Recall that a spreadsheet consists of

- (1) Polynomial equations which solve for a variable.
- (2) Polynomial equations which do not involve any unknowns.
- (3) User selected and user created polynomial equations.
- (4) Undigested polynomials.

- I. Let be the categories. The simplest way is to replace with a minimal set such that the 's and the 's generate the same ideal.
- II. The most drastic
way to shrink
is to
pick an ordering
on categories of undigested
polynomial equations
(for example, the one induced by the
ordering underlying the run) and
output the subset and
defined to satisfy
- (1) A minimal generating set for the digested
polynomials
*D*. Call it . - (2) A minimal set of the form
which is a generating set for the ideal generated by
the union of the digested polynomials
*D*and the category . - (3) A minimal set of the form
which is a generating set for the ideal generated by
the union of the digested polynomial
*D*and the categories and . - (4) etc.

Here

*D*is the set of digested polynomials. - (1) A minimal generating set for the digested
polynomials
- III. An intermediate course which
is less sensitive to ordering is
to output the subset and
defined to satisfy
- (1)
A minimal generating set for the digested
polynomials
*D*. Call it . - (2)
A minimal set of the form
which is a generating set for the ideal generated by
the union of the digested polynomials
*D*and the category . - (3)
A minimal set of the form
which is a generating set for the ideal generated by
the union of the digested polynomials
*D*and the category . - (4) etc.

*D*is the set of digested polynomials. - (1)
A minimal generating set for the digested
polynomials

Wed Jul 3 10:27:42 PDT 1996