FormalReductionMapleExamples.mw

• 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
  • Version 1 (ex 15 in paper)
  • Version 2 (ex 16 in paper)
• 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)