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3.5 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 mapping 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:
 
LIB "ncalg.lib";
def Usl2 = sl2();
setring Usl2;
poly  C  = 4*e*f+h^2-2*h; // the central element of U(sl2)
ideal I  = e^3,f^3,h^3-4*h;
ideal J  = twostd(I);
J;
==> J[1]=h3-4h
==> J[2]=fh2-2fh
==> J[3]=eh2+2eh
==> J[4]=f2h-2f2
==> J[5]=2efh-h2-2h
==> J[6]=e2h+2e2
==> J[7]=f3
==> J[8]=ef2-fh
==> J[9]=e2f-eh-2e
==> J[10]=e3
ideal QC = twostd(C);
qring Q  = QC;
ideal QJ = fetch(Usl2,J);
QJ = std(QJ);
QJ; 
==> QJ[1]=h
==> QJ[2]=f
==> QJ[3]=e
See imap; map; qring; ring.


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