std matrix M computation

Compute a standard (or Groebner) basis of the submodule generated by the columns of the matrix M with r rows, where R is the base ring of M. If M has one row, I is the ideal of R generated by the entries of the matrix of M. In this case, the result is the usual standard, or Groebner, basis of this ideal.

To obtain the standard basis as a matrix after the computation has finished, use the putstd command. However, there are many other commands which manipulate standard bases (see Chapter 8).

A minimal set of generators for I is computed, but no change of basis matrix is computed. If one is desired (e.g. for use with the reduce or lift commands), use lift-std instead.

For example,

%  type j
; ab-c2 bc-d2 cd-e2 

%  std j w
; 23.4.5.
; computation complete after degree 5

%  type w
; ab-c2 bc-d2 cd-e2 

%  putstd w
; 1
; 5
; d3-be2
; cd-e2
; c3-ad2
; bc-d2
; ab-c2

The std command