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poincareDuality -- Apply the isomorphism Hom(A^k(X),ZZ) = A_k(X)

Synopsis

Description

This function calculates the list of coefficients of a toric cycle corresponding to a list of Minkowski weights.

i1 : X = toricProjectiveSpace 3;
i2 : k = 2;
i3 : l = toList(#orbits(X,1):3)

o3 = {3, 3, 3, 3, 3, 3}

o3 : List
i4 : poincareDuality(l, X, k)

o4 = {3, 0, 0, 0}

o4 : List
i5 : poincareMatrix(X,2)

o5 = | 1 1 1 1 |
     | 1 1 1 1 |
     | 1 1 1 1 |
     | 1 1 1 1 |
     | 1 1 1 1 |
     | 1 1 1 1 |

              6        4
o5 : Matrix QQ  <--- QQ

Ways to use poincareDuality :

For the programmer

The object poincareDuality is a method function.