7.3.7 fetch (plural)
fetch ( ring_name
- number, poly, vector, ideal, module, matrix or list
(the same type as the second argument)
- 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 (plural) 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.
- Compared with
fetch uses the position of the ring
variables, not their names.
def Usl2 = makeUsl2(); // this algebra is U(sl_2)
poly C = 4*e*f+h^2-2*h; // the central element of Usl2
ideal I = e^3,f^3,h^3-4*h;
ideal J = twostd(I);
// print a compact presentation of J:
print(matrix(ideal(J[1..5]))); // first 5 generators
print(matrix(ideal(J[6..size(J)]))); // last generators
ideal QC = twostd(C-8);
qring Q = QC;
ideal QJ = fetch(Usl2,J);
QJ = std(QJ);
// thus QJ is the image of I in the factor-algebra QC
print(matrix(QJ)); // print QJ compactly