Singular 2-0-4 Manual: D.9.1.2 NSplaces

D.9.1.2 NSplaces

Procedure from library brnoeth.lib (see brnoeth_lib).

Usage:

NSplaces( h, CURVE ), where h is an intvec and CURVE is a list

Return:

list L with updated data of CURVE after computing all non-singular affine closed places whose degrees are in the intvec h:

   in L[1][1]: (affine ring) lists Aff_Points(d) with affine non-singular
               (closed) points of degree d (if non-empty),
   in L[3]:    the newly computed closed places are added,
   in L[5]:    local rings created/updated to store (repres. of) new places.

See Adj_div for a description of the entries in L.

Note:

The list_expression should be the output of the procedure Adj_div.
If printlevel>=0 additional comments are displayed (default: printlevel=0).

Example:

LIB "brnoeth.lib";
int plevel=printlevel;
printlevel=-1;
ring s=2,(x,y),lp;
list C=Adj_div(x3y+y3+x);
→ The genus of the curve is 3
// The list of computed places:
C[3];
→ [1]:
→    1,1
→ [2]:
→    1,2
// create places up to degree 4
list L=NSplaces(1..4,C);
// The list of computed places is now:
L[3];
→ [1]:
→    1,1
→ [2]:
→    1,2
→ [3]:
→    1,3
→ [4]:
→    2,1
→ [5]:
→    3,1
→ [6]:
→    3,2
→ [7]:
→    3,3
→ [8]:
→    3,4
→ [9]:
→    3,5
→ [10]:
→    3,6
→ [11]:
→    3,7
→ [12]:
→    4,1
→ [13]:
→    4,2
→ [14]:
→    4,3
// e.g., affine non-singular points of degree 4 :
def aff_r=L[1][1];
setring aff_r;
Aff_Points(4);
→ [1]:
→    [1]:
→       _[1]=y2+y+1
→       _[2]=x2+xy+x+1
→    [2]:
→       12
→ [2]:
→    [1]:
→       _[1]=y4+y3+y2+y+1
→       _[2]=x+y2+y+1
→    [2]:
→       13
→ [3]:
→    [1]:
→       _[1]=y4+y3+1
→       _[2]=x+y3+y
→    [2]:
→       14
// e.g., base point of the 1st place of degree 4 :
def S(4)=L[5][4][1];
setring S(4);
POINTS[1];
→ [1]:
→    (a3)
→ [2]:
→    (a2+a)
→ [3]:
→    1
printlevel=plevel;

See also: Adj_div; closed_points.

User manual for Singular version 2-0-4, October 2002, generated by texi2html.