sorted variables in multivariate polynomial ring wrong order

[dkrenn]

We have

sage: R.<a,b> = QQ[]
sage: sorted([a,b])
[b, a]

which looks weird to me and is not what one would expect.

This is also inconsistent with

sage: var('a, b')
(a, b)
sage: sorted([a,b])
[a, b]

(but in this case the ordering seems always to be alphabetically.)

However, in the multivariate polynomial ring this ordering depends on the definition:

sage: R.<b,a> = QQ[]
sage: sorted([a,b])
[a, b]

Component: algebra

Issue created by migration from https://trac.sagemath.org/ticket/17550

[dkrenn]

comment:1

Still there in 6.6

[nbruin]

comment:2

Polynomial rings have a monomial order which should affect how monomials (and hence terms) compare:

sage: A.<a,b>=PolynomialRing(Rationals(),order="lex")
sage: sorted([a^i*b^j for i in [0..2] for j in [0..2]])
[1, b, b^2, a, a*b, a*b^2, a^2, a^2*b, a^2*b^2]
sage: A.<a,b>=PolynomialRing(Rationals(),order="deglex")
sage: sorted([a^i*b^j for i in [0..2] for j in [0..2]])
[1, b, a, b^2, a*b, a^2, a*b^2, a^2*b, a^2*b^2]
sage: A.<a,b>=PolynomialRing(Rationals(),order="degrevlex")
sage: sorted([a^i*b^j for i in [0..2] for j in [0..2]])
[1, b, a, b^2, a*b, a^2, a*b^2, a^2*b, a^2*b^2]

[lftabera]

comment:3

By default sage uses 'degrevlex' for term orders. This is somehow standard in multivariate polynomial rings. I would not change this default. If you want a>b I suggest you to use 'deglex' term order instead.

I propose to resolve the ticket as wontfix.

[bgrenet]

comment:4

Replying to @lftabera:

By default sage uses 'degrevlex' for term orders. This is somehow standard in multivariate polynomial rings. I would not change this default. If you want a>b I suggest you to use 'deglex' term order instead.

I propose to resolve the ticket as wontfix.

I agree with you that this is related to the term orders. Yet, the order on the variables themselves doesn't change between "degrevlex" and "deglex". This is due to the fact that there are two distinct changes between these two orders.

[dkrenn]

comment:5

Replying to @nbruin:

Polynomial rings have a monomial order which should affect how monomials (and hence terms) compare:

sage: A.<a,b>=PolynomialRing(Rationals(),order="lex")
sage: sorted([a^i*b^j for i in [0..2] for j in [0..2]])
[1, b, b^2, a, a*b, a*b^2, a^2, a^2*b, a^2*b^2]
sage: A.<a,b>=PolynomialRing(Rationals(),order="deglex")
sage: sorted([a^i*b^j for i in [0..2] for j in [0..2]])
[1, b, a, b^2, a*b, a^2, a*b^2, a^2*b, a^2*b^2]
sage: A.<a,b>=PolynomialRing(Rationals(),order="degrevlex")
sage: sorted([a^i*b^j for i in [0..2] for j in [0..2]])
[1, b, a, b^2, a*b, a^2, a*b^2, a^2*b, a^2*b^2]

I understand that the original posted "problem" is not one, since we use "degrevlex", but using "lex" or "deglex" the output of the lines above should definitely start with [1, a, ...].