Top
Back: locus
Forward: envelop
FastBack:
FastForward:
Up: grobcov_lib
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

D.2.4.11 locusdg

Procedure from library grobcov.lib (see grobcov_lib).

Usage:
locusdg(L) The call must be locusdg(locus(grobcov(S))).

Return:
The output is the list of the 'Relevant' components of the locus in Dynamic Geometry:(C1,..,C:m), where
C_i= ( p_i,(p_i1,..p_is_i), 'Relevant', level_i )
The 'Relevant' components are the 'Normal' and 'Accumulation' components of the locus. (See help for locus).

Note:
It can only be called after computing the locus.
Calling sequence: locusdg(locus(grobcov(S)));

Example:
 
LIB "grobcov.lib";
ring R=(0,a,b),(x,y),dp;
short=0;
// Concoid
ideal S96=x^2+y^2-4,(b-2)*x-a*y+2*a,(a-x)^2+(b-y)^2-1;
// System S96=
S96;
==> S96[1]=x^2+y^2-4
==> S96[2]=(b-2)*x+(-a)*y+(2*a)
==> S96[3]=x^2+y^2+(-2*a)*x+(-2*b)*y+(a^2+b^2-1)
locus(grobcov(S96));
==> [1]:
==>    [1]:
==>       _[1]=(a^4+2*a^2*b^2-9*a^2+b^4-9*b^2+4*b+12)
==>    [2]:
==>       [1]:
==>          _[1]=(b-2)
==>          _[2]=(a)
==>       [2]:
==>          _[1]=(2*b-3)
==>          _[2]=(4*a^2-3)
==>    [3]:
==>       Normal
==>    [4]:
==>       1
==> [2]:
==>    [1]:
==>       _[1]=(a^2+b^2-4*b+3)
==>    [2]:
==>       [1]:
==>          _[1]=(2*b-3)
==>          _[2]=(4*a^2-3)
==>    [3]:
==>       [1]:
==>          Special
==>       [2]:
==>          y-2,x
==>    [4]:
==>       1
==> [3]:
==>    [1]:
==>       _[1]=(b-2)
==>       _[2]=(a)
==>    [2]:
==>       [1]:
==>          _[1]=1
==>    [3]:
==>       Normal
==>    [4]:
==>       2
==> [4]:
==>    [1]:
==>       _[1]=(2*b-3)
==>       _[2]=(4*a^2-3)
==>    [2]:
==>       [1]:
==>          _[1]=1
==>    [3]:
==>       Normal
==>    [4]:
==>       2
locusdg(locus(grobcov(S96)));
==> [1]:
==>    [1]:
==>       _[1]=(a^4+2*a^2*b^2-9*a^2+b^4-9*b^2+4*b+12)
==>    [2]:
==>       [1]:
==>          _[1]=(b-2)
==>          _[2]=(a)
==>       [2]:
==>          _[1]=(2*b-3)
==>          _[2]=(4*a^2-3)
==>    [3]:
==>       Relevant
==>    [4]:
==>       1
==> [2]:
==>    [1]:
==>       _[1]=(b-2)
==>       _[2]=(a)
==>    [2]:
==>       [1]:
==>          _[1]=1
==>    [3]:
==>       Relevant
==>    [4]:
==>       2
==> [3]:
==>    [1]:
==>       _[1]=(2*b-3)
==>       _[2]=(4*a^2-3)
==>    [2]:
==>       [1]:
==>          _[1]=1
==>    [3]:
==>       Relevant
==>    [4]:
==>       2
kill R;
//********************************************
ring R=(0,a,b),(x4,x3,x2,x1),dp;
ideal S=(x1-3)^2+(x2-1)^2-9,
(4-x2)*(x3-3)+(x1-3)*(x4-1),
(3-x1)*(x3-x1)+(4-x2)*(x4-x2),
(4-x4)*a+(x3-3)*b+3*x4-4*x3,
(a-x1)^2+(b-x2)^2-(x1-x3)^2-(x2-x4)^2;
short=0;
locus(grobcov(S));
==> locus detected that the mover must avoid point (x1-3,x2-4) in order to ob\
   tain the correct locus
==> [1]:
==>    [1]:
==>       _[1]=(a^4-12*a^3+2*a^2*b^2-13*a^2*b+236*a^2-12*a*b^2+78*a*b-1200*a+\
   b^4-13*b^3+60*b^2-85*b+1495)
==>    [2]:
==>       [1]:
==>          _[1]=(7*b-4)
==>          _[2]=(49*a^2-294*a+387)
==>       [2]:
==>          _[1]=(b+2)
==>          _[2]=(a-3)
==>       [3]:
==>          _[1]=(b-4)
==>          _[2]=(a-3)
==>    [3]:
==>       Normal
==>    [4]:
==>       1
==> [2]:
==>    [1]:
==>       _[1]=(a^2-6*a+b^2+b+7)
==>    [2]:
==>       [1]:
==>          _[1]=(7*b-4)
==>          _[2]=(49*a^2-294*a+387)
==>       [2]:
==>          _[1]=(b-2)
==>          _[2]=(a^2-6*a+13)
==>       [3]:
==>          _[1]=(b+2)
