# Interpreting a chain of m's and o's from Macaulay2

This has been crossed referenced here as well in case a software developer understands this language.

I am using Macaulay2 and does anyone know how to read the following?

Example 1:

-- [gb]{1}(6)mmmmmm{2}(2)mm{3}(2)mm{4}(1)o{5}(1)m{6}(2)oo

-- number of (nonminimal) gb elements = 11

-- number of monomials = 59

-- ncalls = 1

-- nloop = 24

-- nsaved = 0

Example 2:

-- [gb]{1}(6)mmmmmm{2}(3)mmm{3}(2)mm{4}(4)mmmo{5}(6)mooooo{6}(4)oooo{7}(1)o

-- number of (nonminimal) gb elements = 15

-- number of monomials = 94

-- ncalls = 11

-- nloop = 190

-- nsaved = 0

I do not understand the chain of m's and o's and the curly bracket with a number in it, for example, {2}, and the round bracket (2). Here is what the chain of those symbols is supposed to mean, but I am not a computer programmer so it is somewhat difficult to interpret the above information.

For example: do I read this $$[gb]\{1\}(6)\mbox{mmmmmm}\{2\}(3)\mbox{mmm}\{3\}(2)\mbox{mm}\{4\}(4)\mbox{mmmo}\{5\}(6)\mbox{mooooo}\{6\}(4)\mbox{oooo}\{7\}(1)\mbox{o}$$ from left to right, or should we interpret each set $$\{1\}(6)\mbox{mmmmmm}$$ or $$(6) \mbox{mmmmmm} \{2\}$$ separately?

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Actually I figured it out. Consider Example 1:

$$\mbox{[gb]{1}(6)mmmmmm{2}(2)mm{3}(2)mm{4}(1)o{5}(1)m{6}(2)oo}.$$

$\mbox{{1}(6)mmmmmm}\;$ means you started out with 6 polynomials of degree 1 and you have to keep all 6 of them in the Groebner basis (gb).

$\mbox{{2}(2)mm}\;$ means you have 2 polynomials of degree 2 in your gb and you have to keep both polynomials in gb because of the two m's because they do not reduce to zero.

$\mbox{{3}(2)mm}\;$ means you have 2 polynomials of degree 3 and you have to keep both of them in your gb.

$\mbox{{4}(1)o}\;$ means you have 1 polynomial of degree 4 but o means it reduced to zero so you can get rid of it from your gb.

$\mbox{{5}(1)m}\;$ means you have 1 polynomial of degree 5 but you have to keep it in your gb.

$\mbox{{6}(2)oo}\;$ means you ahve 2 polynomials of degree 6 in your gb but they both reduce to zero so you can get rid of them.

Thus, we have $6+ 2+ 2+ 0+1+0 = 11$ $=$ total number of generators in gb. The reason why we are throwing away some of the polynomials is because Macaulay2 automatically produces a minimal Groebner basis. So it throws out extraneous basis elements.

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