|
|
|
last edited 11 years ago by test1 |
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/codeaxiom)set output tex off )set output algebra onaxiomjb:=IJB('x,'u,'p,4,3);Type: Domainaxiomjbe:=JBE jb;Type: Domainaxiomde:=DE(jb,jbe);Type: Domainaxiomck:=CK(jb,jbe);Type: Domainaxiomeq1: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 1axiomeq2: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 1axiomeq3: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 1axiomeq4:jbe := P(1,[1]) + P(2,[2]) + P(3,[3]) 3 2 1 (8) p + p + p 3 2 1axiomeuler: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 1Type: DifferentialEquation?(IndexedJetBundle?(x,u,p,4,3),JetBundleExpression? IndexedJetBundle?(x,u,p,4,3))axiomsetOutMode(14)$ck (10) 0Type: NonNegativeInteger?axiomsetSimpMode(1)$ck (11) 0Type: NonNegativeInteger?\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}axiomcomplete eulerType: Void
Some or all expressions may not have rendered properly, because Latex returned the following error:
This is pdfeTeX, Version 3.141592-1.21a-2.2 (Web2C 7.5.4) \write18 enabled. entering extended mode (./6832687165070070213-18px.tex LaTeX2e <2003/12/01> Babel <v3.8d> and hyphenation patterns for american, french, german, ngerman, b ahasa, basque, bulgarian, catalan, croatian, czech, danish, dutch, esperanto, e stonian, finnish, greek, icelandic, irish, italian, latin, magyar, norsk, polis h, portuges, romanian, russian, serbian, slovak, slovene, spanish, swedish, tur kish, ukrainian, nohyphenation, loaded. (/usr/share/texmf-tetex/tex/latex/base/article.cls Document Class: article 2004/02/16 v1.4f Standard LaTeX document class (/usr/share/texmf-tetex/tex/latex/base/size10.clo)) (/usr/share/texmf-tetex/tex/latex/amsmath/amsmath.sty For additional information on amsmath, use the `?' option. (/usr/share/texmf-tetex/tex/latex/amsmath/amstext.sty (/usr/share/texmf-tetex/tex/latex/amsmath/amsgen.sty)) (/usr/share/texmf-tetex/tex/latex/amsmath/amsbsy.sty) (/usr/share/texmf-tetex/tex/latex/amsmath/amsopn.sty)) (/usr/share/texmf-tetex/tex/latex/amsfonts/amsfonts.sty) (/usr/share/texmf-tetex/tex/latex/amsfonts/amssymb.sty) (/usr/share/texmf-tetex/tex/latex/amscls/amsthm.sty) (/usr/share/texmf-tetex/tex/generic/xypic/xy.sty (/usr/share/texmf-tetex/tex/generic/xypic/xy.tex Bootstrap'ing: catcodes, docmode, (/usr/share/texmf-tetex/tex/generic/xypic/xyrecat.tex) (/usr/share/texmf-tetex/tex/generic/xypic/xyidioms.tex)Xy-pic version 3.7 <1999/02/16> Copyright (c) 1991-1998 by Kristoffer H. Rose <krisrose@ens-lyon.fr> Xy-pic is free software: see the User's Guide for details.
Loading kernel: messages; fonts; allocations: state, direction, utility macros; pictures: \xy, positions, objects, decorations; kernel objects: directionals, circles, text; options; algorithms: directions, edges, connections; Xy-pic loaded) (/usr/share/texmf-tetex/tex/generic/xypic/xyall.tex Xy-pic option: All features v.3.3 (/usr/share/texmf-tetex/tex/generic/xypic/xycurve.tex Xy-pic option: Curve and Spline extension v.3.7 curve, circles, loaded) (/usr/share/texmf-tetex/tex/generic/xypic/xyframe.tex Xy-pic option: Frame and Bracket extension v.3.7 loaded) (/usr/share/texmf-tetex/tex/generic/xypic/xycmtip.tex Xy-pic option: Computer Modern tip extension v.3.3 (/usr/share/texmf-tetex/tex/generic/xypic/xytips.tex Xy-pic option: More Tips extension v.3.3 loaded) loaded) (/usr/share/texmf-tetex/tex/generic/xypic/xyline.tex Xy-pic option: Line styles extension v.3.6 loaded) (/usr/share/texmf-tetex/tex/generic/xypic/xyrotate.tex Xy-pic option: Rotate and Scale extension v.3.3 loaded) (/usr/share/texmf-tetex/tex/generic/xypic/xycolor.tex Xy-pic option: Colour extension v.3.3 loaded) (/usr/share/texmf-tetex/tex/generic/xypic/xymatrix.tex Xy-pic option: Matrix feature v.3.4 loaded) (/usr/share/texmf-tetex/tex/generic/xypic/xyarrow.tex Xy-pic option: Arrow and Path feature v.3.5 path, \ar, loaded) (/usr/share/texmf-tetex/tex/generic/xypic/xygraph.tex Xy-pic option: Graph feature v.3.7 loaded) loaded)) (/usr/share/texmf-tetex/tex/latex/graphics/graphicx.sty (/usr/share/texmf-tetex/tex/latex/graphics/keyval.sty) (/usr/share/texmf-tetex/tex/latex/graphics/graphics.sty (/usr/share/texmf-tetex/tex/latex/graphics/trig.sty) (/usr/share/texmf-tetex/tex/latex/graphics/graphics.cfg) (/usr/share/texmf-tetex/tex/latex/graphics/dvips.def))) (/usr/share/texmf-tetex/tex/latex/tools/verbatim.sty) (/usr/share/texmf-tetex/tex/latex/graphviz/graphviz.sty (/usr/share/texmf-tetex/tex/latex/psfrag/psfrag.sty)) (/usr/share/texmf-tetex/tex/latex/sage/sagetex.sty Writing sage input file 6832687165070070213-18px.sage (./6832687165070070213-18px.sout)) (./6832687165070070213-18px.aux) (/usr/share/texmf-tetex/tex/latex/amsfonts/umsa.fd) (/usr/share/texmf-tetex/tex/latex/amsfonts/umsb.fd) Missing $ inserted. <inserted text> $ l.62 \newpage
Display math should end with $$. <to be read again> \par l.62 \newpage
[1] [2] Missing $ inserted. <inserted text> $ l.69 \newpage
Display math should end with $$. <to be read again> \par l.69 \newpage
[3] [4] Missing $ inserted. <inserted text> $ l.76 \newpage
Display math should end with $$. <to be read again> \par l.76 \newpage
[5] [6] [7] [8] [9] Missing $ inserted. <inserted text> $ l.95 \newpage
Display math should end with $$. <to be read again> \par l.95 \newpage
[10] [11] Missing $ inserted. <inserted text> $ l.106 \newpage
Display math should end with $$. <to be read again> \par l.106 \newpage
[12] [13] Missing $ inserted. <inserted text> $ l.112 \newpage
Display math should end with $$. <to be read again> \par l.112 \newpage
[14] [15] [16] [17] Missing $ inserted. <inserted text> $ l.141 \newpage
Display math should end with $$. <to be read again> \par l.141 \newpage
[18]
LaTeX Error: \begin{equation*} on input line 139 ended by \end{document}.
See the LaTeX manual or LaTeX Companion for explanation. Type H <return> for immediate help. ...
l.144 \end{document}
[19] (./6832687165070070213-18px.aux) ) (\end occurred inside a group at level 7)
### 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.