M. Hickman, The use of Maple in the search for symmetries, in: Proc. 14th IMACS World Congress on Computational and Applied Mathematics, Atlanta, Georgia, 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....degree. Reid and Wittkopf s package [241] facilitates automated interfacing with major symmetry packages such as DIMSYM [277] LIESYMM [49] and SYMMGRP.MAX [52] and also with the differential Gr obner basis package DIFFGROB2 [189] A T E X interface between standard form and Hickman s program [142, 143] that uses physical variable notation has been provided by Lisle. Full details and many illustrative examples of the package, which, besides the function standard form, includes other powerful algorithms for symmetry analysis of PDEs, are given in [241] Reid and McKinnon developed a recursive ....

....Maple version of LIE, which computes Lie point symmetries, was still being tested and, therefore, was not yet released. The version of the program computes the determining equations, solves them, and gives the explicit forms of the (vector eld) coecients together with the generators. Hickman [142, 143] o ers a collection of Maple routines that aid in the computation of Liepoint symmetries, non local symmetries, and Wahlquist Estabrook type prolongations. The tools for symmetry analysis include user friendly procedures to enter names of variables, to create total derivatives, to generate and ....

M. Hickman, The use of Maple in the search for symmetries, in: Proc. 14th IMACS World Congress on Computational and Applied Mathematics, Atlanta, Georgia, 1994.

....degree. Reid and Wittkopf s package [241] facilitates automated interfacing with major symmetry packages such as DIMSYM [277] LIESYMM [49] and SYMMGRP.MAX [52] and also with the differential Gr obner basis package DIFFGROB2 [189] A T E X interface between standard form and Hickman s program [142, 143] that uses physical variable notation has been provided by Lisle. Full details and many illustrative examples of the package, which, besides the function standard form, includes other powerful algorithms for symmetry analysis of PDEs, are given in [241] Reid and McKinnon developed a recursive ....

....Maple version of LIE, which computes Lie point symmetries, was still being tested and, therefore, was not yet released. The version of the program computes the determining equations, solves them, and gives the explicit forms of the (vector eld) coecients together with the generators. Hickman [142, 143] o ers a collection of Maple routines that aid in the computation of Liepoint symmetries, non local symmetries, and Wahlquist Estabrook type prolongations. The tools for symmetry analysis include user friendly procedures to enter names of variables, to create total derivatives, to generate and ....

M. Hickman, The Use of Maple in the Search for Symmetries, Research Report no. 77, Department of Mathematics (University of Canterbury, Christchurch, New Zealand, 1993).

....degree. Reid and Wittkopf s package [71] facilitates automated interfacing with major symmetry packages such as DIMSYM [85, 86] LIESYMM [12] and SYMMGRP.MAX [13] and also with the di erential Gr obner basis package DIFFGROB2 [54] A T E X interface between standard form and Hickman s program [45] that uses physical variable notation has been provided by Lisle. Full details and examples of the package, which includes other powerful algorithms for symmetry analysis of PDEs, are given in [67] and [71] Reid and McKinnon developed a recursive algorithm called Rsolve Pdesys [69] that builds ....

....in Vu s program perform polynomial decomposition of PDEs, decoupling of PDEs, integration of simple PDEs and ODEs. Vu adopted some of the integration methods from CRACK, the decoupling method from the Reid Wittkopf standard form algorithm, and ideas from Mans eld s DIFFGROB package. Hickman [45] wrote a collection of Maple routines that aid in the computation of Lie point symmetries, non local symmetries, and Wahlquist Estabrook type prolongations. His tools for symmetry analysis include user friendly procedures to enter names of variables, to create total derivatives, to generate and ....

M. Hickman, The use of Maple in the search for symmetries, In Proc. 14th IMACS World Congress on Computational and Applied Mathematics, Vol. 1, Atlanta, Georgia, 1994, (Edited by W.F. Ames), pp. 226-229, IMACS, New Brunswick, New Jersey (1994).

....of Donsig s di erential forms package di orms, also available in Maple. Khai Vu (Monash University, Melbourne) has translated Head s muMATH program LIE [81] discussed below, into Maple syntax. The Maple version of LIE is currently under testing and is 11 therefore not yet released. Hickman [85] o ers a collection of Maple routines that aid in the computation of Lie point symmetries, non local symmetries, and Wahlquist Estabrook type prolongations. The tools for symmetry analysis include user friendly procedures to enter names of variables, to create total derivatives, to generate and ....

M. Hickman, The Use of Maple in the Search for Symmetries, Research Report no. 77, Department of Mathematics (University of Canterbury, Christchurch, New Zealand, 1993).

