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	Jet Bundles
Jet Figure 4 ←	↑	→ Jet LUDecomposition

Jet Figure 5

Edit detail for Jet Figure 5 revision 6 of 6

	1 2 3 4 5 6
Editor: test1 Time: 2013/05/17 13:50:34 GMT+0
Note:

changed:
-)lib JBC JBFC JBC- JBFC- BFC BFC- JB JBX JBLF DE SEM  DIFF JBE IJB CK
jb := IJB('x,'u,'p,4,3);
jbe := JBE jb;
de := JDE(jb,jbe);
ck := CKP(jb,jbe);

removed:
-
-\begin{axiom}
-jb:=IJB('x,'u,'p,4,3);
-jbe:=JBE jb;
-de:=DE(jb,jbe);
-ck:=CK(jb,jbe);
-\end{axiom}

changed:
-euler:de := generate [eq1,eq2,eq3,eq4]
euler:de := makeSystem([eq1,eq2,eq3,eq4])

changed:
-  !\begin{axiom}
-  -- complete euler
-  \end{axiom}
-
\begin{axiom}
complete(euler)$ck
\end{axiom}

fricas

(1) -> 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)

Type: NonNegativeInteger?

fricas

setSimpMode(1)$ck

$\label{eq7}0$

(7)

Type: NonNegativeInteger?

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)

$\label{eq20}\mbox{\rm \hbox{\axiomType{Final}\ } \hbox{\axiomType{Result}\ } }$

(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