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D.15.3.19 chProdE
Procedure from library chern.lib (see chern_lib).
- Usage:
- chProdE(c, C); c, C lists of polynomials
- Return:
- list of polynomials
- Purpose:
- computes the list of Chern classes of the product
of two vector bundles in terms of their Chern clases
- Note:
- makes sense only for (lists of) polynomials;
uses elimination, hence very inefficient;
included only for comparison with chProd(...)
Example:
| | LIB "chern.lib";
ring H = 0, ( c(1..3), C(1..2) ), dp;
list l=c(1..3);
list L=C(1..2);
// the Chern classes of the tensor product of a vector bundle E of rank 3
// with Chern classes c(1), c(2), c(3)
// and a vector bundle F of rank 2 with Chern classes C(1) and C(2):
print( chProdE(l, L) );
==> [1]:
==> 2*c(1)+3*C(1)
==> [2]:
==> -c(1)^2-5*c(1)*C(1)-3*C(1)^2-2*c(2)-3*C(2)
==> [3]:
==> -2*c(1)^2*C(1)-4*c(1)*C(1)^2-C(1)^3-2*c(1)*c(2)-4*c(2)*C(1)-4*c(1)*C(2\
)-6*C(1)*C(2)-2*c(3)
==> [4]:
==> -c(1)^2*C(1)^2-c(1)*C(1)^3-3*c(1)*c(2)*C(1)-3*c(2)*C(1)^2-2*c(1)^2*C(2\
)-6*c(1)*C(1)*C(2)-3*C(1)^2*C(2)-c(2)^2-2*c(1)*c(3)-3*c(3)*C(1)-3*C(2)^2
==> [5]:
==> -c(1)*c(2)*C(1)^2-c(2)*C(1)^3-2*c(1)^2*C(1)*C(2)-2*c(1)*C(1)^2*C(2)-c(\
2)^2*C(1)-2*c(1)*c(3)*C(1)-3*c(3)*C(1)^2-2*c(1)*c(2)*C(2)-2*c(1)*C(2)^2-3\
*C(1)*C(2)^2-2*c(2)*c(3)+6*c(3)*C(2)
==> [6]:
==> -c(1)*c(3)*C(1)^2-c(3)*C(1)^3-c(1)*c(2)*C(1)*C(2)-c(2)*C(1)^2*C(2)-c(1\
)^2*C(2)^2-c(1)*C(1)*C(2)^2-c(2)*c(3)*C(1)-c(2)^2*C(2)+2*c(1)*c(3)*C(2)+3\
*c(3)*C(1)*C(2)+2*c(2)*C(2)^2-C(2)^3-c(3)^2
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