Singular Manual: PtoCrep

| #### D.2.4.7 PtoCrep Procedure from library `grobcov.lib` (see grobcov_lib). Usage: PtoCrep(list L) list L= [ Comp_1, .. , Comp_s ] where list Comp_i=[p_i,[p_i1,..,p_is_i] ], is the P-representation of a locally closed set V(N) \ V(M). To be called in a ring Q[a][x] or a ring Q[a]. But the ideals can contain only the parameters in Q[a]. Return: The canonical C-representation [P,Q] of the locally closed set. A pair of radical ideals with P included in Q, representing the set V(P) \ V(Q) Example:
    LIB "grobcov.lib";
    if(defined(R)){kill R;}
    ring R=0,(a,b,c),lp;
    short=0;
    ideal p=a*(a^2+b^2+c^2-25);
    ideal q=a*(a-3),b-4;
    // C-representaion of V(p) \ V(q)
    def Cr=Crep(p,q);
    Cr;
    ==> [1]:
    ==>    _[1]=a^3+a*b^2+a*c^2-25*a
    ==> [2]:
    ==>    _[1]=b-4
    ==>    _[2]=a*c
    ==>    _[3]=a^2-3*a
    // C-representation of V(p) \ V(q)
    def L=Prep(p,q);
    L;
    ==> [1]:
    ==>    [1]:
    ==>       _[1]=a^2+b^2+c^2-25
    ==>    [2]:
    ==>       [1]:
    ==>          _[1]=c-3
    ==>          _[2]=b-4
    ==>          _[3]=a
    ==>       [2]:
    ==>          _[1]=c+3
    ==>          _[2]=b-4
    ==>          _[3]=a
    ==>       [3]:
    ==>          _[1]=c
    ==>          _[2]=b-4
    ==>          _[3]=a-3
    ==> [2]:
    ==>    [1]:
    ==>       _[1]=a
    ==>    [2]:
    ==>       [1]:
    ==>          _[1]=b-4
    ==>          _[2]=a
    PtoCrep(L);
    ==> [1]:
    ==>    _[1]=a^3+a*b^2+a*c^2-25*a
    ==> [2]:
    ==>    _[1]=b-4
    ==>    _[2]=a*c
    ==>    _[3]=a^2-3*a

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