==>          _[2]=(a-3)
==>    [3]:
==>       Normal
==>    [4]:
==>       1
==> [3]:
==>    [1]:
==>       _[1]=(7*b-4)
==>       _[2]=(49*a^2-294*a+387)
==>    [2]:
==>       [1]:
==>          _[1]=1
==>    [3]:
==>       Normal
==>    [4]:
==>       2
==> [4]:
==>    [1]:
==>       _[1]=(b+2)
==>       _[2]=(a-3)
==>    [2]:
==>       [1]:
==>          _[1]=1
==>    [3]:
==>       Normal
==>    [4]:
==>       2
==> [5]:
==>    [1]:
==>       _[1]=(b-2)
==>       _[2]=(a^2-6*a+13)
==>    [2]:
==>       [1]:
==>          _[1]=1
==>    [3]:
==>       Accumulation
==>    [4]:
==>       1
==> [6]:
==>    [1]:
==>       _[1]=(b-4)
==>       _[2]=(a-3)
==>    [2]:
==>       [1]:
==>          _[1]=1
==>    [3]:
==>       Accumulation
==>    [4]:
==>       1
locusdg(locus(grobcov(S)));
==> locus detected that the mover must avoid point (x1-3,x2-4) in order to ob\
   tain the correct locus
==> [1]:
==>    [1]:
==>       _[1]=(a^4-12*a^3+2*a^2*b^2-13*a^2*b+236*a^2-12*a*b^2+78*a*b-1200*a+\
   b^4-13*b^3+60*b^2-85*b+1495)
==>    [2]:
==>       [1]:
==>          _[1]=(7*b-4)
==>          _[2]=(49*a^2-294*a+387)
==>       [2]:
==>          _[1]=(b-4)
==>          _[2]=(a-3)
==>       [3]:
==>          _[1]=(b+2)
==>          _[2]=(a-3)
==>    [3]:
==>       Relevant
==>    [4]:
==>       1
==> [2]:
==>    [1]:
==>       _[1]=(a^2-6*a+b^2+b+7)
==>    [2]:
==>       [1]:
==>          _[1]=(b-2)
==>          _[2]=(a^2-6*a+13)
==>       [2]:
==>          _[1]=(7*b-4)
==>          _[2]=(49*a^2-294*a+387)
==>       [3]:
==>          _[1]=(b+2)
==>          _[2]=(a-3)
==>    [3]:
==>       Relevant
==>    [4]:
==>       1
==> [3]:
==>    [1]:
==>       _[1]=(7*b-4)
==>       _[2]=(49*a^2-294*a+387)
==>    [2]:
==>       [1]:
==>          _[1]=1
==>    [3]:
==>       Relevant
==>    [4]:
==>       2
==> [4]:
==>    [1]:
==>       _[1]=(b+2)
==>       _[2]=(a-3)
==>    [2]:
==>       [1]:
==>          _[1]=1
==>    [3]:
==>       Relevant
==>    [4]:
==>       2
==> [5]:
==>    [1]:
==>       _[1]=(b-2)
==>       _[2]=(a^2-6*a+13)
==>    [2]:
==>       [1]:
==>          _[1]=1
==>    [3]:
==>       Relevant
==>    [4]:
==>       1
==> [6]:
==>    [1]:
==>       _[1]=(b-4)
==>       _[2]=(a-3)
==>    [2]:
==>       [1]:
==>          _[1]=1
==>    [3]:
==>       Relevant
==>    [4]:
==>       1
kill R;
//********************************************
ring R=(0,x,y),(x1,x2),dp;
short=0;
ideal S=-(x - 5)*(x1 - 1) - (x2 - 2)*(y - 2),
(x1 - 5)^2 + (x2 - 2)^2 - 4,
-2*(x - 5)*(x2 - 2) + 2*(x1 - 5)*(y - 2);
locus(grobcov(S));
==> [1]:
==>    [1]:
==>       _[1]=(3*x^2-30*x-y^2+4*y+71)
==>    [2]:
==>       [1]:
==>          _[1]=(y-2)
==>          _[2]=(x-5)
==>    [3]:
==>       [1]:
==>          Special
==>       [2]:
==>          x1-4,x2^2-4*x2+1
==>    [4]:
==>       1
==> [2]:
==>    [1]:
==>       _[1]=(y-2)
==>       _[2]=(x-5)
==>    [2]:
==>       [1]:
==>          _[1]=1
==>    [3]:
==>       Accumulation
==>    [4]:
==>       1
locusdg(locus(grobcov(S)));
==> [1]:
==>    [1]:
==>       _[1]=(y-2)
==>       _[2]=(x-5)
==>    [2]:
==>       [1]:
==>          _[1]=1
==>    [3]:
==>       Relevant
==>    [4]:
==>       1


Top Back: locus Forward: envelop FastBack: FastForward: Up: grobcov_lib Top: Singular Manual Contents: Table of Contents Index: Index About: About this document
            User manual for Singular version 4-0-3, 2016, generated by texi2html.