| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
|
|---|
| Outline of Final Research Achievements |
I introduced a new GCD of two monic polynomials defined over rings with nilpotent elements. This was applied to the computation of cofactors (also known as Bezout coefficients) in the Chinese Remainder Theorem for polynomials with coefficients in such rings. Then, this was exploited to estimate the coefficients growth in the computation of a non-radical triangular set (a special lexicographic Groebner basis). This Chinese Remainder Remainder theorem can be seen as a kind of Hermite interpolation. Then we have investigated in some special cases the conversion to the more amenable barycentric form of Hermite interpolation.
This new ability to treat polynomials with coefficients in such rings opens the way to new directions of research, which were limited so far to the "radical" case. Some of these directions are ongoing research.
|
