| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Outline of Final Research Achievements |
D-module is an algebraic concept corresponding to a system of linear (ordinary or partial) differential equations. Holonomic systems are an important class of D-modules; their solutions constitute a finite dimensional vector space. Hence properties of a holonomic function are expected to be extracted from the corresponding holonomic system. I constructed an algorithm for computing a holonomic system for the integral of a holonomic function over the domain defined by polynomial inequalities. I also gave a rigorous proof that the result of the algorithm is in fact a holonomic system. As an application, I computed holonomic systems for density functions for various stochastic distributions, as well as for the Feynman integral associated with the triangle Feynman diagram in the two-dimensional space-time.
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