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Jet Figure 4

Edit detail for Jet Figure 4 revision 4 of 4

	1 2 3 4
Editor: test1 Time: 2013/05/17 13:48:41 GMT+0
Note:

changed:
-)lib JBC JBFC JBC- JBFC- BFC BFC- JB JBX   JBLF  DE SEM  DIFF JBE CK
jb := JBUNDLE(['x,'y,'z],['u]);
jbx := JBX jb;
jbl := JBLF(jb,jbx);
de := JDE(jb,jbl);
ck := CKP(jb,jbl);

removed:
-
-\begin{axiom}
-jb:=JB(['x,'y,'z],['u]);
-jbx:=JBX jb;
-jbl:=JBLF(jb,jbx);
-de:=DE(jb,jbl);
-ck:=CK(jb,jbl);
-\end{axiom}

changed:
-printSys [eq1,eq2]
printSys([eq1,eq2])$de

changed:
-janet:de := generate [eq1,eq2]
janet:de := makeSystem([eq1,eq2])$de

changed:
-Fix::
-
-  !\begin{axiom}
-  complete janet
-  \end{axiom}
-


\begin{axiom}
complete(janet)$ck
\end{axiom}

fricas

(1) -> 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)

Type: OutputForm?

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)

Type: NonNegativeInteger?

fricas

setRedMode(1)$ck

$\label{eq6}0$

(6)

Type: NonNegativeInteger?

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)

$\label{eq34}\mbox{\rm \hbox{\axiomType{Final}\ } \hbox{\axiomType{Result}\ } }$

(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