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3.6 imap

Syntax:
imap ( ring_name, name )
Type:
number, poly, vector, ideal, module, matrix or list (the same type as the second argument)
Purpose:
identity map on common subrings. imap is the map between rings and qrings with compatible ground fields which is the identity on variables and parameters of the same name and 0 otherwise. (See map for a description of possible mapping between different ground fields). Useful for mapping from a homogenized ring to the original ring or for mappings from/to rings with/without parameters. Compared with fetch, imap uses the names of variables and parameters. Unlike map and fetch imap can map parameters to variables.
Example:
 
LIB "ncalg.lib";
ring ABP=0,(p4,p5,a,b),dp;
def Usl3 = sl(3);
def BIG = Usl3+ABP;
setring BIG;
poly P4 = 3*x(1)*y(1)+3*x(2)*y(2)+3*x(3)*y(3)+h(1)^2+h(1)*h(2)+h(2)^2-3*h(1)-3*h(2);  // central element of U(sl_3) of degree 2
poly P5 = 4*x(1)*y(1) + h(1)^2 - 2*h(1); // central element of the subalgebra of U(sl_3), isomorphic to U(sl_2)
ideal J = x(1),x(2),h(1)-a,h(2)-b; // we are interested in the module U(sl_3)/J, depending on parameters a,b
ideal I = p4-P4,p5-P5;
ideal K = I,J;
ideal E = eliminate(K,x(1)*x(2)*x(3)*y(1)*y(2)*y(3)*h(1)*h(2));
E; // this is the ideal of central characters
==> E[1]=a*b+b^2-p4+p5+a+3*b
==> E[2]=a^2-p5+2*a
==> E[3]=b^3+p4*a-p5*a-a^2-p4*b+3*b^2
ring abP = (0,a,b),(p4,p5),dp; // what are the characters on nonzero a,b?
ideal abE = imap(BIG, E);
option(redSB);
option(redTail);
abE = std(abE);
abE; // here they are - we have only one character  
==> abE[1]=p5+(-a^2-2*a)
==> abE[2]=p4+(-a^2-a*b-3*a-b^2-3*b)
See fetch; map; qring; ring.


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