share/tensor/lckdt.mac

   1 /* Copyright (C) 2003 Valerij Pipin <pip@iszf.irk.ru>
   2  *
   3  * This program is free software; you can redistribute it and/or
   4  * modify it under the terms of the GNU General Public License as
   5  * published by the Free Software Foundation; either version 2 of
   6  * the License, or (at your option) any later version.
   7  *
   8  * This program is distributed in the hope that it will be
   9  * useful, but WITHOUT ANY WARRANTY; without even the implied
  10  * warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
  11  * PURPOSE.  See the GNU General Public License for more details.
  12  *
  13  * Commentary:
  14  * Simplification of expressions containing the Levi-Civita symbol.
  15 */
  16 /*
  17 lc2kdt(exp):=block([i1,tem],
  18         tem:0,
  19         if nterms(exp)=1 then _lc2kdt0(exp)
  20         else
  21         (
  22                 for i1 thru nterms(exp) do
  23                         tem:tem+_lc2kdt0(part(exp,i1)),
  24                 tem
  25         )
  26 );
  27 */
  28 lc2kdt(exp):=block(
  29   [exp:expand(exp),n:nterms(exp)],
  30   sum(_lc2kdt0(if n>1 then part(exp,i%) else exp),i%,1,n)
  31 );
  32
  33 /*
  34 _lc2kdt0(exp):=block([temp1:1,temp2:1,temp,i1],
  35         if part(exp,0)="-" then for i1 thru length(part(num(exp),1)) do
  36         (
  37                 temp:part(num(exp),1,i1),
  38                 if tenpr(temp) and verbify(name(temp))=levi_civita then
  39                 (
  40                         temp1:_lcprod(temp1,temp),
  41                         temp2:temp2*temp
  42                 )
  43         )
  44         else for i1 thru length(num(exp)) do
  45         (
  46                 temp:part(num(exp),i1),
  47                 if tenpr(temp) and verbify(name(temp))=levi_civita then
  48                 (
  49                         temp1:_lcprod(temp1,temp),
  50                         temp2:temp2*temp
  51                 )
  52         ),
  53         temp1*ratsimp(exp/temp2)
  54 );*/
  55
  56 _lc2kdt0(exp):=block(
  57   [res:1,fre:1,fac],
  58   if op(exp)="-" then return(-_lc2kdt0(part(exp,1))),
  59   if op(num(exp))#"*" then return(exp),
  60   for i thru length(num(exp)) do
  61   (
  62     fac:part(num(exp),i),
  63     if tenpr(fac) and verbify(name(fac))=levi_civita then
  64       res:_lcprod(res,fac)
  65     else fre:fre*fac
  66   ),
  67   ratsimp(res*fre)/denom(exp)
  68 );
  69
  70 /*_lcprod(lc1,lc2):=block([temp1,tempk,ln11,lf,l1,l2,l11,l22,lku,lkl],
  71         if numberp(lc1) or symbolp(lc1) then lc1*lc2
  72         else if tenpr(lc2) then /* so name(LC1)=LC */
  73         (
  74                 if verbify(name(lc2))=levi_civita and tenpr(lc1) then
  75                 (               /* again test if LC1 is a single */
  76                         l1:covi(lc1),
  77                         l11:conti(lc1),
  78                         l2:covi(lc2),
  79                         l22:conti(lc2),
  80                         lkl:append(l1,l2),
  81                         lku:append(l11,l22),
  82                         if lkl=[] then
  83                         (
  84                                 lf:length(l11),
  85                                 ln11:makelist(idummy(),i,1,lf),
  86                                 (
  87                                         tempk:1,
  88                                         for i thru lf do
  89                                                 tempk:tempk*kdelta([],[ln11[i],l11[i]])
  90                                 ),
  91                                 kdelta(ln11,l22)*tempk
  92                         )
  93                         else if lku=[] then
  94                         (
  95                                 lf:length(l1),
  96                                 ln11:makelist(idummy(),i,1,lf),
  97                                 (
  98                                         tempk:1,
  99                                         for i thru lf do
 100                                                 tempk:tempk*kdelta([l1[i],ln11[i]],[])
 101                                 ),
 102                                 kdelta(l2,ln11)*tempk
 103                         )
 104                         else kdelta(lkl,lku)
 105                 )
 106                 else lc1*lc2
 107         )
 108         else
 109         (
 110                 if numberp(lc2) or symbolp(lc2) then lc2*lc1
 111                 else
 112                 (
 113                         temp1:_extlc(lc1,lc2),
 114                         _lcprod(lc1,temp1)*(lc2/temp1)
 115                 )
 116         )
 117 );*/
 118
 119 _lcprod(lc1,lc2):=block([temp1,ln11,lf,l1,l2,l11,l22,lku,lkl],
 120         if numberp(lc1) or symbolp(lc1) then lc1*lc2
 121         else if tenpr(lc2) then /* so name(LC1)=LC */
 122         (
 123                 if verbify(name(lc2))=levi_civita and tenpr(lc1) then
 124                 (               /* again test if LC1 is a single */
 125                         l1:covi(lc1),
 126                         l11:conti(lc1),
 127                         l2:covi(lc2),
 128                         l22:conti(lc2),
 129                         lkl:append(l1,l2),
 130                         lku:append(l11,l22),
 131                         if lkl=[] then
 132                         (
 133                                 lf:length(l11),
 134                                 ln11:makelist(idummy(),i,1,lf),
 135                                 kdelta(ln11,l22)*prod(ev(imetric)([-ln11[i%],-l11[i%]],[]),i%,1,lf)
 136                         )
 137                         else if lku=[] then
 138                         (
 139                                 lf:length(l1),
 140                                 ln11:makelist(idummy(),i,1,lf),
 141                                 kdelta(l2,ln11)*prod(ev(imetric)([l1[i%],ln11[i%]],[]),i%,1,lf)
 142                         )
 143                         else kdelta(lkl,lku)
 144                 )
 145                 else lc1*lc2
 146         )
 147         else
 148         (
 149                 if numberp(lc2) or symbolp(lc2) then lc2*lc1
 150                 else
 151                 (
 152                         temp1:_extlc(lc1,lc2),
 153                         _lcprod(lc1,temp1)*(lc2/temp1)
 154                 )
 155         )
 156 );
 157
 158
 159 _extlc(lc1,lc2):=block([temp],
 160         if covi(lc1)#[] then
 161         (
 162                 temp:part(num(lc2),1,1),
 163                 if tenpr(temp) and verbify(name(temp))=levi_civita and conti(temp)#[] then temp
 164                 else 1.
 165         )
 166         else
 167         (
 168                 temp:part(num(lc2),1,1),
 169                 if tenpr(temp) and verbify(name(temp))=verbify(name(lc1)) and covi(temp)#[] then temp
 170                 else 1.
 171         )
 172 );