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D.2.4.23 Levels
Procedure from library grobcov.lib (see grobcov_lib).
- Usage:
- Levels(list L);
The input list L must be the output of the call to the
routine ConsLevels of a constructible set:
L=[a1,a2,..,ak], where the a's are the closures
of the levels, determined by ConsLevels.
Levels selects the levels of the
constructible set. To be called in a ring Q[a][x]
or a ring Q[a]. But the ideals can contain
only the parameters in Q[a].
- Return:
- The levels of the constructible set:
Lc=[ [1,[a1,a2]],[3,[a3,a4]],..,
[2l-1,[a_{2l-1},a_{2l}]] ]
the list of levels of S
Example:
| | LIB "grobcov.lib";
// EXAMPLE:
if(defined(R)){kill R;}
ring R=0,(x,y,z),lp;
short=0;
ideal P1=(x^2+y^2+z^2-1);
ideal Q1=z,x^2+y^2-1;
ideal P2=y,x^2+z^2-1;
ideal Q2=z*(z+1),y,x*(x+1);
ideal P3=x;
ideal Q3=5*z-4,5*y-3,x;
list Cr1=Crep(P1,Q1);
list Cr2=Crep(P2,Q2);
list Cr3=Crep(P3,Q3);
list L=list(Cr1,Cr2,Cr3);
L;
==> [1]:
==> [1]:
==> _[1]=x^2+y^2+z^2-1
==> [2]:
==> _[1]=z
==> _[2]=x^2+y^2-1
==> [2]:
==> [1]:
==> _[1]=y
==> _[2]=x^2+z^2-1
==> [2]:
==> _[1]=z^2+z
==> _[2]=y
==> _[3]=x+z+1
==> [3]:
==> [1]:
==> _[1]=x
==> [2]:
==> _[1]=5*z-4
==> _[2]=5*y-3
==> _[3]=x
def LL=ConsLevels(L);
LL;
==> [1]:
==> _[1]=x^3+x*y^2+x*z^2-x
==> [2]:
==> _[1]=z
==> _[2]=x^2+y^2-1
==> [3]:
==> _[1]=z
==> _[2]=x+y^2-1
==> _[3]=x*y
==> _[4]=x^2-x
==> [4]:
==> _[1]=1
def LLL=Levels(LL);
LLL;
==> [1]:
==> [1]:
==> 1
==> [2]:
==> [1]:
==> _[1]=x^3+x*y^2+x*z^2-x
==> [2]:
==> _[1]=z
==> _[2]=x^2+y^2-1
==> [2]:
==> [1]:
==> 3
==> [2]:
==> [1]:
==> _[1]=z
==> _[2]=x+y^2-1
==> _[3]=x*y
==> _[4]=x^2-x
==> [2]:
==> _[1]=1
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