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  • Committer: Bazaar Package Importer
  • Author(s): Camm Maguire
  • Date: 2004-11-13 18:39:14 UTC
  • mto: (2.1.2 hoary) (3.2.1 sid) (1.1.5 upstream)
  • mto: This revision was merged to the branch mainline in revision 3.
  • Revision ID: james.westby@ubuntu.com-20041113183914-ttig0evwuatnqosl
Tags: upstream-5.9.1
Import upstream version 5.9.1

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share/tensor/ex_calc.mac
 
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/* Copyright (C) 2003 Valerij Pipin <pip@iszf.irk.ru>
 
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 *
 
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 * This program is free software; you can redistribute it and/or
 
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 * modify it under the terms of the GNU General Public License as
 
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 * published by the Free Software Foundation; either version 2 of
 
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 * the License, or (at your option) any later version.
 
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 *
 
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 * This program is distributed in the hope that it will be
 
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 * useful, but WITHOUT ANY WARRANTY; without even the implied
 
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 * warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
 
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 * PURPOSE.  See the GNU General Public License for more details.
 
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 *
 
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 * Commentary:
 
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 * Its purpose is to extend the maxima's itensor ability to manage the
 
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 exterior forms. We introduce the "&" operator for the exterior product,
 
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 the "|_" for the inner product of a form with a vector and "@L" for the
 
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 Lie derivative of the form. 
 
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*/
 
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load("tensor/itensor")$
 
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infix("&");
 
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declare("&",additive); 
 
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"&"(ANY,BODY):=block(local(I),
 
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  L1:first(indices(ANY)),
 
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  L2:first(indices(BODY)),
 
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  if L1=[] then return(ANY*BODY)
 
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  else if L2=[] then return(ANY*BODY)
 
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  else ( L11 : MAKELIST(DUMMY(), I,1, LENGTH(L1)),
 
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    L22 : MAKELIST(DUMMY(), I,1, LENGTH(L2)),
 
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    L1S:MAP("=",L1,L11), L2S:MAP("=",L2,L22),
 
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    LK1:append(L1,L2),LK2:append(L11,L22),
 
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    ANY:sublis(L1S,ANY), BODY:sublis(L2S,BODY),
 
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    evf:(if evenp(length(LK1)) then 1 else -1),
 
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    canform(contract(
 
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        expand(evf*KDELTA(LK1,LK2)*ANY*BODY/(length(LK1)-1)!)))));
 
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infix("@");
 
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declare("@",additive);
 
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"@"(forma,ind):=block(L1:first(indices(forma)),
 
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  if L1=[] then return(diff(forma,ind))
 
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  else ( L11 : MAKELIST(DUMMY(), I,1, LENGTH(L1)),
 
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    L1S:MAP("=",L1,L11),
 
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    LK1:append([ind],L1),
 
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    indd:dummy(),LK2:append(L11,[indd]),
 
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    forma:sublis(L1S,forma),
 
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    evf:(if evenp(length(LK1)) then 1 else -1),
 
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    contract(canform(ratexpand(
 
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          evf*kdelta(LK1,LK2)*diff(forma,indd)/(length(LK1)-1)!)))));
 
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/* VTT: To ensure consistent application of the "first" index in |_ */
 
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PERMUTATOR(L):=BLOCK([RESULT:1,TEMP],
 
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        FOR I THRU LENGTH(L)-1 DO IF ORDERLESSP(L[I+1],L[I]) THEN
 
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        (TEMP:L[I+1],L[I+1]:L[I],L[I]:TEMP,I:0,RESULT:-RESULT),
 
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        [RESULT,L]
 
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);
 
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infix("|_");
 
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declare("|_",additive);
 
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/* VTT: ADDITIVE doesn't always do the trick so we break up sums manually */
 
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"|_"(forma,vec):=BLOCK(LOCAL(ind,perm),
 
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  IF NOT(ATOM(forma)) AND (OP(forma)="+" OR OP(forma)="=") THEN
 
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    APPLY(OP(forma),[PART(forma,1)|_vec,REST(forma)|_vec])
 
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  ELSE (perm:PERMUTATOR(first(indices(forma))),
 
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    IF perm[2]=[] THEN 0
 
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    ELSE perm[1]*(CONTRACT(CANFORM(EXPAND(forma*vec([],[FIRST(perm[2])])))))));
 
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infix("@L");
 
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declare("@L",additive);
 
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"@L"(forma,L1):=block(local(temp1,temp2,ind1),
 
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  vec:first(L1),ind1:second(L1),
 
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  if ind1=0 then (ind1:dummy(),V([],[ind1])*diff(forma,ind1))
 
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  else(
 
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/* VTT: some black magic needed because MAXIMA doesn't handle ADDITIVE as expected */
 
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  temp1:rename(forma@ind1),
 
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  temp1:ev(temp1|_vec,noeval),
 
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  temp1:ev(temp1,eval),
 
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  temp2:rename(forma),
 
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  temp2:ev(temp2|_vec,noeval),
 
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  temp2:ev(temp2,eval)@ind1,
 
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  temp1+temp2));
 
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