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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
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