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7.5.13.0. polSol
Procedure from library dmodloc.lib (see dmodloc_lib).
- Usage:
- polSol(I[,w,m]); I ideal, w optional intvec, m optional int
- Assume:
- The basering is the n-th Weyl algebra W over a field of
characteristic 0 and for all 1<=i<=n the identity
var(i+n)*var(i)=var(i)*var(i+1)+1 holds, i.e. the sequence of
variables is given by x(1),...,x(n),D(1),...,D(n), where D(i) is the
differential operator belonging to x(i).
Moreover, assume that I is holonomic.
- Return:
- ideal, a basis of the polynomial solutions to the given system of
linear PDEs with polynomial coefficients, encoded via I
- Remarks:
- If w is given, w should consist of n strictly negative entries.
Otherwise and by default, w is set to -1:n.
In this case, w is used as weight vector for the computation of a
b-function.
If m is given, m is assumed to be the minimal integer root of the
b-function of I w.r.t. w. Note that this assumption is not checked.
Reference: (OTT), Algorithm 2.4
- Note:
- If printlevel=1, progress debug messages will be printed,
if printlevel>=2, all the debug messages will be printed.
Example:
| | LIB "dmodloc.lib";
ring r = 0,(x,y,Dx,Dy),dp;
def W = Weyl();
setring W;
poly tx,ty = x*Dx, y*Dy;
ideal I = // Appel F1 with parameters (2,-3,-2,5)
tx*(tx+ty+4)-x*(tx+ty+2)*(tx-3),
ty*(tx+ty+4)-y*(tx+ty+2)*(ty-2),
(x-y)*Dx*Dy+2*Dx-3*Dy;
intvec w = -1,-1;
polSol(I,w);
==> _[1]=10*x^3*y^2-30*x^3*y-45*x^2*y^2+24*x^3+144*x^2*y+72*x*y^2-126*x^2-252\
*x*y-42*y^2+252*x+168*y-210
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See also:
polSolFiniteRank;
ratSol.
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