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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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