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5.1.31 fetch

Syntax:
fetch ( ring_name, name )
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, the i-th variable of the source ring is mapped to the i-th variable of the basering. 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.
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
See imap; map; qring; ring.

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