Example 1 (ex. in section 3.6  in paper)  

Example 2 (ex. 11 in paper)  

Example 3 (ex. 13 in paper)  

Example 4 (ex. 15 and 16 in paper)  New version 1 and 2 

Example 5 (ex. 16 in paper) 

Example : Example 3.6 in paper "A new approach for formal reduction of singular linear
differential systems using eigenrings". 

Example Version1-1 : This is a case where the exponential parts have (conjugated) algebraic coefficients 2x2 (mu=1, d=2, r=1). 

Example V1-2 :  This is a case where the exponential parts are copies 2x2 (mu=2, d=1, r=1). 

Example V1-3 :  This is a case where we have one simple exponential part and 2 conjugated 3x3 (mu=1, d=1, r=1)+(mu=1, d=2, r=1). 

Example V1-4 :  This is a case where we have 3 different exponential parts (mu=1, d=1, r=1)+(mu=1, d=1, r=1)+(mu=1, d=1, r=1). 

Example V1-5 :  This is a case where we have one simple exponential part and a ramification of degree2 3x3 (mu=1,d=1,r=1)+(mu=1,d=1,r=2) 

Example V1-6 :  This is a case where we have one ramification of degree2 2x2 (mu=1,d=1,r=2) 

Example V1-7: This is a case where we have two copies of conjuguates exponential parts by the action x-t^2=0 (mu=2,d=1,r=1) 

Example V1-8 : This is a case where we have one ramification of degree3 3x3 (mu=1,d=1,r=3). 

Example V1-9 : (mu=1,d=1,r=1)+(mu=1,d=1,r=2)+(mu=1,d=2,r=3) 

Example v1-10 :(mu=1,d=2,r=2) 

Example Version2-1 : This is a case where the exponential parts have (conjugated) algebraic coefficients 2x2 (mu=1, d=2, r=1) 

Example V2-2 :  This is a case where the exponential parts are copies 2x2 (mu=2, d=1, r=1). 

Example V2-3 :  This is a case where we have one simple exponential part and 2 conjugated 3x3 (mu=1, d=1, r=1)+(mu=1, d=2, r=1). 

Example V2-4 : This is a case where we have 3 different exponential parts (mu=1, d=1, r=1)+(mu=1, d=1, r=1)+(mu=1, d=1, r=1). 

Example V2-5 :  This is a case where we have one simple exponential part and a ramification of degree2 3x3 (mu=1,d=1,r=1)+(mu=1,d=1,r=2). 

Example V2-6 : This is a case where we have one ramification of degree2 2x2 (mu=1,d=1,r=2). 

Example V2-7: This is a case where we have two copies of conjuguates exponential parts by the action x-t^2=0 (mu=2,d=1,r=1) 

Example V2-8 : This is a case where we have one ramification of degree3 3x3 (mu=1,d=1,r=3). 

Example V2-9: (mu=1,d=1,r=1)+(mu=1,d=1,r=2)+(mu=1,d=2,r=3) 

Example V2-10: (mu=1,d=2,r=2)