/* Copyright (C) 2003 Valerij Pipin <pip@iszf.irk.ru>
 *
 * This program is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public License as
 * published by the Free Software Foundation; either version 2 of
 * the License, or (at your option) any later version.
 *
 * This program is distributed in the hope that it will be
 * useful, but WITHOUT ANY WARRANTY; without even the implied
 * warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
 * PURPOSE.  See the GNU General Public License for more details.
 *
 * Commentary:
 * Simplification of expressions containing the Levi-Civita symbol.
*/
/*
lc2kdt(exp):=block([i1,tem],
	tem:0,
	if nterms(exp)=1 then _lc2kdt0(exp)
	else
	(
		for i1 thru nterms(exp) do
			tem:tem+_lc2kdt0(part(exp,i1)),
		tem
	)
);
*/
lc2kdt(exp):=block(
  [exp:expand(exp),n:nterms(exp)],
  sum(_lc2kdt0(if n>1 then part(exp,i%) else exp),i%,1,n)
);

/*
_lc2kdt0(exp):=block([temp1:1,temp2:1,temp,i1],
	if part(exp,0)="-" then for i1 thru length(part(num(exp),1)) do
	(
		temp:part(num(exp),1,i1),
		if tenpr(temp) and verbify(name(temp))=levi_civita then
		(
			temp1:_lcprod(temp1,temp),
			temp2:temp2*temp
		)
	)
	else for i1 thru length(num(exp)) do
	(
		temp:part(num(exp),i1),
		if tenpr(temp) and verbify(name(temp))=levi_civita then
		(
			temp1:_lcprod(temp1,temp),
			temp2:temp2*temp
		)
	),
	temp1*ratsimp(exp/temp2)
);*/

_lc2kdt0(exp):=block(
  [res:1,fre:1,fac],
  if op(exp)="-" then return(-_lc2kdt0(part(exp,1))),
  if op(num(exp))#"*" then return(exp),
  for i thru length(num(exp)) do
  (
    fac:part(num(exp),i),
    if tenpr(fac) and verbify(name(fac))=levi_civita then
      res:_lcprod(res,fac)
    else fre:fre*fac
  ),
  ratsimp(res*fre)/denom(exp)
);

/*_lcprod(lc1,lc2):=block([temp1,tempk,ln11,lf,l1,l2,l11,l22,lku,lkl],
	if numberp(lc1) or symbolp(lc1) then lc1*lc2
	else if tenpr(lc2) then	/* so name(LC1)=LC */
	(
		if verbify(name(lc2))=levi_civita and tenpr(lc1) then
		(		/* again test if LC1 is a single */
			l1:covi(lc1),
			l11:conti(lc1),
			l2:covi(lc2),
			l22:conti(lc2),
			lkl:append(l1,l2),
			lku:append(l11,l22),
			if lkl=[] then
			(
				lf:length(l11),
				ln11:makelist(idummy(),i,1,lf),
				(
					tempk:1,
					for i thru lf do
						tempk:tempk*kdelta([],[ln11[i],l11[i]])
				),
				kdelta(ln11,l22)*tempk
			)
			else if lku=[] then
			(
				lf:length(l1),
				ln11:makelist(idummy(),i,1,lf),
				(
					tempk:1,
					for i thru lf do
						tempk:tempk*kdelta([l1[i],ln11[i]],[])
				),
				kdelta(l2,ln11)*tempk
			)
			else kdelta(lkl,lku)
		)
		else lc1*lc2
	)
	else
	(
		if numberp(lc2) or symbolp(lc2) then lc2*lc1
		else
		(
			temp1:_extlc(lc1,lc2),
			_lcprod(lc1,temp1)*(lc2/temp1)
		)
	)
);*/

_lcprod(lc1,lc2):=block([temp1,ln11,lf,l1,l2,l11,l22,lku,lkl],
	if numberp(lc1) or symbolp(lc1) then lc1*lc2
	else if tenpr(lc2) then	/* so name(LC1)=LC */
	(
		if verbify(name(lc2))=levi_civita and tenpr(lc1) then
		(		/* again test if LC1 is a single */
			l1:covi(lc1),
			l11:conti(lc1),
			l2:covi(lc2),
			l22:conti(lc2),
			lkl:append(l1,l2),
			lku:append(l11,l22),
			if lkl=[] then
			(
				lf:length(l11),
				ln11:makelist(idummy(),i,1,lf),
				kdelta(ln11,l22)*prod(ev(imetric)([-ln11[i%],-l11[i%]],[]),i%,1,lf)
			)
			else if lku=[] then
			(
				lf:length(l1),
				ln11:makelist(idummy(),i,1,lf),
				kdelta(l2,ln11)*prod(ev(imetric)([l1[i%],ln11[i%]],[]),i%,1,lf)
			)
			else kdelta(lkl,lku)
		)
		else lc1*lc2
	)
	else
	(
		if numberp(lc2) or symbolp(lc2) then lc2*lc1
		else
		(
			temp1:_extlc(lc1,lc2),
			_lcprod(lc1,temp1)*(lc2/temp1)
		)
	)
);


_extlc(lc1,lc2):=block([temp],
	if covi(lc1)#[] then
	(
		temp:part(num(lc2),1,1),
		if tenpr(temp) and verbify(name(temp))=levi_civita and conti(temp)#[] then temp
		else 1.
	)
	else
	(
		temp:part(num(lc2),1,1),
		if tenpr(temp) and verbify(name(temp))=verbify(name(lc1)) and covi(temp)#[] then temp
		else 1.
	)
);