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D.9.1.10 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]=y2+y+1 → _[2]=x+y → [2]: → _[1]=y2+y+1 → _[2]=x+1 → [3]: → _[1]=y2+y+1 → _[2]=x+y+1 → [4]: → _[1]=y2+y+1 → _[2]=x → [5]: → _[1]=y+1 → _[2]=x2+x+1 → [6]: → _[1]=y+1 → _[2]=x+1 → [7]: → _[1]=y+1 → _[2]=x → [8]: → _[1]=y → _[2]=x2+x+1 → [9]: → _[1]=y → _[2]=x+1 → [10]: → _[1]=y → _[2]=x |
See also: triang_lib.