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module eds; % % EDS V2.2 % % % Author: David Hartley % Physics and Mathematical Physics % University of Adelaide SA 5005 % Australia % % email: DHartley@physics.adelaide.edu.au % % % Description: EDS is a REDUCE package for symbolic analysis of partial % differential equations using the geometrical approach of % exterior differential systems. The package implements % much of exterior differential systems theory, including % prolongation and involution analysis, and has been % optimised for large, non-linear problems. % % % Requires: REDUCE 3.8 % % Created: 23/6/90 V0 as es.red (with Robin W Tucker) % % Modified: 8/8/90 V0.1 Added quasi-linear solving and consist- % ency conditions for simultaneous eqns % 11/9/90 V0.2 Added resimp in front of all subf, subsq % etc as temporary fix for subf bug. % 14/5/91 V0.3 Switched off factor (and on exp) in % various routines to make simplifications % work. % 22/5/91 V0.4 Added subs2 in front of all resimp as % temporary fix for unseen power LET rule % bug. % 26/11/91 V0.5 Altered algorithm in regchn so that % alpha coefficients are not chosen until % entire chain has been constructed. % 30/6/92 V1 Renamed exsys.red. % Radically altered exsolve to use modulo % rather than contraction. Eliminated need % for frame vectors. Added extra switches % to allow given, random or (as before) % generic combinations of the independence % 1-forms to be used to construct a % regular chain. % Removed many utilities to tools.red. % 23/7/92 V1.1 Added module `complete' % 14/3/94 V1.2 Renamed eds.red. % Modified for independent compilation, % and for compatibility with new xideal. % 25/4/96 V2.0 Total rewrite using parts of earlier % versions. % Added types for EDS and coframing. % 26/11/96 V2.1 Made cross a bundle product when arguments % share submanifold % 08/07/03 V2.2 Various bug fixes and updates for REDUCE 3.8 % % Other packages which must be loaded at run-time. load_package solve,excalc,xideal; create!-package('( eds % Header module edseval % Definition and manipulation of eds structure for exterior systems edscfrm % Coframing structure for EDS systems % Operations on exterior differential systems tableaux % Definition and manipulation of tableaux using tab structure contact % Contact systems on jet bundles and Grassmann bundles invol % Cartan characters, reduced characters, involution test prolong % Prolonged systems, tableaux pullback % Pullback transformations restrict % Restrict to a subset of a coframing transfrm % Cobasis transformations edspde % PDE interface to EDS edsequiv % Check if EDS structures are equivalent edsuser % Miscellaneous user functions edsnorml % Converting exterior systems to internal form edssolve % Specialised solvers for EDS disjoin % Convert a variety to a disjoint union of sub-coframings element % Generate a random integral element edsaux % Miscellaneous support functions edsexptl % Experimental (algebraic mode) operators edspatch % Various patches for other parts of Reduce. ),'(contrib eds)); % Switches fluid '(!*edsverbose !*edsdebug !*edssloppy !*edsdisjoint !*genpos !*ranpos); switch edsverbose; % prints calculation traces when on switch edsdebug; % prints debugging information when on switch edsdisjoint; % allows automatic variety decomposition when on switch edssloppy; % treat quasilinear systems as semilinear switch genpos; % Calculate characters with system in general % position switch ranpos; % Calculate characters with system in random % position put('genpos,'simpfg,'((t (setq !*ranpos nil)))); put('ranpos,'simpfg,'((t (setq !*genpos nil)))); % Global variables fluid '(cfrmcob!* cfrmcrd!* cfrmdrv!* cfrmrsx!* pullback_maps dependencies); cfrmcob!* := nil; % cobasis for background coframing cfrmcrd!* := nil; % coordinates for background coframing cfrmdrv!* := nil; % structure equations for background coframing cfrmrsx!* := nil; % restrictions for background coframing as pf pullback_maps:= makelist {}; % list of maps used by last call to prolong dependencies := makelist {}; % dependencies removed by pde2eds flag('(pullback_maps dependencies),'share); % Macros used throughout symbolic smacro procedure eds_sys s; cadr s; symbolic smacro procedure eds_ind s; caddr s; symbolic smacro procedure eds_cfrm s; cadddr s; symbolic smacro procedure eds_props s; car cddddr s; symbolic smacro procedure cfrm_cob m; cadr m; symbolic smacro procedure cfrm_crd m; caddr m; symbolic smacro procedure cfrm_drv m; cadddr m; symbolic smacro procedure cfrm_rsx m; nth(m,5); % Macro for edscall symbolic macro procedure edscall u; % evaluate form cadr u within edsprotect function edsprotect . foreach x in cdr u collect function list . mkquote car x . cdr x; %%%% Form function for edscall %%% %%% %%%put('edscall,'formfn,'formedscall); %%% %%%symbolic procedure formedscall(u,v,mode); %%% % evaluate form cadr u within edsprotect %%% function edsprotect . %%% foreach x in formlis(cdr u,v,mode) collect %%% function list . mkquote car x . cdr x; % Macros from excalc for compilation smacro procedure !*k2pf u; u .* (1 ./ 1) .+ nil; smacro procedure negpf u; multpfsq(u,(-1) ./ 1); smacro procedure lowerind u; list('minus,u); endmodule; end;