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Edit detail for Jet Figure 5 revision 2 of 6

1 2 3 4 5 6
Editor: 127.0.0.1
Time: 2007/11/11 19:16:48 GMT-8
Note: transferred from axiom-developer

added:

\begin{axiom}
)set output tex off
)set output algebra on
\end{axiom}

axiom
)lib JBC JBFC JBC- JBFC- BFC BFC- JB JBX JBLF DE SEM DIFF JBE IJB CK JetBundleCategory is now explicitly exposed in frame initial JetBundleCategory will be automatically loaded when needed from /var/zope2/var/LatexWiki/JBC.NRLIB/code JetBundleFunctionCategory is now explicitly exposed in frame initial JetBundleFunctionCategory will be automatically loaded when needed from /var/zope2/var/LatexWiki/JBFC.NRLIB/code JetBundleCategory& is now explicitly exposed in frame initial JetBundleCategory& will be automatically loaded when needed from /var/zope2/var/LatexWiki/JBC-.NRLIB/code JetBundleFunctionCategory& is now explicitly exposed in frame initial JetBundleFunctionCategory& will be automatically loaded when needed from /var/zope2/var/LatexWiki/JBFC-.NRLIB/code BaseFunctionCategory is now explicitly exposed in frame initial BaseFunctionCategory will be automatically loaded when needed from /var/zope2/var/LatexWiki/BFC.NRLIB/code BaseFunctionCategory& is now explicitly exposed in frame initial BaseFunctionCategory& will be automatically loaded when needed from /var/zope2/var/LatexWiki/BFC-.NRLIB/code JetBundle is now explicitly exposed in frame initial JetBundle will be automatically loaded when needed from /var/zope2/var/LatexWiki/JB.NRLIB/code JetBundleXExpression is now explicitly exposed in frame initial JetBundleXExpression will be automatically loaded when needed from /var/zope2/var/LatexWiki/JBX.NRLIB/code JetBundleLinearFunction is now explicitly exposed in frame initial JetBundleLinearFunction will be automatically loaded when needed from /var/zope2/var/LatexWiki/JBLF.NRLIB/code DifferentialEquation is now explicitly exposed in frame initial DifferentialEquation will be automatically loaded when needed from /var/zope2/var/LatexWiki/DE.NRLIB/code SparseEchelonMatrix is now explicitly exposed in frame initial SparseEchelonMatrix will be automatically loaded when needed from /var/zope2/var/LatexWiki/SEM.NRLIB/code Differential is now explicitly exposed in frame initial Differential will be automatically loaded when needed from /var/zope2/var/LatexWiki/DIFF.NRLIB/code JetBundleExpression is now explicitly exposed in frame initial JetBundleExpression will be automatically loaded when needed from /var/zope2/var/LatexWiki/JBE.NRLIB/code IndexedJetBundle is now explicitly exposed in frame initial IndexedJetBundle will be automatically loaded when needed from /var/zope2/var/LatexWiki/IJB.NRLIB/code CartanKuranishi is now explicitly exposed in frame initial CartanKuranishi will be automatically loaded when needed from /var/zope2/var/LatexWiki/CK.NRLIB/code

axiom
)set output tex off )set output algebra on

axiom
jb:=IJB('x,'u,'p,4,3);
Type: Domain
axiom
jbe:=JBE jb;
Type: Domain
axiom
de:=DE(jb,jbe);
Type: Domain
axiom
ck:=CK(jb,jbe);
Type: Domain

axiom
eq1:jbe := P(1,[4]) + U(1)*P(1,[1]) + U(2)*P(1,[2]) + U(3)*P(1,[3]) 1 3 1 2 1 1 1 (5) p + u p + u p + u p 4 3 2 1
Type: JetBundleExpression? IndexedJetBundle?(x,u,p,4,3)
axiom
eq2:jbe := P(2,[4]) + U(1)*P(2,[1]) + U(2)*P(2,[2]) + U(3)*P(2,[3]) 2 3 2 2 2 1 2 (6) p + u p + u p + u p 4 3 2 1
Type: JetBundleExpression? IndexedJetBundle?(x,u,p,4,3)
axiom
eq3:jbe := P(3,[4]) + U(1)*P(3,[1]) + U(2)*P(3,[2]) + U(3)*P(3,[3]) 3 3 3 2 3 1 3 (7) p + u p + u p + u p 4 3 2 1
Type: JetBundleExpression? IndexedJetBundle?(x,u,p,4,3)
axiom
eq4:jbe := P(1,[1]) + P(2,[2]) + P(3,[3]) 3 2 1 (8) p + p + p 3 2 1
Type: JetBundleExpression? IndexedJetBundle?(x,u,p,4,3)

axiom
euler:de := generate [eq1,eq2,eq3,eq4] (9) 1 3 1 2 1 1 1 p + u p + u p + u p = 0 4 3 2 1 2 3 2 2 2 1 2 p + u p + u p + u p = 0 4 3 2 1 3 3 3 2 3 1 3 p + u p + u p + u p = 0 4 3 2 1 3 2 1 p + p + p = 0 3 2 1
Type: DifferentialEquation?(IndexedJetBundle?(x,u,p,4,3),JetBundleExpression? IndexedJetBundle?(x,u,p,4,3))

axiom
setOutMode(14)$ck (10) 0
Type: NonNegativeInteger?
axiom
setSimpMode(1)$ck (11) 0
Type: NonNegativeInteger?