....program LIESYMM, now added to the standard library of Maple, for creating the determining equations via the Harrison Estabrook procedure [18] Within LIESYMM various interactive tools are available for integrating the determining equations, and for working with Cartan s di erential forms. Hickman [22] o ers a collection of Maple routines that can aid in the computation of Lie point symmetries, non local symmetries, and Wahlquist Estabrook type prolongations. The program LIE by Head [19] comes bundled with a limited version of muMATH. Therefore, LIE is self contained and runs on IBM compatible ....

M. Hickman, The use of Maple in the search for symmetries, Preprint, Dept. of Math., Univ. Canterbury, Christchurch, New Zealand, 1993.

....of Donsigs differential forms package difforms, also available in Maple. Khai Vu (Monash University, Melbourne) has translated Head s muMATH program LIE[81] discussed below, into Maple syntax. The Maple version of LIE is currently under testing and is therefore not yet released. Hickman [85] offers a collection of Maple routines that aid in the computation of Lie point symmetries, non local symmetries, and Wahlquist Estabrook type prolongations. The tools for symmetry analysis include user friendly procedures to enter names of variables, to create total derivatives, to generate and ....

M. Hickman, The Use of Maple in the Search for Symmetries, Research Report no. 77, Department of Mathematics (University of Canterbury, Christchurch, New Zealand, 1993).

....paper. We now give the result of applying our algorithms to some pdes of physical interest known to possess infinite symmetry pseudogroups. First the infinitesimal defining system for the point symmetry vector fields is derived by the usual method [1, 19, 20] for this we used the Maple program [12]. Next the defining system is brought to involutive form. We used the program [28] for this; an involutivity check showed each system to be involutive at second order. Next a test for structural transitivity is applied. For the examples below, the defining systems contained no 0 th order equations ....

M. Hickman. 1993. The use of Maple in the search for symmetries. Research Report no. 77, Dept. of Mathematics (University of Canterbury, Christchurch, New Zealand).

....It has been implemented in many computer packages [40] The calculations in this section were carried out in MAPLE V Release 5, on a 333 MHZ Pentium II PC running under Linux. When time derivatives in (2. 1) were chosen as the terms to be substituted in the prolongation, Hickman s program Symmetry [41] automatically generated a raw classical determining system for the system (2.1) This system of 1888 linear PDE was generated in about 16 seconds using about 9 MB of RAM. When second order derivatives in x were chosen as the terms to be substituted in the prolongation, Symmetry automatically ....

....i F b I j = F b I and e Gammav e w e v b I = b I, so e Gammav e w e v is a nonclassical vector field of Delta = 0. 4 Nonclassical Reductions, Case 1: 1 The nonclassical determining equations for the case = 1 were automatically generated using the MAPLE program [41] using the algorithm described in [23] As in x2, the calculations in this section were carried out in MAPLE V Release 5, on a 333 MHZ Pentium II PC running under Linux. Hickman s MAPLE program Symmetry [41] automatically generated a raw nonlinear nonclassical determining system of 856 PDE in ....

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M. Hickman, The use of Maple in the search for symmetries, Research Report no. 77, Department of Mathematics, University of Canterbury, Christchurch, New Zealand (1993).

....a nonclassical vector field of (6.1) 3] Thus we can split the search for nonclassical vector fields into two cases: v 4 = 1 and v 4 = 0. We analyse the case v 4 = 1 in this paper. The nonclassical determining equations for the case v 4 = 1 were automatically generated using the Maple program [27]. The resulting nonlinear system consisted of 856 pdes and was automatically simplified by the grobner rif algorithm to a system of 120 pdes. This system, which was not yet in rif form, contained a simple subsystem of single term equations, with all second order partial derivatives of v 5 ; v 6 ; ....

Hickman, M. 1993. The Use of Maple in the Search for Symmetries, Research Report no. 77, Department of Mathematics (University of Canterbury, Christchurch, New Zealand).

....in this paper. We now present a sequence of examples of differential equations with infinite Lie symmetry pseudogroups. In each case the infinitesimal defining system for the point symmetry vector fields was derived by the usual method [1, 31, 32] In particular we used the Maple program [19] to obtain the infinitesimal defining systems. These systems were then automatically brought to canonical form using the program [40] None of the defining systems contained 0 th order equations so the pseudogroups are all transitive. An involutivity check showed that in each case the defining ....

Hickman, M. 1993. The Use of Maple in the Search for Symmetries, Research Report no. 77, Department of Mathematics (University of Canterbury, Christchurch, New Zealand).

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