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7.7.4.0. initialIdealW
Procedure from library dmodapp.lib (see dmodapp_lib).
- Usage:
- initialIdealW(I,u,v [,s,t,w]); I ideal, u,v intvecs, s,t optional ints,
w an optional intvec
- Return:
- ideal, GB of initial ideal of the input ideal w.r.t. the weights u and v
- Assume:
- The basering is the n-th Weyl algebra in 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).
- Purpose:
- computes the initial ideal with respect to given weights.
- Note:
- u and v are understood as weight vectors for x(1..n) and D(1..n)
respectively.
If s<>0, std is used for Groebner basis computations,
otherwise, and by default, slimgb is used.
If t<>0, a matrix ordering is used for Groebner basis computations,
otherwise, and by default, a block ordering is used.
If w consist of 2n strictly positive entries, w is used for weighted
homogenization, otherwise, and by default, no weights are used.
- Display:
- If printlevel=1, progress debug messages will be printed,
if printlevel>=2, all the debug messages will be printed.
Example:
| LIB "dmodapp.lib";
ring @D = 0,(x,Dx),dp;
def D = Weyl();
setring D;
intvec u = -1; intvec v = 2;
ideal I = x^2*Dx^2,x*Dx^4;
ideal J = initialIdealW(I,u,v); J;
==> J[1]=Dx^2
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