# cmClass -- Computes the Chern-Mather class of a projective toric variety

## Synopsis

• Usage:
cmClass(A)
• Inputs:
• A, , a full rank integer matrix with the vector (1,1,...,1) in its row space defining a projective toric variety XA
• Optional inputs:
• ForceAmat => , default value false, if A defines a codimension two toric variety a faster method will be used by default, setting this to true forces the general purpose method
• Output => a list, default value RingElement, this can be set to HashTable to return a HashTable with all computed values
• TextOutput => ... (missing documentation),
• Outputs:
• cm, , the Chern-Mather class of the projective toric variety XA pushedforward to the Chow ring of the ambient projective space.

## Description

This function computes the Chern-Mather class of the projective toric variety XA pushedforward to the Chow ring of the ambient projective space, we do not assume that XA is normal.

 ```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 : cmClass(A) 5 4 3 o2 = - 12h + 20h + 35h ZZ[h] o2 : ----- 6 h``` ```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 : cmh=cmClass(A,Output=>HashTable);` ```i5 : cmh#"CM class" 5 4 3 2 o5 = 20h + 23h + 31h + 28h ZZ[h] o5 : ----- 6 h``` ```i6 : cmh#"polar degrees" o6 = {45, 98, 81, 28} o6 : List``` ```i7 : cmh#"dual degree" o7 = 45 o7 : QQ``` ```i8 : cmh#"dual codim" o8 = 1``` ```i9 : cmh#"ED" o9 = 252 o9 : QQ``` ```i10 : cmh#"degree" o10 = 28 o10 : QQ```

## Ways to use cmClass :

• cmClass(Matrix)
• cmClass(Matrix,QuotientRing) (missing documentation)