Monomial order in Macaulay2

Question

When I define the ring to work on in Macaulay2, I would like to change the order of the variables for building the Grobner basis of ideals with respect to this new order. For instance, if set R = QQ [x_1..x_5], then how may I define the lexicographic monomial order induced by x_3<x_2<x_1<x_5<x_4?

Answer 1

The default ordering of the variables is whatever order you use to write them when creating the ring.

For instance, to get the order you want, you should use

R = QQ[x_3, x_2, x_1, x_5, x_4]

Indeed, on my version of Macaualy2 we can see the desired behavior:

i1 : R = QQ[x_3, x_2, x_1, x_5, x_4]
o1 = R
o1 : PolynomialRing
i2 : x_1 + x_2 + x_4
o2 = x  + x  + x
      2    1    4
o2 : R

I'm not sure if there's a way to do this automatically, though, and a quick look through the documentation makes it look like there might not be a way to do that.

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I hope this helps ^_^