Home Online Manual
Top
Back: graphics_lib
Forward: mathinit
FastBack:
FastForward:
Up: graphics_lib
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

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 evalutation of the cell with SHIFT RETURN