axiom
complete euler
\begin{equation} \label{eq1}\end{equation} \begin{equation} \label{eq2}\mbox{\rm Symbol } {M \sb {1}} \mbox{\rm involutive! } \mbox{\rm Dimension: } 8\end{equation} \begin{equation} \label{eq3}\end{equation} \begin{equation} \label{eq4}\mbox{\rm Equation } {R \sb {1}} \mbox{\rm not involutive! } \mbox{\rm Dimension: } {11}\end{equation} \begin{equation} \label{eq5}\end{equation} \begin{equation} \label{eq6}\mbox{\rm ======= } 1 \mbox{\rm . Projection =======}\end{equation} \begin{equation} \label{eq7}\mbox{\rm Integrability condition(s)}\end{equation} \begin{equation} \label{eq8}\begin{array}{c}{\ }\{{{2 \ {p \sb {{2}} \sp {3}} \ {p \sb {{3}} \sp {2}}}+{2 \ {p \sb {{1}} \sp {3}} \ {p \sb {{3}} \sp {1}}}+{2 \ {{p \sb {{2}} \sp {2}} \sp 2}}+{2 \ {p \sb {{1}} \sp {1}} \ {p \sb {{2}} \sp {2}}}+{2 \ {p \sb {{1}} \sp {2}} \ {p \sb {{2}} \sp {1}}}+{2 \ {{p \sb {{1}} \sp {1}} \sp 2}}}=0}\\end{array}\end{equation} \begin{equation} \label{eq9}=============================\end{equation} \begin{equation} \label{eq10}\end{equation} \begin{equation} \label{eq11}\mbox{\rm Symbol } {ALTSUPERSUB \left( {M, \: 1, \: {\left( 1 \right)}} \right)} \mbox{\rm involutive! } \mbox{\rm Dimension: } 7\end{equation} \begin{equation} \label{eq12}\end{equation} \begin{equation} \label{eq13}\mbox{\rm ************ Final Result ************}\end{equation} \begin{equation} \label{eq14}\end{equation} \begin{equation} \label{eq15}\mbox{\rm Equation } {ALTSUPERSUB \left( {R, \: 1, \: {\left( 1 \right)}} \right)} \mbox{\rm involutive!}\end{equation} \begin{equation} \label{eq16}\mbox{\rm System without prolonged equations. Dimension: } {14}\end{equation} \begin{equation} \label{eq17}\begin{array}{c}{\ }\{{{p \sb {{4}} \sp {3}}+{{u \sp {3}} \ {p \sb {{3}} \sp {3}}}+{{u \sp {2}} \ {p \sb {{2}} \sp {3}}}+{{u \sp {1}} \ {p \sb {{1}} \sp {3}}}}=0}\{\ }\{{{p \sb {{4}} \sp {2}}+{{u \sp {3}} \ {p \sb {{3}} \sp {2}}}+{{u \sp {2}} \ {p \sb {{2}} \sp {2}}}+{{u \sp {1}} \ {p \sb {{1}} \sp {2}}}}=0}\{\ }\{{{p \sb {{4}} \sp {1}}+{{u \sp {3}} \ {p \sb {{3}} \sp {1}}}+{{u \sp {2}} \ {p \sb {{2}} \sp {1}}}+{{u \sp {1}} \ {p \sb {{1}} \sp {1}}}}=0}\{\ }\{{{p \sb {{3}} \sp {3}}+{p \sb {{2}} \sp {2}}+{p \sb {{1}} \sp {1}}}=0}\{\ }\{{{2 \ {p \sb {{2}} \sp {3}} \ {p \sb {{3}} \sp {2}}}+{2 \ {p \sb {{1}} \sp {3}} \ {p \sb {{3}} \sp {1}}}+{2 \ {{p \sb {{2}} \sp {2}} \sp 2}}+{2 \ {p \sb {{1}} \sp {1}} \ {p \sb {{2}} \sp {2}}}+{2 \ {p \sb {{1}} \sp {2}} \ {p \sb {{2}} \sp {1}}}+{2 \ {{p \sb {{1}} \sp {1}} \sp 2}}}=0}\\end{array}\end{equation} \begin{equation} \label{eq18}\end{equation} \begin{equation} \label{eq19}\mbox{\rm Cartan characters: } {3, \: 3, \: 1, \: 0}\end{equation}
Type: Void


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### semi simple group (level 7) entered at line 139 (\begingroup) ### semi simple group (level 6) entered at line 110 (\begingroup) ### semi simple group (level 5) entered at line 104 (\begingroup) ### semi simple group (level 4) entered at line 93 (\begingroup) ### semi simple group (level 3) entered at line 74 (\begingroup) ### semi simple group (level 2) entered at line 67 (\begingroup) ### semi simple group (level 1) entered at line 60 (\begingroup) ### bottom level (see the transcript file for additional information) Output written on 6832687165070070213-18px.dvi (19 pages, 4100 bytes). Transcript written on 6832687165070070213-18px.log.