| Project/Area Number |
22740009
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Shizuoka University |
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Principal Investigator |
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| Project Period (FY) |
2010 – 2012
|
| Project Status |
Completed (Fiscal Year 2012)
|
| Budget Amount *help |
¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | モジュラー不変式論 / 計算不変式論 / グレブナー基底 / 有限巡回群 |
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| Research Abstract |
We studied computational algebraic methods in modular invarianttheory of finite cyclic groups, and we constructed the following algorithms. We constructed, via defining a Reynolds-like operator, an algorithm for computing generators of modular invariant rings of cyclic groups of prime order. Furthermore, given a polynomial ring over a field of positive characteristic pand an automorphism of order pof the polynomial ring, we constructed the image membership algorithm for the twisted derivation associated with the automorphism
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