Singular Manual: dim

  | ### 5.1.24 dim `Syntax:` `dim (` ideal_expression `)` `dim (` module_expression `)` `dim (` resolution_expression `)` `dim (` ideal_expression `,` ideal_expression `)` `dim (` module_expression `,` ideal_expression `)` `Type:` int `Purpose:` computes the dimension of the ideal, resp. module, generated by the leading monomials of the given generators of the ideal, resp. module. This is also the dimension of the ideal if it is represented by a standard basis. `dim(I,J)` is the dimension of `I/J`. `dim(` res `)` computes the cohomological dimension of res[1]. `Note:` The dimension of an ideal I means the Krull dimension of the basering modulo I. The dimension of a module is the dimension of its annihilator ideal. In the case of ideal (1), -1 is returned. `Example:`
        ring r=32003,(x,y,z),dp;
        ideal I=x2-y,x3;
        dim(std(I));
      ==> 1
        dim(std(ideal(1)));
      ==> -1
See degree; ideal; mult; std; vdim.

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