option nolet
!***********************************************************
! symbol : general :Levi-Civita,symbol: change position
! info:https://en.wikipedia.org/wiki/Levi-Civita_symbol
!***********************************************************
! website :https://petervlaschemeng.weebly.com/
! topic :fluid dynamics (2019)
!*****************************************************************
!filename :FLUIDGENERALLEVICIVITASYMBOLPOSITIONINPUTSUBVERSION1CFINALFINAL
!*****************************************************************
print
print "**************************************************************"
print "--------------------------------------------------------------"
print " fluid:general :Levi-Civita symbol(position,sub),version 1.0c "
print " peter.vlasschaert@gmail.com,29/08/2019                       "
print "--------------------------------------------------------------"
print " ref : maple code: Denis Constales (Prof UGent)               "
print "**************************************************************"
!*****************************************************************
! ref code :peterperm.mw
!*****************************************************************
print "--------------------------------------------"
print " example : epsilon(1,2,3) => sign = 1,even  "
print " example : epsilon(2,1,3) => sign = -1,odd  "
print " example : epsilon(1,1,3) => sign = 0       "
print "--------------------------------------------"
!****************************************
! even or  odd interchanges of position *
!****************************************
print 
dim a(1),b(1,1)
mat a = 0
mat b = 0
m1$ = " not a permutation " 
!*******************************************************
! how to use program , input integer = 1 for the example
!*******************************************************
input prompt " example = 1, input(epsilon),seq = 2  =>  ":s
print
if s=1 then
n = 5 ! use 1,2,3,4,5
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   
else
    input prompt " how many numbers (n:integer): seq. of epsilon =>  ": m
    print
    n=m  ! integer : the length seq : sequence  
  call matrix_inp(n,a())
end if
! copy a matrix
dim dd(1)
mat redim dd(n)
mat dd = a
print
print "**************************"
print " input permutation symbol "
print "**************************"
mat print a ! input matrix for the permutation
k=0         ! init : counter dimension matrix b (number of rows)
print "*************************************************"
print "change position : interchange of position        "
print "*************************************************"
print
call algo_perm(n,a(),b(,),m2$,k)
call epsilon_sign(m1$,m2$,k,eps,b(,))
print "************************************"
print " value permutation symbol (epsilon) "
print "************************************"
print
if s=1 then
print "************"
print " example    "
print "************"
print
print " epsilon(4,5,2,1,3) = ";" ,k = ";k;" , sign = ";eps
else
print "************"
print " output     "
print "************"
print
call epsilon_str(a(),kk$)
print kk$ ;" ,k = ";k;" , sign = ";eps
end if
print
!******************************
! How to use swap : see example
!******************************
if s=1 then
print " how to use swap of two elements "
print
dim h(4)
h(1) = 3
h(2) = 2
h(3) = 4
h(4) = 1
print " input => "
mat print h
! intechange element (2,3)
call swap_el(2,3,h())
print " output => call swap_el(2,3,h())"
print " swap element 2 and element 3   "
mat print h
end if
print "***********************"
print " final output sequence "
print "***********************"
dim mo(1,1),mo1(1,1)
mat redim mo1(k+1,n),mo(k+1,n)
mat mo  = zero
mat mo1 = zero
for i3 = 1 to n
    mo1(1,i3) = dd(i3)
next i3

!************************************
! matrix input all output, matrix mo
dim mo2(1,1)
mat redim mo2(k,n)
!************************************
print
! use b matrix
for i=1 to k
call swap_el(b(i,1),b(i,2),dd())
! mat print dd
! or
! use mo2 , matrix
for i1 = 1 to n
      mo2(i,i1) = dd(i1)
next i1
! end mo2
next i
! moh => same dimension as mo1, redimension for mo2
dim moh(1,1)
mat redim moh(k+1,n)
mat moh = 0
for l1=2 to k+1
  for l2 = 1 to n
moh(l1,l2)=mo2(l1-1,l2)
  next l2
next l1
mat mo = mo1+moh
mat print mo
end

sub matrix_inp(n,a())
mat redim a(n)
   for j = 1 to n
       print "position ,in the string epsilon(";j;") = ";
       input a(j)
   next j
end sub

sub epsilon_str(a(),kk$)
!*****************************
! how to build string epsilon
!*****************************
kk$ = "epsilon("& str$(a(1))
for i=2 to n
kk$ = kk$ & "," & str$(a(i))
next i
kk$ = kk$ & ") = "
!**************************
! end build epsilon string
!**************************
end sub

sub algo_perm(n,a(),b(,),m2$,k)
for i= 1 to n
   if a(i) <> i then  ! value matrix ( 1 on position one,....) otherwise
      for j=i+1 to n  ! all values except the first
        if a(j) = i then
          exit for    
        end if
      next j
     if n < j then    
        m2$ = " not a permutation "  
        exit for
     end if
! interchange 
     a(j) = a(i)
     a(i) = i
! output : begin
         k=k+1
         mat redim b(k,2)
! don't forget first index b must be k
         b(k,1) = i
         b(k,2) = j
! output : end
       end if
next i
end sub

sub epsilon_sign(m1$,m2$,k,eps,b(,))
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
end sub

sub swap_el(h1,h2,h())
temp1 = h(h1)
h(h1) = h(h2)
h(h2) = temp1
end sub