Top
Back: dim
Forward: dump
FastBack: Functions and system variables
FastForward: Control structures
Up: Functions
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

5.1.20 division

Syntax:
division ( ideal_expression, ideal_expression )
division ( module_expression, module_expression )
Type:
list
Purpose:
computes the transformation matrix which expresses the generators of a module sm (the first argument) in terms of the generators of a module m (the second argument) and a rest R. Uses different algorithms depending on whether the modules are, resp. are not, represented by standard bases.
Returns the list T,U,R, where T,U are matrices and R is a module (resp. ideal) such that matrix(sm)*U+matrix(R) = matrix(m)*T and module(sm*U+matrix(R)) = module(matrix(m)*T) (resp. ideal(sm*U+matrix(R)) = ideal(matrix(m)*T)).
U is a diagonal matrix of units (if the basering is a polynomial ring then U is the identity matrix).
T is the transformation matrix as returned by lift.
Example:
 
  ring r;
  ideal m=3x2+yz,7y6+2x2y+5xz;
  poly f=y7+x3+xyz+z2;
  ideal i=jacob(f)+x;
  division(m,i);
==> [1]:
==>    _[1,1]=0
==>    _[1,2]=0
==>    _[2,1]=0
==>    _[2,2]=1
==>    _[3,1]=-16001y
==>    _[3,2]=-15999x
==>    _[4,1]=16001y2+3x
==>    _[4,2]=16001xy-z
==> [2]:
==>    _[1,1]=1
==>    _[1,2]=0
==>    _[2,1]=0
==>    _[2,2]=1
==> [3]:
==>    _[1]=0
==>    _[2]=0
See ideal; lift; module.

Top Back: dim Forward: dump FastBack: Functions and system variables FastForward: Control structures Up: Functions Top: Singular Manual Contents: Table of Contents Index: Index About: About this document
            User manual for Singular version 2-0-2, August 2001, generated by texi2html.