pfp_omega
---------

pfp_omega(P)
     : It returns the Gauss-Manin connection Omega for the generalized hypergeometric function P F P-1 (aa1,aa2, ...; cc1, cc2, ...;x) .

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
-------------------

pfpcoh_intersection(P)
     : pfpcoh_intersection(P) returns an intersection matrix for cocycles associated to the generalized hypergeometric function p F_(p-1).

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
-------------------

pfphom_intersection(P)
     : intersection matrix of homology cycles.

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
----------------------------

pfphom_monodromy_pair_kyushu(P)
     :

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.