Geodesic
Justification of an effective algorithm for determining the pointwise completeness and pointwise degeneracy of linear delay systems of order 12
Sibirskij žurnal industrialʹnoj matematiki, Tome 17 (2014) no. 2, pp. 59-73

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We justify an effective algorithm for the reduction of a linear system or order 12 with delay $h$ to the normal form. In case the active matrix of the system is degenerate, we also justify a modified algorithm for checking the poitwise completeness of the system. To this end, it suffices to find all real roots of one polynomial of degree 4 whose all coefficients depend on the geometric invariants of the normal form and the exponent of the product of one-half of the active matrix by $h$.
Keywords: pointwise completeness of a delay system of ordinary differential equations. 
A. A. Korobov. Justification of an effective algorithm for determining the pointwise completeness and pointwise degeneracy of linear delay systems of order 12. Sibirskij žurnal industrialʹnoj matematiki, Tome 17 (2014) no. 2, pp. 59-73. http://geodesic.mathdoc.fr/item/SJIM_2014_17_2_a6/
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     title = {Justification of an effective algorithm for determining the pointwise completeness and pointwise degeneracy of linear delay systems of order~12},
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[1] Korobov A. A., “Effektivnye usloviya tochechnoi polnoty dlya lineinykh sistem s zapazdyvaniem”, Sib. zhurn. industr. matematiki, 10:1(29) (2007), 96–114 | MR | Zbl

[2] Korobov A. A., “O tochechno polnykh parakh lineinykh preobrazovanii”, Sib. zhurn. industr. matematiki, 13:3(43) (2010), 58–67 | MR | Zbl

[3] Korobov A. A., “Novye effektivnye usloviya tochechnoi polnoty dlya lineinykh sistem s zapazdyvaniem”, Vychisl. matematika, differentsialnye uravneniya, informatsionnye tekhnologii, Materialy Mezhdunar. konf., posvyasch. pamyati Ts. B. Shoinzhurova, Izd. VSGTU, Ulan-Ude, 2009, 216–223