Shift Equivalence of P-finite Sequences(11)

We present an algorithm which decides the shift equivalence problem for Pfinite sequences. A sequence is called P-finite if it satisfies a homogeneous linear recurrence equation with polynomial coefficients. Two sequences are called shift equivalent if shi

WehaveL·f1=L·f2=0for

L=E3+E2 E 1=(E+1)(E 1)2∈k[E].

ComputingtheJordandecompositionofthecompanionmatrix,we nd

010

C:= 001 111 1 1001/4 1/21/41/4 1/21/4

= 1/41/23/4 011 1/41/23/4 =:T 1JT.

001 1/201/2 1/201/2

ApplyingTtothevectorsofinitialvaluesleadsto

018 1

u¯=T 0 = 3 ,v¯=T 8 = 5 .

424 2

Itremainsto nds∈suchthat

s 11 100 3 = 011 5 .

22001

ThematrixJconsistsoftwoJordanblockswhichhavetobeconsideredseparately.The rstblockhaslength1,anditrestrictsthesolutionstotheset

S1:={s∈:1

2 ( 5

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