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ToricInvariants :: polarDegrees

polarDegrees -- Computes the polar degrees of a projective toric variety

Synopsis

Description

This function computes the polar degrees of 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.

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 : polarDegrees(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 = {53, 85, 35}

o2 : List
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 : pdh=polarDegrees(A,Output=>HashTable);
i5 : pdh#"polar degrees"

o5 = {45, 98, 81, 28}

o5 : List
i6 : pdh#"dual degree"

o6 = 45

o6 : QQ
i7 : pdh#"dual codim"

o7 = 1
i8 : pdh#"ED"

o8 = 252

o8 : QQ
i9 : pdh#"degree"

o9 = 28

o9 : QQ

Ways to use polarDegrees :