Singular Manual: chSymm

| #### D.5.2.28 chSymm Procedure from library `chern.lib` (see chern_lib). Usage: chSymm(k, r, c[, pos]); k, r integers, c list of polynomials, pos list of integers Return: list with entries: int N, list of polynomials l Purpose: computes the rank and the Chern classes of the symmetric power of a vector bundle Note: for the second symmetric power chSymm2L(...) could be faster Example:
    LIB "chern.lib";
    ring r=0, (c(1..5)), dp;
    list l=c(1..5);
    // the rank and the Chern classes of the second symmetric power of a vector bundle of rank 3
    print( chSymm(2, 3, l) );
    ==> [1]:
    ==>    6
    ==> [2]:
    ==>    [1]:
    ==>       4*c(1)
    ==>    [2]:
    ==>       5*c(1)^2+5*c(2)
    ==>    [3]:
    ==>       2*c(1)^3+11*c(1)*c(2)+7*c(3)
    ==>    [4]:
    ==>       6*c(1)^2*c(2)+4*c(2)^2+14*c(1)*c(3)
    ==>    [5]:
    ==>       4*c(1)*c(2)^2+8*c(1)^2*c(3)+4*c(2)*c(3)
    ==>    [6]:
    ==>       8*c(1)*c(2)*c(3)-8*c(3)^2
    // the rank and the first 3 Chern classes
    // of the second symmetric power of a vector bundle of rank 5
    print( chSymm(2, 5, l, 1, 2, 3) );
    ==> [1]:
    ==>    15
    ==> [2]:
    ==>    [1]:
    ==>       6*c(1)
    ==>    [2]:
    ==>       14*c(1)^2+7*c(2)
    ==>    [3]:
    ==>       16*c(1)^3+31*c(1)*c(2)+9*c(3)

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