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0 := [<0 _{N}, 0_{N}>]; 1 := [<1_{N}, 0_{N}>]; 2 := [<2_{N}, 0_{N}>]:=xsuchainNxN:x= [a]

x+y:= [< x_{0}+_{N}y_{0},x_{1}+_{N}y_{1}>]- x:= [< x_{1},x_{0}>]x-y:= [< x_{0}+_{N}y_{1},y_{0}+_{N}x_{1}>]x*y:= [<( x_{0}*_{N}y_{0})+_{N}(x_{1}*_{N}y_{1}), (x_{0}*_{N}y_{1})+_{N}(x_{1}*_{N}y_{0})>]x<=y: <=> x_{0}+y_{1}<=_{N}y_{0}+x_{1}

*Since ~ _{Z} is a congruence relation, functions are uniquely
defined.*

Author: Wolfgang Schreiner

Last Modification: January 12, 2000