# Glue code for the symplectic module
# Author: Michel Barbeau, Carleton University
# Version: November 21, 2016 
def Cliffordspec(S):
	"""
	Returns a specification of the i-th Clifford in group Cn
	in a form that can be used by function "Clifford" of the 
	QuaEC module.

	Example

	import qecc	
	import SYMPLECTIC
	import cliffordglue
	S=SYMPLECTIC.symplectic(1,1)
	T=cliffordglue.Cliffordspec(S)
	C=qecc.Clifford(T[0],T[1])
	print C
	X |->  +Z
	Z |->  +X
	"""
    # X bar
	Xbar=[]
    # Z bar
	Zbar=[]
	for j in range(0,len(S),2):          
		Xj=''
		Zj=''
		for i in range(0,len(S),2):
			# X bar 
			if S[j,i] and S[j,i+1]:
				Xj=Xj+'Y'
			elif S[j,i]:
				Xj=Xj+'X'
			elif S[j,i+1]:
				Xj=Xj+'Z'
			else:
				Xj=Xj+'I'
    		# Z bar
			if S[j+1,i] and S[j+1,i+1]:
				Zj=Zj+'Y'
			elif S[j+1,i]:
				Zj=Zj+'X'
			elif S[j+1,i+1]:
				Zj=Zj+'Z'
			else:
				Zj=Zj+'I'
		Xbar.append(Xj)	
		Zbar.append(Zj)
	return [Xbar,Zbar]