3036.sagews

from fractions import Fraction

def Index_string(a,b, L):
 k_0=0; k_1 = 0; Ind=0 ; 
 for i in range(0,len(L)):
   if L[i] == a: k_0= k_0 + 1 
   for j in range(0,len(L)):
       if L[j] == b: 
           if j < i: Ind = Ind-1 
           if j > i: Ind = Ind+1
 k_1 = len(L) - k_0 
 return Fraction(Ind, 2*k_0*k_1) 
   #[k_0,k_1,Ind,Ind/(2*k_0*k_1)] 

def Curvature(a,b,c,L):
  # curvature of 3-character word. Use: 
  # Curvarure(first chararacter , second character, third character, word );
 Lab =""; Lac=""; Lbc=""; 
 for i in range(0,len(L)):
   if L[i] == a: Lab=Lab+L[i]; Lac=Lac+L[i]
   if L[i] == b: Lab=Lab+L[i]; Lbc=Lbc+L[i]
   if L[i] == c: Lac=Lac+L[i]; Lbc=Lbc+L[i]
 return Index_string(a,b,Lab)-Index_string(a,c,Lac)+Index_string(b,c,Lbc)

print Curvature("a","p","s","papaspaspsa")
print Curvature("s","e","l","selllesseels")
print Curvature("l","g","u","lguguglu")

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