next | previous | forward | backward | up | top | index | toc | Macaulay2 website
Dmodules :: RatSols

RatSols -- rational solutions of a holonomic system

Synopsis

Description

The rational solutions of a holonomic system form a finite-dimensional vector space. The only possibilities for the poles of a rational solution are the codimension one components of the singular locus. An algorithm to compute rational solutions is based on Gr\"obner deformations and works for ideals $I$ of PDE's - see the paper Polynomial and rational solutions of a holonomic system by Oaku, Takayama and Tsai (2000).

i1 : makeWA(QQ[x])

o1 = QQ[x, dx]

o1 : PolynomialRing, 1 differential variables
i2 : I = ideal((x+1)*dx+5)

o2 = ideal(x*dx + dx + 5)

o2 : Ideal of QQ[x, dx]
i3 : RatSols I

                     1
o3 = {-------------------------------}
       5     4      3      2
      x  + 5x  + 10x  + 10x  + 5x + 1

o3 : List

Caveat

The most efficient method to find rational solutions of a system of differential equations is to find the singular locus, then try to find its irreducible factors. With these, call RatSols(I, ff, w), where w should be generic enough so that the PolySols routine will not complain of a non-generic weight vector.

See also

Ways to use RatSols :

For the programmer

The object RatSols is a method function.