Singular

5.1.59 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 mappings 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.
Mapping rational functions which are not polynomials to polynomials is undefined (i.e. the result depends on the version).

Example:

ring r=0,(x,y,z,a,b,c),dp; ideal i=xy2z3a4b5+1,homog(xy2z3a4b5+1,c); i; ==> i[1]=xy2z3a4b5+1 ==> i[2]=xy2z3a4b5+c15 ring r1=0,(a,b,x,y,z),lp; ideal j=imap(r,i); j; ==> j[1]=a4b5xy2z3+1 ==> j[2]=a4b5xy2z3 ring r2=(0,a,b),(x,y,z),ls; ideal j=imap(r,i); j; ==> j[1]=1+(a4b5)*xy2z3 ==> j[2]=(a4b5)*xy2z3