This function computes (generic) Euclidean distance degree the projective toric variety XA, we do not assume that XA is normal. The default output is a list of polar degrees; other values of interest computed by the program are also output. To suppress text output use the option Output =>HashTable. This function uses polarDegrees internally.
i1 : A=matrix{{0, 0, 0, 1, 1,5}, {7,0, 1, 3, 0, -2},{1,1, 1, 1, 1, 1}}
o1 = | 0 0 0 1 1 5 |
| 7 0 1 3 0 -2 |
| 1 1 1 1 1 1 |
3 6
o1 : Matrix ZZ <--- ZZ
|
i2 : edDeg(A)
The toric variety has degree = 35
The dual variety has degree = 53, and codimension = 1
Chern-Mather Volumes: (V_0,..,V_(d-1)) = {-12, 20, 35}
Polar Degrees: {53, 85, 35}
ED Degree = 173
5 4 3
Chern-Mather Class: - 12h + 20h + 35h
o2 = 173
o2 : QQ
|
i3 : A=matrix{{3, 0, 0, 1, 1,2}, {3,5,0,2,1,3},{0, 1, 2, 0, 2,0},{1, 1, 1, 1, 1,1}}
o3 = | 3 0 0 1 1 2 |
| 3 5 0 2 1 3 |
| 0 1 2 0 2 0 |
| 1 1 1 1 1 1 |
4 6
o3 : Matrix ZZ <--- ZZ
|
i4 : time edDeg(A)
The toric variety has degree = 28
The dual variety has degree = 45, and codimension = 1
Chern-Mather Volumes: (V_0,..,V_(d-1)) = {20, 23, 31, 28}
Polar Degrees: {45, 98, 81, 28}
ED Degree = 252
5 4 3 2
Chern-Mather Class: 20h + 23h + 31h + 28h
-- used 0.546615 seconds
o4 = 252
o4 : QQ
|
i5 : time edDeg(A,ForceAmat=>true)
The toric variety has degree = 28
The dual variety has degree = 45, and codimension = 1
Chern-Mather Volumes: (V_0,..,V_(d-1)) = {20, 23, 31, 28}
Polar Degrees: {45, 98, 81, 28}
ED Degree = 252
5 4 3 2
Chern-Mather Class: 20h + 23h + 31h + 28h
-- used 2.09942 seconds
o5 = 252
o5 : QQ
|