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D.9.1.1 staircase
Procedure from library graphics.lib (see graphics_lib).
- Usage:
- staircase(s,I); s a string, I ideal in two variables
- Return:
- string with Mathematica input for displaying staircase diagrams of an
ideal I, i.e. exponent vectors of the initial ideal of I
- Note:
- ideal I should be given by a standard basis. Let s="" and copy and
paste the result into a Mathematica notebook.
Example:
| | LIB "graphics.lib";
ring r0 = 0,(x,y),ls;
ideal I = -1x2y6-1x4y2, 7x6y5+1/2x7y4+6x4y6;
staircase("",std(I));
==>
==> Show[Graphics[{
==> {GrayLevel[0.5],Map[Rectangle[#,{9,9}] &, {{2,6},{6,2}}]},
==> {PointSize[0.03], Map[Point,{{2,6},{6,2}}]},
==> Table[Circle[{i,j},0.1],{i,0,9},{j,0,9}]},
==> Axes->True,AspectRatio->Automatic]]
==>
ring r1 = 0,(x,y),dp;
ideal I = fetch(r0,I);
staircase("",std(I));
==>
==> Show[Graphics[{
==> {GrayLevel[0.5],Map[Rectangle[#,{12,9}] &, {{2,6},{7,4},{9,2}}]},
==> {PointSize[0.03], Map[Point,{{2,6},{7,4},{9,2}}]},
==> Table[Circle[{i,j},0.1],{i,0,12},{j,0,9}]},
==> Axes->True,AspectRatio->Automatic]]
==>
ring r2 = 0,(x,y),wp(2,3);
ideal I = fetch(r0,I);
staircase("",std(I));
==>
==> Show[Graphics[{
==> {GrayLevel[0.5],Map[Rectangle[#,{13,9}] &, {{2,6},{8,3},{10,2},{6,5}}]},
==> {PointSize[0.03], Map[Point,{{2,6},{8,3},{10,2},{6,5}}]},
==> Table[Circle[{i,j},0.1],{i,0,13},{j,0,9}]},
==> Axes->True,AspectRatio->Automatic]]
==>
// Paste the output into a Mathematica notebook
// active evaluation of the cell with SHIFT RETURN
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