Singular Manual: Crep

| #### D.2.4.6 Crep Procedure from library `grobcov.lib` (see grobcov_lib). Usage: Crep(N,M); Input: ideal N (null ideal) (not necessarily radical nor maximal) ideal M (hole ideal) (not necessarily containing N) RETURN: The canonical C-representation of the locally closed set. [ P,Q ], a pair of radical ideals with P included in Q, representing the set V(P) \ V(Q) = V(N) \ V(M) NOTE: Operates in a ring R=Q[a] (a=parameters) KEYWORDS: locally closed set, canoncial form EXAMPLE: Crep; shows an example Example:
    LIB "grobcov.lib";
    if(defined(Grobcov::@P)){kill Grobcov::@R; kill Grobcov::@P; kill Grobcov::@RP;}
    ring R=0,(x,y,z),lp;
    short=0;
    ideal E=x*(x^2+y^2+z^2-25);
    ideal N=x*(x-3),y-4;
    def Cr=Crep(E,N);
    Cr;
    ==> [1]:
    ==>    _[1]=x^3+x*y^2+x*z^2-25*x
    ==> [2]:
    ==>    _[1]=y-4
    ==>    _[2]=x*z
    ==>    _[3]=x^2-3*x
    def L=Prep(E,N);
    L;
    ==> [1]:
    ==>    [1]:
    ==>       _[1]=x^2+y^2+z^2-25
    ==>    [2]:
    ==>       [1]:
    ==>          _[1]=z
    ==>          _[2]=y-4
    ==>          _[3]=x-3
    ==>       [2]:
    ==>          _[1]=z+3
    ==>          _[2]=y-4
    ==>          _[3]=x
    ==>       [3]:
    ==>          _[1]=z-3
    ==>          _[2]=y-4
    ==>          _[3]=x
    ==> [2]:
    ==>    [1]:
    ==>       _[1]=x
    ==>    [2]:
    ==>       [1]:
    ==>          _[1]=y-4
    ==>          _[2]=x
    def Cr1=PtoCrep(L);
    Cr1;
    ==> [1]:
    ==>    _[1]=x^3+x*y^2+x*z^2-25*x
    ==> [2]:
    ==>    _[1]=y-4
    ==>    _[2]=x*z
    ==>    _[3]=x^2-3*x

User manual for Singular version 4-0-2, 2015, generated by texi2html.