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D.10.1.10 closed_points
Procedure from library brnoeth.lib (see brnoeth_lib).
- Usage:
- closed_points(I); I an ideal
- Return:
- list of prime ideals (each a Groebner basis), corresponding to
the (distinct affine closed) points of V(I)
- Note:
- The ideal must have dimension 0, the basering must have 2
variables, the ordering must be lp, and the base field must
be finite and prime.
It might be convenient to set the option(redSB) in advance.
Example:
| | LIB "brnoeth.lib";
ring s=2,(x,y),lp;
// this is just the affine plane over F_4 :
ideal I=x4+x,y4+y;
list L=closed_points(I);
// and here you have all the points :
L;
==> [1]:
==> _[1]=y+1
==> _[2]=x+1
==> [2]:
==> _[1]=y+1
==> _[2]=x
==> [3]:
==> _[1]=y+1
==> _[2]=x2+x+1
==> [4]:
==> _[1]=y
==> _[2]=x+1
==> [5]:
==> _[1]=y
==> _[2]=x
==> [6]:
==> _[1]=y
==> _[2]=x2+x+1
==> [7]:
==> _[1]=y2+y+1
==> _[2]=x+1
==> [8]:
==> _[1]=y2+y+1
==> _[2]=x+y+1
==> [9]:
==> _[1]=y2+y+1
==> _[2]=x+y
==> [10]:
==> _[1]=y2+y+1
==> _[2]=x
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See also:
triang_lib.
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