Singular Manual: restrictionIdeal

| ##### 7.5.5.0. restrictionIdeal Procedure from library `dmodapp.lib` (see dmodapp_lib). Usage: restrictionIdeal(I,w,[,eng,m,G]); I ideal, w intvec, eng and m optional ints, G optional ideal Return: ring (a Weyl algebra) containing an ideal 'resIdeal' Assume: The basering is the n-th Weyl algebra 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). Further, assume that I is holonomic and that w is n-dimensional with non-negative entries. Purpose: computes the restriction ideal of a holonomic ideal to the subspace defined by the variables corresponding to the non-zero entries of the given intvec Note: The output ring is the Weyl algebra defined by the zero entries of w. It contains an ideal 'resIdeal' being the restriction ideal of I wrt w. If there are no zero entries, the input ring is returned. If eng<>0, `std` is used for Groebner basis computations, otherwise, and by default, `slimgb` is used. The minimal integer root of the b-function of I wrt the weight (-w,w) can be specified via the optional argument m. The optional argument G is used for specifying a Groebner basis of I wrt the weight (-w,w), that is, the initial form of G generates the initial ideal of I wrt the weight (-w,w). Further note, that the assumptions on m and G (if given) are not checked. 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 r = 0,(a,x,b,Da,Dx,Db),dp;
    def D3 = Weyl();
    setring D3;
    ideal I = a*Db-Dx+2*Da,
    x*Db-Da,
    x*Da+a*Da+b*Db+1,
    x*Dx-2*x*Da-a*Da,
    b*Db^2+Dx*Da-Da^2+Db,
    a*Dx*Da+2*x*Da^2+a*Da^2+b*Dx*Db+Dx+2*Da;
    intvec w = 1,0,0;
    def D2 = restrictionIdeal(I,w);
    setring D2; D2;
    ==> // coefficients: QQ
    ==> // number of vars : 4
    ==> //        block   1 : ordering C
    ==> //        block   2 : ordering dp
    ==> //                  : names    x b Dx Db
    ==> // noncommutative relations:
    ==> //    Dxx=x*Dx+1
    ==> //    Dbb=b*Db+1
    resIdeal;
    ==> resIdeal[1]=2*x*Db-Dx
    ==> resIdeal[2]=x*Dx+2*b*Db+2
    ==> resIdeal[3]=4*b*Db^2+Dx^2+6*Db

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