Singular Manual: product

| #### D.2.3.14 product Procedure from library `general.lib` (see general_lib). Usage: product(id[,v]); id ideal/vector/module/matrix/intvec/intmat/list, v intvec (default: v=1..number of entries of id) Assume: list members can be multiplied. Return: The product of all entries of id [with index given by v] of type depending on the entries of id. Note: If id is not a list, id is treated as a list of polys resp. integers. A module m is identified with the corresponding matrix M (columns of M generate m). If v is outside the range of id, we have the empty product and the result will be 1 (of type int). Example:
    LIB "general.lib";
    ring r= 0,(x,y,z),dp;
    ideal m = maxideal(1);
    product(m);
    ==> xyz
    product(m[2..3]);
    ==> yz
    matrix M[2][3] = 1,x,2,y,3,z;
    product(M);
    ==> 6xyz
    intvec v=2,4,6;
    product(M,v);
    ==> xyz
    intvec iv = 1,2,3,4,5,6,7,8,9;
    v=1..5,7,9;
    product(iv,v);
    ==> 7560
    intmat A[2][3] = 1,1,1,2,2,2;
    product(A,3..5);
    ==> 4

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