option nolet
!**********************************************************************
! symbol : general :Levi-Civita,symbol: change position(correctedwhile)
! info:https://en.wikipedia.org/wiki/Levi-Civita_symbol
!**********************************************************************
! website :https://petervlaschemeng.weebly.com/
! topic :fluid dynamics (2019)
!*****************************************************************
!filename :fluidgeneralleviCivitasymbolpositionversion1final.tru
!*****************************************************************
print
print "**********************************************************"
print "----------------------------------------------------------"
print " fluid:general :Levi-Civita symbol(position),version 1.0  "
print " peter.vlasschaert@gmail.com,26/08/2019                   "
print "----------------------------------------------------------"
print " ref : maple code: Denis Constales (Prof UGent)           "
print "**********************************************************"
!*****************************************************************
! ref code :peterperm.mw
!*****************************************************************
print 
print "--------------------------------------------"
print " example : epsilon(1,2,3) => sign = 1       "
print " example : epsilon(2,1,3) => sign = -1      "
print " example : epsilon(1,1,3) => sign = 0       "
print "--------------------------------------------"
n = 5 ! use 1,2,3,4,5
dim a(1),b(1,1)
mat redim a(n),b(1,2)
m1$ = " not a permutation " 
a(1) = 4
a(2) = 5
a(3) = 2
a(4) = 1
a(5) = 3
mat b = 0
print
print "**************************"
print " input permutation symbol "
print "**************************"
print
mat print a ! input matrix for the permutation
k=0         ! init : counter dimension matrix b (number of rows)
for i= 1 to n
   if a(i) <> i then
    !***********************************************
    ! not use exit some other languages use 'break'
    !***********************************************
    j = i+1
         do while ( j <= n and a(j) <> i)
            j =j+1 
         loop
    !************************************************
    ! end loop
    !************************************************
        if n < j then    
             m2$ = " not a permutation " 
             exit for
        end if
     a(j) = a(i)
     a(i) = i
! output : begin
         k=k+1
         mat redim b(k,2)
         ! corrected i to k
         b(k,1) = i
         b(k,2) = j
! output : end
       end if
next i
print "*************************************************"
print "change position : interchange of position        "
print "*************************************************"
print
if m1$ = m2$ then
   print m1$ 
   eps = 0  ! when two symbols are the same 
else 
mat print b
! even or odd
  if mod(k,2) = 0 then
     eps = 1  ! even
     print " k = ";k
  else
     eps = -1 ! odd
     print " k = ";k
  end if
end if
print "************************************"
print " value permutation symbol (epsilon) "
print "************************************"
print
print "************"
print " example    "
print "************"
print
print " epsilon(4,5,2,1,3) = ";" ,k = ";k;" , sign = ";eps
end