22.214.171.124 map declarations (plural)
- defines a ring map from
preimage_ring to basering.
Maps the variables of the
preimage ring to the generators of the ideal.
If the ideal contains less elements than the number of variables in the
preimage_ring, the remaining variables are mapped to 0.
If the ideal contains more elements, extra elements are ignored.
The image ring is always the current basering.
For the mapping of coefficients from different fields see map (plural).
- There are standard mappings for maps which are close to the identity
fetch (plural) and
The name of a map serves as the function which maps objects from the
preimage_ring into the basering. These objects must be defined
by names (no evaluation in the preimage ring is possible).
// an easy example
ring r1 = 0,(a,b),dp; // a commutative ring
poly P = a^2+ab+b^3;
ring r2 = 0,(x,y),dp;
def W=nc_algebra(1,-1); // a Weyl algebra
map M = r1, x^2, -y^3;
// note: M is just a map and not a morphism of K-algebras
// now, a more involved example
def Usl2 = makeUsl2();
// this algebra is U(sl_2), generated by e,f,h
poly P = 4*e*f+h^2-2*h; // the central el-t of Usl2
poly Q = e^3*f-h^4; // some polynomial
ring W1 = 0,(D,X),dp;
setring W2; // this is the opposite Weyl algebra
map F = Usl2, -X, D*D*X, 2*D*X;
F(P); // 0, because P is in the kernel of F
ideal expressions (plural);