Singular Manual: modulo

  | ### 5.1.94 modulo `Syntax:` `modulo (` ideal_expression`,` ideal_expression `)` `modulo (` module_expression`,` module_expression `)` `modulo (` ideal_expression`,` ideal_expression{,} string_expression `)` `modulo (` module_expression`,` module_expression{,} string_expression `)` `modulo (` ideal_expression`,` ideal_expression{,} matrix_name `)` `Type:` module `Purpose:` `modulo(h1,h2)` represents 154#154where 155#155 and 156#156are considered as submodules of the same free module 157#157(l=1 for ideals). Let 158#158, resp. 159#159,be the matrices of size 160#160, resp. 161#161, having the generators of 155#155, resp. 156#156,as columns. Then 162#162where 163#163 is the induced map. `modulo(h1,h2)` returns generators of the kernel of this induced map. An optional third string argument give the GB algorithm to use. (default: "std", else: "groebner", "modstd", "slimgb"). An optional third argument (a name of a matrix) gives the matrix to store the transformation of the input to the GB (see liftstd). `Note:` If for at least one of `h1` or `h2` the attribute `"isHomog"` is set, `modulo(h1,h2)` also sets the attribute `"isHomog"` (if possible, that is, if the weights are compatible). `Example:`
        ring r;
        ideal h1=x,y,z;
        ideal h2=x;
        module m=modulo(h1,h2);
        print(m);
      ==> 1,0, 0,0,
      ==> 0,-z,x,0,
      ==> 0,y, 0,x
See hom_kernel; syz.

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