Singular Manual: fetch (letterplace)

  | ### 7.8.2 fetch (letterplace) `Syntax:` `fetch (` ring_name`,` name `)` `fetch (` ring_name`,` name`,` 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. The intvec in the 3rd argument 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. 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 factor 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:`
        LIB "freegb.lib";
        ring r = (0,a),(x,y,z),dp;
        ring R = freeAlgebra(r,4,2); // free bimodule of rank 2
        poly p = z^2/a - a*y;
        ideal I = x,y,z,a*z*y*x - x*y + 7;
        module M = (x*y*a +3)*ncgen(1)*gen(1), ncgen(2)*gen(2)*z, ncgen(2)*gen(2)*(x*y*a - 7);
        M; // note that a stands on the left
      ==> M[1]=(a)*x*y*ncgen(1)*gen(1)+3*ncgen(1)*gen(1)
      ==> M[2]=ncgen(2)*z*gen(2)
      ==> M[3]=(a)*ncgen(2)*x*y*gen(2)-7*ncgen(2)*gen(2)
        ring r2 = 0,(a,z,y,x),dp; // note: a is a variable in r2
        ring R2 = freeAlgebra(r2,6,2);
        fetch(R,p); // correctly processes incorrect input
      ==> // ** Not defined: Cannot map a rational fraction and make a polynomial o\
         ut of it! Ignoring the denominator.
      ==> y*y
        fetch(R,I);
      ==> _[1]=a
      ==> _[2]=z
      ==> _[3]=y
      ==> _[4]=-a*z+7
        fetch(R,M);
      ==> _[1]=3*ncgen(1)*gen(1)
      ==> _[2]=ncgen(2)*y*gen(2)
      ==> _[3]=-7*ncgen(2)*gen(2)
        setring R; // now we show the factor ring behavior
        ideal J = y*x-x*y,z; J = twostd(J); J;
      ==> J[1]=z
      ==> J[2]=y*x-x*y
        qring Q = J;
        fetch(R,p);
      ==> 1/(a)*z*z+(-a)*y
        NF(_, twostd(0)); // the canonical representative in Q
      ==> (-a)*y
        fetch(R,I);
      ==> _[1]=x
      ==> _[2]=y
      ==> _[3]=z
      ==> _[4]=(a)*z*y*x-x*y+7
        NF(_, twostd(0)); // the canonical representative in Q
      ==> _[1]=x
      ==> _[2]=y
      ==> _[3]=0
      ==> _[4]=-x*y+7
        fetch(R,M);
      ==> _[1]=(a)*x*y*ncgen(1)*gen(1)+3*ncgen(1)*gen(1)
      ==> _[2]=ncgen(2)*z*gen(2)
      ==> _[3]=(a)*ncgen(2)*x*y*gen(2)-7*ncgen(2)*gen(2)
        NF(_, twostd(0)); // the canonical representative in Q
      ==> _[1]=(a)*x*y*ncgen(1)*gen(1)+3*ncgen(1)*gen(1)
      ==> _[2]=0
      ==> _[3]=(a)*ncgen(2)*x*y*gen(2)-7*ncgen(2)*gen(2)
See imap (letterplace); map; qring; ring.

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