##################################################### # INFO INFO INFO INFO INFO INFO INFO INFO INFO INFO # ##################################################### PACKAGE : resol2.mu CONTENTS : Functions to compute the resolution of singularities of a singular 1-form in the complex plane. AUTHOR : P. Fortuny (pfortuny@agt.uva.es) STATUS : Experimental, although almost completely functional SYSTEMS : Any with MuPAD INSTALLED : 21.01.2000 What is it for? --------------- (Some knowledge of resolution of singularities is assumed). Give a polynomial plane vector field at (0,0), there is a finite sequence of blowing-ups which transforms the singularity into so-called "simple" one, which are those with non-nilpo- tent linear part and such that the eigenvalues of this linear part have not a positive rational quotient. The process has some associated invariants: the dual graph of the reduction and the quotient of eigenvalues at the final singularities. These are computed by RESOL2. Moreover, it also calculates the separatrices (power series expansions of the solutions) up to a (up to date fixed, but easily modifiable) given degree. There are (undocumented still) functions to produce PS-draw files to draw the graph and place it in a LaTeX document. See the comments at the beginning of each .mu file. How to install it? ------------------ Place the .tar archive in the same directory of the MuPAD library (unix systems ...MuPAD/share/lib). How to use it? -------------- Export the library >> export(resol2); and use the functions. The easiest way to reduce a 1-form a(x,y) dx + b(x,y) dy is to write >> red([a,b]); (notice that the variables in a and b MUST be 'x' and 'y'; there are other ways to use different variables, but they require more information than what this info-file is for) the output is something like [[[a1,b1],[a2,b2],...,[ak,bk]],k], Network(), table(1=table( 1=f(t),2=g(t),3="str") which means ai-> kind of singularity (corner or regular point) bi-> quotient of the eigenvalues Network-> dual graph of the reduction table()....-> parametrization of the separatrices at the regular points >> setuserinfo(resol2,1) gives information on the reduction process (which blowing-ups are done and where) >> setuserinfo(resol2,2) even more. There is more information in the .tar archive, in the files RESOL2/DOC/resol2.help RESOL2/resol2.txt and at the beginning of the .mu files in RESOL2/RESOL2 ##################################################### #####################################################