Top
Back: map
Forward: map expressions
FastBack: list
FastForward: matrix
Up: map
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

4.11.1 map declarations

Syntax:
map name = preimage_ring_name , ideal_expression ;
map name = preimage_ring_name , list_of_poly_and_ideal_expressions ;
map name = map_expression ;

Purpose:
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 variables in the preimage_ring the remaining variables are mapped to 0, if the ideal contains more elements these are ignored. The image ring is always the current basering. For the mapping of coefficients from different fields see map.

Default:
none

Note:
There are standard mappings for maps which are close to the identity map: fetch and imap.

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).

Example:
 
  ring r1=32003,(x,y,z),dp;
  ideal i=x,y,z;
  ring r2=32003,(a,b),dp;
  map f=r1,a,b,a+b;
  // maps from r1 to r2,
  // x -> a
  // y -> b
  // z -> a+b
  f(i);
==> _[1]=a
==> _[2]=b
==> _[3]=a+b
  // operations like f(i[1]) or f(i*i) are not allowed
  ideal i=f(i);
  // objects in different rings may have the same name
  map g   = r2,a2,b2;
  map phi = g(f);
  // composition of map f and g
  // maps from r1 to r2,
  // x -> a2
  // y -> b2
  // z -> a2+b2
  phi(i);
==> _[1]=a2
==> _[2]=b2
==> _[3]=a2+b2

See fetch; ideal expressions; imap; map; ring.


Top Back: map Forward: map expressions FastBack: list FastForward: matrix Up: map Top: Singular Manual Contents: Table of Contents Index: Index About: About this document
            User manual for Singular version 4.3.2, 2023, generated by texi2html.