> restart; > kernelopts(printbytes=false): > with(LinearAlgebra): > interface(rtablesize=1000): > Digits:=14: > infolevel[MultiStructure]:=1: > DZ3, (2/5*7^(1/2)+1/5*5^(1/2),-1/5*7^(1/2)+2/5*5^(1/2)) is 5-fold zero and depth is 4 > read`/home/nan/Work/MultiplicityStructure/MultiplicityStructureBreadthOneSymbolic.mpl`: > mroot:=Vector([2*sqrt(7)/5+sqrt(5)/5,-sqrt(7)/5+2*sqrt(5)/5]); [ 1/2 1/2 ] [ 2 7 5 ] [ ------ + ---- ] [ 5 5 ] mroot := [ ] [ 1/2 1/2] [ 7 2 5 ] [- ---- + ------] [ 5 5 ] > lsys:=[14*x+33*y-3*sqrt(5)*(x^2+4*x*y+4*y^2+2)+sqrt(7)+x^3+6*x^2*y+12*x*y^2+8*y^3,41*x-18*y-sqrt(5)+8*x^3-12*x^2*y+6*x*y^2-y^3+3*sqrt(7)*(4*x*y-4*x^2-y^2-2)]; 1/2 2 2 1/2 3 lsys := [14 x + 33 y - 3 5 (x + 4 x y + 4 y + 2) + 7 + x 2 2 3 1/2 3 + 6 x y + 12 x y + 8 y , 41 x - 18 y - 5 + 8 x 2 2 3 1/2 2 2 - 12 x y + 6 x y - y + 3 7 (4 x y - 4 x - y - 2)] > MultiStructure(lsys,[x,y],mroot); MultiStructure: The multiplicity is:, 5 MultiStructure: The dual basis of original polynomial at isolated zero is:, [1, 2 2 3 x + y, 9 x + 3 x y + y , 3 2 2 3 4 27 x + 9 x y + 3 x y + y + 25/2 x - 75/2 y, 81 x 3 2 2 3 4 2 2 + 27 x y + 9 x y + 3 x y + y + 75 x - 100 x y - 75 y ] MultiStructure: The dual basis , 1, [0] acts on original polynomial at isolated zero is:, [ ] [0] MultiStructure: The dual basis , 2, [0] acts on original polynomial at isolated zero is:, [ ] [0] MultiStructure: The dual basis , 3, [0] acts on original polynomial at isolated zero is:, [ ] [0] MultiStructure: The dual basis , 4, [0] acts on original polynomial at isolated zero is:, [ ] [0] MultiStructure: The dual basis , 5, [0] acts on original polynomial at isolated zero is:, [ ] [0] > read`/home/nan/Work/MultiplicityStructure/MultiplicityStructureBreadthOneNumeric.mpl`: > Digits:=5: > mroot:=evalf(Vector([2*sqrt(7)/5+sqrt(5)/5,-sqrt(7)/5+2*sqrt(5)/5])); [1.5055 ] mroot := [ ] [0.36528] > lsys:=evalf([14*x+33*y-3*sqrt(5)*(x^2+4*x*y+4*y^2+2)+sqrt(7)+x^3+6*x^2*y+12*x*y^2+8*y^3,41*x-18*y-sqrt(5)+8*x^3-12*x^2*y+6*x*y^2-y^3+3*sqrt(7)*(4*x*y-4*x^2-y^2-2)]); 2 2 lsys := [14. x + 33. y - 6.7083 x - 26.833 x y - 26.833 y 3 2 2 3 - 10.771 + x + 6. x y + 12. x y + 8. y , 41. x - 18. y 3 2 2 3 - 18.111 + 8. x - 12. x y + 6. x y - 1. y + 31.749 x y 2 2 - 31.749 x - 7.9374 y ] > Digits:=14: > tol:=2*10.^(-3); tol := 0.0020000000000000 > MultiStructure(lsys,[x,y],mroot,tol); MultiStructure: The multiplicity is:, 5 MultiStructure: The dual basis of original polynomial at isolated zero is:, [1, 0.948659778854976543 x + 0.316298314859290552 y, 2 -0.89995537363650 x - 0.30005948863286 x y 2 - 0.10004462371818 y + 0.000023006514189684 x 3 - 0.000069002437376624 y, -0.53331296099243 x 2 2 - 0.17781505510662 x y - 0.059286378046637 x y 3 2 - 0.019767024900007 y + 0.000027267290276930 x 2 - 0.000036345123950316 x y - 0.000027267290276930 y - 0.24699381659577 x + 0.74079781150440 y, 4 3 0.50593255562942 x + 0.16868599085247 x y 2 2 3 + 0.056242602286150 x y + 0.018752181470033 x y 4 3 + 0.0062522766655775 y - 0.000038801072345658 x 2 2 + 0.000030166858266111 x y + 0.000024429592240584 x y 3 2 + 0.000012936896947901 y + 0.46862619918552 x 2 - 0.62464136105218 x y - 0.46862619588062 y -5 -5 - 0.15595526745339 10 x + 0.46774985064153 10 y] MultiStructure: The dual basis , 1, acts on original polynomial at isolated zero is:, [-0.00066377487298] [ ] [-0.0003933052652 ] MultiStructure: The dual basis , 2, acts on original polynomial at isolated zero is:, [-0.0002334241854] [ ] [ 0.000233413762 ] MultiStructure: The dual basis , 3, acts on original polynomial at isolated zero is:, [ -5] [-0.996980147094 10 ] [ ] [ -5] [0.9969359036624 10 ] MultiStructure: The dual basis , 4, acts on original polynomial at isolated zero is:, [-0.0006059285021] [ ] [0.00060608282013] MultiStructure: The dual basis , 5, acts on original polynomial at isolated zero is:, [0.00080432080903428 ] [ ] [-0.00080428488410375] >