Singular Manual: fetch

  | ### 5.1.38 fetch `Syntax:` `fetch (` ring_name`,` name `)` `fetch (` ring_name`,` name`,` intvec_expression `)` `fetch (` ring_name`,` name`,` intvec_expression`,` intvec_expression `)` `Type:` number, poly, vector, ideal, module, matrix or list (the same type as the second argument) `Purpose:` maps objects between rings. `fetch` is the identity map between rings and qrings, in the first case the i-th variable of the source ring is mapped to the i-th variable of the basering. If the basering has less variables than the source ring these variables are mapped to zero. In the 3rd and 4th arguments the intvec describes the permutation of the variables: an i at position j maps the variable `var(j)` of the source to the variable `var(i)` of the destination. Negative numbers (and the fourth argument) describe mapping of parameters. A zero means that that variable/parameter is mapped to 0. The coefficient fields must be compatible. (See map for a description of possible mappings between different ground fields). `fetch` offers a convenient way to change variable names or orderings, or to map objects from a ring to a quotient ring of that ring or vice versa. `option(Imap);` reports the mapping. `Note:` Compared with `imap`, `fetch` uses the position of the ring variables, not their names. `Example:`
        ring r=0,(x,y,z),dp;
        ideal i=maxideal(2);
        ideal j=std(i);
        poly f=x+y2+z3;
        vector v=[f,1];
        qring q=j;
        poly f=fetch(r,f);
        f;
      ==> z3+y2+x
        vector v=fetch(r,v);
        v;
      ==> z3*gen(1)+y2*gen(1)+x*gen(1)+gen(2)
        ideal i=fetch(r,i);
        i;
      ==> i[1]=z2
      ==> i[2]=yz
      ==> i[3]=y2
      ==> i[4]=xz
      ==> i[5]=xy
      ==> i[6]=x2
        ring rr=0,(a,b,c),lp;
        poly f=fetch(q,f);
        f;
      ==> a+b2+c3
        vector v=fetch(r,v);
        v;
      ==> a*gen(1)+b2*gen(1)+c3*gen(1)+gen(2)
        ideal k=fetch(q,i);
        k;
      ==> k[1]=c2
      ==> k[2]=bc
      ==> k[3]=b2
      ==> k[4]=ac
      ==> k[5]=ab
      ==> k[6]=a2
        fetch(q,i,1..nvars(q)); // equivalent to fetch(q,i)
      ==> _[1]=c2
      ==> _[2]=bc
      ==> _[3]=b2
      ==> _[4]=ac
      ==> _[5]=ab
      ==> _[6]=a2
See imap; map; option; qring; ring.

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