Singular Manual: imap

  | ### 5.1.59 imap `Syntax:` `imap (` ring_name`,` name `)` `Type:` number, poly, vector, ideal, module, matrix or list (the same type as the second argument) `Purpose:` identity map on common subrings. `imap` is the map between rings and qrings with compatible ground fields which is the identity on variables and parameters of the same name and 0 otherwise. (See map for a description of possible mappings between different ground fields). Useful for mapping from a homogenized ring to the original ring or for mappings from/to rings with/without parameters. Compared with `fetch`, `imap` uses the names of variables and parameters. Unlike `map` and `fetch` `imap` can map parameters to variables. Mapping rational functions which are not polynomials to polynomials is undefined (i.e. the result depends on the version). `Example:`
        ring r=0,(x,y,z,a,b,c),dp;
        ideal i=xy2z3a4b5+1,homog(xy2z3a4b5+1,c); i;
      ==> i[1]=xy2z3a4b5+1
      ==> i[2]=xy2z3a4b5+c15
        ring r1=0,(a,b,x,y,z),lp;
        ideal j=imap(r,i); j;
      ==> j[1]=a4b5xy2z3+1
      ==> j[2]=a4b5xy2z3
        ring r2=(0,a,b),(x,y,z),ls;
        ideal j=imap(r,i); j;
      ==> j[1]=1+(a4b5)*xy2z3
      ==> j[2]=(a4b5)*xy2z3
See fetch; homog; map; qring; ring.

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