Singular Manual: envelopdg

| #### D.2.4.13 envelopdg Procedure from library `grobcov.lib` (see grobcov_lib). Usage: envelopdg(L); The input list L must be the output of the call to the routine 'envolop' of the family of curves Return: The relevant components of the envelop in Dynamic Geometry. 'Normal' and 'Accumulation' components are always considered 'Relevant'. 'Special' components of the envelop outputs three objects in its characterization: 'Special', the antiimage ideal, and the integer 0 or 1, that indicates that the given component is formed (1) or is not formed (0) by curves of the family. Only if yes, 'envelopdg' considers the component as 'Relevant' . Note: It must be called to the output of the 'envelop' routine. The basering R, must be of the form Q[a,b,..][x,y,..]. Example:
    LIB "grobcov.lib";
    // 1. Take a fixed line l: x1-y1=0  and consider
    //    the family F of a lines parallel to l passing through the mover point M
    // 2. Consider a circle x1^2+x2^2-25, and a mover point M(x1,x2) on it.
    // 3. Compute the envelop of the family of lines.
    ring R=(0,x,y),(x1,y1),lp;
    short=0;
    poly F=(y-y1)-(x-x1);
    ideal C=x1^2+y1^2-25;
    short=0;
    // Curves Family F=
    F;
    ==> x1-y1+(-x+y)
    // Conditions C=
    C;
    ==> C[1]=x1^2+y1^2-25
    envelop(F,C);
    ==> [1]:
    ==>    [1]:
    ==>       _[1]=(x^2-2*x*y+y^2-50)
    ==>    [2]:
    ==>       [1]:
    ==>          _[1]=1
    ==>    [3]:
    ==>       [1]:
    ==>          Special
    ==>       [2]:
    ==>          2*y1^2-25,x1+y1
    ==>       [3]:
    ==>          1
    ==>    [4]:
    ==>       1
    envelopdg(envelop(F,C));
    ==> [1]:
    ==>    [1]:
    ==>       _[1]=(x^2-2*x*y+y^2-50)
    ==>    [2]:
    ==>       [1]:
    ==>          _[1]=1
    ==>    [3]:
    ==>       Relevant
    ==>    [4]:
    ==>       1

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