,[4]) + U(1)*P(2,[1]) + U(2)*P(2,[2]) + U(3)*P(2,[3])

\label{eq2}{p_{4}^{2}}+{{u^{3}}\ {p_{3}^{2}}}+{{u^{2}}\ {p_{2}^{2}}}+{{u^{1}}\ {p_{1}^{2}}}(2)
Type: JetBundleExpression?(IndexedJetBundle?(x,u,p,4,3))
fricas
eq3:jbe := P(3,[4]) + U(1)*P(3,[1]) + U(2)*P(3,[2]) + U(3)*P(3,[3])

\label{eq3}{p_{4}^{3}}+{{u^{3}}\ {p_{3}^{3}}}+{{u^{2}}\ {p_{2}^{3}}}+{{u^{1}}\ {p_{1}^{3}}}(3)
Type: JetBundleExpression?(IndexedJetBundle?(x,u,p,4,3))
fricas
eq4:jbe := P(1,[1]) + P(2,[2]) + P(3,[3])

\label{eq4}{p_{3}^{3}}+{p_{2}^{2}}+{p_{1}^{1}}(4)
Type: JetBundleExpression?(IndexedJetBundle?(x,u,p,4,3))

fricas
euler:de := makeSystem([eq1,eq2,eq3,eq4])

\label{eq5}\begin{array}{c}
{\ }
\
{{{p_{4}^{1}}+{{u^{3}}\ {p_{3}^{1}}}+{{u^{2}}\ {p_{2}^{1}}}+{{u^{1}}\ {p_{1}^{1}}}}= 0}
\
{\ }
\
{{{p_{4}^{2}}+{{u^{3}}\ {p_{3}^{2}}}+{{u^{2}}\ {p_{2}^{2}}}+{{u^{1}}\ {p_{1}^{2}}}}= 0}
\
{\ }
\
{{{p_{4}^{3}}+{{u^{3}}\ {p_{3}^{3}}}+{{u^{2}}\ {p_{2}^{3}}}+{{u^{1}}\ {p_{1}^{3}}}}= 0}
\
{\ }
\
{{{p_{3}^{3}}+{p_{2}^{2}}+{p_{1}^{1}}}= 0}
\
(5)
Type: JetDifferentialEquation?(IndexedJetBundle?(x,u,p,4,3),JetBundleExpression?(IndexedJetBundle?(x,u,p,4,3)))

fricas
setOutMode(14)$ck

\label{eq6}0(6)
fricas
setSimpMode(1)$ck

\label{eq7}0(7)

Fix::

fricas
complete(euler)$ck

\label{eq8}\ (8)

\label{eq9}\mbox{\rm \hbox{\axiomType{Symbol}\ }}{M_{1}}\mbox{\rm involutive !}\mbox{\rm \hbox{\axiomType{Dimension}\ } :}8(9)

\label{eq10}\ (10)

\label{eq11}\mbox{\rm \hbox{\axiomType{Equation}\ }}{R_{1}}\mbox{\rm not involutive !}\mbox{\rm \hbox{\axiomType{Dimension}\ } :}{11}(11)

\label{eq12}\ (12)

\label{eq13}\mbox{\rm = = = = = = =}1 \mbox{\rm.\hbox{\axiomType{Projection}\ } = = = = = = =}(13)

\label{eq14}\mbox{\rm \hbox{\axiomType{Integrability}\ } condition (s)}(14)

\label{eq15}\begin{array}{c}
{\ }
\
{{{2 \ {p_{2}^{3}}\ {p_{3}^{2}}}+{2 \ {p_{1}^{3}}\ {p_{3}^{1}}}+{2 \ {{p_{2}^{2}}^{2}}}+{2 \ {p_{1}^{1}}\ {p_{2}^{2}}}+{2 \ {p_{1}^{2}}\ {p_{2}^{1}}}+{2 \ {{p_{1}^{1}}^{2}}}}= 0}
\
(15)

\label{eq16}\begin{array}{@{}l}
\displaystyle
= = = = = = = = = = = = = = = = = = = 
\
\
\displaystyle
= = = = = = = = = = 
(16)

\label{eq17}\ (17)

\label{eq18}\mbox{\rm \hbox{\axiomType{Symbol}\ }}{\hbox{\axiomType{ALTSUPERSUB}\ } \left({M , \: 1, \:{\left(1 \right)}}\right)}\mbox{\rm involutive !}\mbox{\rm \hbox{\axiomType{Dimension}\ } :}7(18)

\label{eq19}\ (19)

\label{eq20}\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>}(20)

\label{eq21}\ (21)

\label{eq22}\mbox{\rm \hbox{\axiomType{Equation}\ }}{\hbox{\axiomType{ALTSUPERSUB}\ } \left({R , \: 1, \:{\left(1 \right)}}\right)}\mbox{\rm involutive !}(22)

\label{eq23}\mbox{\rm \hbox{\axiomType{System}\ } without prolonged equations.\hbox{\axiomType{Dimension}\ } :}{14}(23)

\label{eq24}\begin{array}{c}
{\ }
\
{{{p_{4}^{3}}+{{u^{3}}\ {p_{3}^{3}}}+{{u^{2}}\ {p_{2}^{3}}}+{{u^{1}}\ {p_{1}^{3}}}}= 0}
\
{\ }
\
{{{p_{4}^{2}}+{{u^{3}}\ {p_{3}^{2}}}+{{u^{2}}\ {p_{2}^{2}}}+{{u^{1}}\ {p_{1}^{2}}}}= 0}
\
{\ }
\
{{{p_{4}^{1}}+{{u^{3}}\ {p_{3}^{1}}}+{{u^{2}}\ {p_{2}^{1}}}+{{u^{1}}\ {p_{1}^{1}}}}= 0}
\
{\ }
\
{{{p_{3}^{3}}+{p_{2}^{2}}+{p_{1}^{1}}}= 0}
\
{\ }
\
{{{2 \ {p_{2}^{3}}\ {p_{3}^{2}}}+{2 \ {p_{1}^{3}}\ {p_{3}^{1}}}+{2 \ {{p_{2}^{2}}^{2}}}+{2 \ {p_{1}^{1}}\ {p_{2}^{2}}}+{2 \ {p_{1}^{2}}\ {p_{2}^{1}}}+{2 \ {{p_{1}^{1}}^{2}}}}= 0}
\
(24)

\label{eq25}\ (25)

\label{eq26}\mbox{\rm \hbox{\axiomType{Cartan}\ } characters :}{3, \: 3, \: 1, \: 0}(26)
Type: Void




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