General monomial orders in Macaulay

The most important monomial orders are those which have been introduced earlier in this section. Occasionally, one needs finer control over the monomial order. Macaulay allows you to construct arbitrary monomials orders.

When you are prompted for the monomial order by the ring command, you are actually specifying the internal representation of monomials for the ring being defined. The representation is a series of 32 bit non-negative integers, one for each specifier given. The specifiers may be

1. ``w'' for a weight vector. The program prompts later to have the weight vectors input, in order.
2. a number, specifying the number of variables to put into the ``next'' block of variables to be created. That is, for ``3 w 5'', the third specifier refers to the 4th through the 8th variable. Within a given block, Macaulay uses the graded reverse lexicographic order.
3. ``c'' for the position of the component number. At most one ``c'' can be used. Except for computing difficult finite free resolutions, this is best omitted: Macaulay will insert it last automatically.
4. ``-'': Put this first to suppress the component.

If the representation is ``incomplete'', it is completed automatically by Macaulay, which adds one or two fields to the end of the list: any variables not included in a given block of variables are made into a block, and a component field (specified by ``c'') is put at the end of the list, unless it is already present or has been inhibited by the presence of a ``-'' specifier.

Caveat: use the ``-'' specifier at your own risk. No matrices with more than one row are allowed in such a ring. This is mostly useful for computing a standard basis of an ideal which will use alot of memory.