zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
DIMSYM and LIE: Symmetry determination packages. (English) Zbl 0918.34007
The authors describe the features of two software packages named DIMSYM and LIE. While LIE is written in LISP and runs under DOS the DIMSYM package is written in REDUCE. Both packages are dealing with Lie symmetries of differential equations. The paper includes examples and lists commands of the packages giving explainations of their functionality. While internal details of the algorithms are explained knowledge of the theory of Lie symmetries of partial differential equations is assumed. For an overview of related software it is referred to W. Hereman [Euromath Bulletin 2, 1993].

34A25Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.)
68W30Symbolic computation and algebraic computation
22E99Lie groups
35C99Representations of solutions of PDE
Full Text: DOI
[1] Head, A. K.: Lie: A PC program for Lie analysis of differential equations. Comp. phys. Comm. 77, 241-248 (1993) · Zbl 0854.65055
[2] Sherring, J.: Dimsym: symmetry determination and linear differential equations package. Research report (1993)
[3] Sherring, J.: Symmetry and computer algebra techniques for differential equations. Ph.d. thesis (1993)
[4] Bluman, G. W.; Kumei, S.: Symmetries and differential equations. Applied mathematical sciences 81 (1989) · Zbl 0698.35001
[5] Olver, P.: Applications of Lie groups to differential equations. (1986) · Zbl 0588.22001
[6] Schwarz, F.: Symmetries of differential equations: from sophus Lie to computer algebra. SIAM rev. 30, 450-481 (1988) · Zbl 0664.35004
[7] Stephani, H.: Differential equations: their solution using symmetries. (1989) · Zbl 0704.34001
[8] Hereman, W.: Review of symbolic software for computation of Lie symmetries of differential equations. Euromath bulletin 2 (1993) · Zbl 0875.68565
[9] Reid, G. J.: Finding abstract Lie symmetry algebras of differential equations without integrating determining equations. European J. Appl. math. 2, 319-340 (1991) · Zbl 0768.35002
[10] Hearn, A. C.: REDUCE users manual. (1995)
[11] Schrüfer, E.: EXCALC: A system for doing calculations in the calculus of modern differential geometry. REDUCE 3.6 miscellaneous documentation (1995)
[12] Kersten, P. H. M.: Infinitesimal symmetries: A computational approach. CWI tract 34 (1987) · Zbl 0648.68052
[13] Schwarz, F.: Automatically determining symmetries of partial differential equations. Computing 34, 91-106 (1985) · Zbl 0555.65076
[14] Reid, G. J.: A triangularization algorithm which determines the Lie symmetry algebra of any system of pdes. J. phys. A 23, L853-L859 (1990) · Zbl 0724.35001
[15] Reid, G. J.: Algorithms for reducing a system of pdes to standard form, determining the dimension of its solution space and calculating its Taylor series solution. Euro. jnl. Of applied mathematics 2, 293-318 (1991) · Zbl 0768.35001
[16] Janet, M.: Sur LES systèmes d’équations aux dérivées partielles. Journal de mathematique 8III, 65-151 (1920) · Zbl 47.0440.04
[17] Schwarz, F.: The riquier-janet theory and its application to nonlinear evolution equations. Phys. D 11, 243-251 (1984) · Zbl 0588.58032
[18] Maccallum, M. A. H.: Odesolve. REDUCE 3.6 miscellaneous documentation (1995)
[19] Reid, G. J.; Wittkopf, A. D.: Long guide to the standard form package. (1993)
[20] Hill, J. M.: The solution of differential equations by means of one-parameter groups. (1988)
[21] Kersten, P. H. M.: Software to compute infinitesimal symmetries of exterior systems, with applications. Acta appl. Math. 16, 207-229 (1989) · Zbl 0702.35003
[22] Schwarz, F.: REDUCE 3.6 miscellaneous documentation. The package SPDE for determining symmetries of partial differential equations, user’s manual (1995)