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D.5.2.49 rHRR
Procedure from library chern.lib (see chern_lib).
- Usage:
- rHRR( N, ch, td); N integer, ch, td lists of polynomials
- Return:
- polynomial
- Purpose:
- computes the the main ingredient of the right-hand side
of the Hirzebruch-Riemann-Roch formula
- Note:
- in order to get the right-hand side of the HRR formula
one needs to be able to compute the degree of the output of this procedure
Example:
| | LIB "chern.lib";
ring r=0, (td(0..3), ch(0..3)), dp;
// Let ch(0), ch(1), ch(2), ch(3) be the terms of the Chern character
// of a vector bundle E on a 3-fold X.
list c = ch(0..3);
// Let td(0), td(1), td(2), td(3) be the terms of the Todd class of X.
list t = td(0..3);
// Then the highest term of the product ch(E).td(X) is:
print( rHRR(3, c, t) );
==> td(3)*ch(0)+td(2)*ch(1)+td(1)*ch(2)+td(0)*ch(3)
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