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elim tex2html_wrap_inline5387 standard basis tex2html_wrap_inline5389 tex2html_wrap_inline5387 result matrix tex2html_wrap_inline5389 [integer n]

Find the subset of the standard basis which lies in a subring. If S is the base ring of the standard basis, and tex2html_wrap_inline7109 is the subring of S defined above, create a matrix whose columns are those elements of the standard basis whose lead monomials lie in tex2html_wrap_inline7109 . If an integer n is not specified, the default value for n is 1.

In other words, this command finds the subset of the standard basis corresponding to the above proposition. This command is in general very useful.

For example, suppose that the ring S is the same as above: the variables are "stabcd", and the monomial order is the product order "2 4". Then

%  putstd j js

%  type js ; the entire standard basis
; c2-bd bc-ad b2-ac t3-d sd-tc sc-tb sb-ta st2-c s2t-b s3-a 

%  elim j k

%  type k  ; the subset not involving s,t
; c2-bd bc-ad b2-ac



Sorin Popescu
Fri Feb 14 17:37:19 EST 1997