Top
Back: coeffs
Forward: create_ring
FastBack:
FastForward:
Up: Singular Manual
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

5.1.13 contract

Syntax:
contract ( ideal_expression, ideal_expression )
Type:
matrix
Purpose:
contracts each of the n elements of the second ideal J by each of the m elements of the first ideal I, producing an $ m \times n $matrix.
Contraction is defined on monomials by:

\begin{displaymath}{\rm contract}(x^A , x^B) := \cases{ x^{(B-A)}, &if $B\ge A$ componentwise\cr 0,&otherwise.\cr}\end{displaymath}

where A and B are the multiexponents of the ring variables represented by $x$.contract is extended bilinearly to all polynomials.
Example:
 
  ring r=0,(a,b,c,d),dp;
  ideal I=a2,a2+bc,abc;
  ideal J=a2-bc,abcd;
  print(contract(I,J));
==> 1,0, 
==> 0,ad,
==> 0,d
See diff.

Top Back: coeffs Forward: create_ring FastBack: FastForward: Up: Singular Manual 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.