この節では超幾何関数 pFq の(コ)ホモロジ群に関連した不変量を計算する関数を解説する.
OpenXM/Risa/Asir での利用にあたっては,
load("pfpcoh.rr")$ load("pfphom.rr")$
が始めに必要.
pfp_omega
Description:
Define a vector valued function Y of which elements are generalized hypergeometric function f_1=F and f_2=xdf_1/dx, f3=xd f_2/dx, ... It satisfies dY/dx= Omega Y. Generalized hypergeometric function is defined by the series p F p-1(aa1,aa2, ...; cc1, cc2, ...;x) = sum(k=0,infty; (aa1)_k (aa2)_k .../( (1)_k (cc1)_k (cc2)_k ... ) x^k)
Example:
pfp_omega(3);
pfpcoh_intersection
Description:
This program pfpcoh.rr computes an intersection matrix S of cocycles of p F p-1 and compares it with the matrix obtained by solving a differential equation for intersection matrix.
Algorithm:
Ohara, Sugiki, Takayama, Quadratic Relations for Generalized Hypergeometric Functions p F p-1
Example:
load("pfpcoh.rr")$ S=pfpcoh_intersection(3);
Author : K.Ohara
pfphom_intersection
Description:
Computing intersection matrix of cycles associated to p F_(p-1). As to the meaning of parameters c1, c2, c3, ..., see the paper Ohara, Kyushu J. Math. Vol. 51 PP.123.
Algorithm:
Ohara, Sugiki, Takayama, Quadratic Relations for Generalized Hypergeometric Functions p F p-1
Example:
SS = pfphom_intersection(3)$
You get the intersection matrix of homologies for 3 F 2.
Author : K.Ohara
pfphom_monodromy_pair_kyushu
Description:
It returns the pair of monodromy matrices.
Algorithm:
Ohara, Kyushu J. Math. Vol.51 PP.123 (1997)
Example:
MP = pfphom_monodromy_pair_kyushu(3)$
You get a pair of monodromy matricies for 3F2 standing for two paths encircling 0 and 1.
Jump to: p
@vfill @eject
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