Singular Manual: vdim

  | ### 5.1.168 vdim `Syntax:` `vdim (` ideal_expression `)` `vdim (` module_expression `)` `Type:` int `Purpose:` computes the vector space dimension of the ring, resp. free module, modulo the ideal, resp. module, generated by the initial terms of the given generators. If the generators form a standard basis, this is the same as the vector space dimension of the ring, resp. free module, modulo the ideal, resp. module. If the ideal, resp. module, is not zero-dimensional, -1 is returned. `Example:`
        ring r=0,(x,y),ds;
        ideal i=x2+y2,x2-y2;
        ideal j=std(i);
        vdim(j);
      ==> 4
See codim; degree; dim; ideal; kbase; mult; std.

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