- Folder for V_2(R^3)
- Risa/Asir program to get the Pfaffian system (sf.rr)
start Risa/Asir with the asir-contrib library. load("sf.rr"); bynd(); myprune(); A=mypf()$ /* Pfaffian system is saved in the file tmp-pf-sf32.ab It is a list of 6 matrices A[0], ..., A[5], which are coefficients of the Pfaffian system. V=dsf(3,2)[1] a list of variables. Let F be a solution vector. Then, dF/dV[i] = A[i]F holds. */

The function dsf(3,2) returns the system of differential equations for c(\Theta).

- Risa/Asir program for the holonomic gradient descent (HGD) (sf2i.rr) See 2011-09-16-comets.txt how to use it.
- R program for evaluation of c(\Theta) by a seires
(etrcalc.r)
Start R. source("etrcalc.r"); SO.init(Ts.Xm) # Initial value for HGD for commets data. The output is embedded in sf2.rr SO.init(TsAst,XmAst) # Initial value for HGD for asteroids data. SO.int2(Ts) # value of c(\Theta) for Ts.

- Risa/Asir program to get a partial Grobner basis for SO(3)
It takes a very long time to get the basis on a 64 bit machine with 48G memory. The result is in
tmp-dso3.ab (right click for the download. It is huge size).
load("sdo.rr"); bynd()$

- Folder for HGD-MLE for SO(3)
- A note (old) for the files and programs in this folder (in Japanese)
- Pfaffian data for SO(3) (pf.ab) (right click for saving)
Start Risa/Asir Pfs=bload("pf.ab")$ /* Pfs[0] is a list of 9 matrices, which are the coefficients of the Pfaffian system. A hashed data structure is used to save polynomials. */

The data is generated by mydso9.rr

- MLE by the HGD for SO(3), commets data(old).
See the files Log.txt and Log16.txt to see how to run it
(A fast machine will be recommended to run it).
Start Risa/Asir load("hgd-test.rr"); load("hgd-test16.rr");