SageMath 9.2 doctest issues

[NathanDunfield]

Should investigate these and fix if needed.

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File "/ext/sage/sage-9.2/local/lib/python3.8/site-packages/spherogram/links/invariants.py", line 179, in spherogram.links.invariants.Link.alexander_matrix
Failed example:
    L.alexander_matrix()
Expected:
    ([   -1 1 - t     t]
    [    t    -1 1 - t]
    [1 - t     t    -1], [t, t, t])
Got:
    ([   -1     t 1 - t]
    [1 - t    -1     t]
    [    t 1 - t    -1], [t, t, t])
**********************************************************************
File "/ext/sage/sage-9.2/local/lib/python3.8/site-packages/spherogram/links/invariants.py", line 240, in spherogram.links.invariants.Link.alexander_polynomial
Failed example:
    K.alexander_polynomial(norm=False)
Expected:
    t2^-1 + t1^-1*t2^-4
Got:
    t1^-1*t2^-1 + t1^-2*t2^-4
**********************************************************************
File "/ext/sage/sage-9.2/local/lib/python3.8/site-packages/spherogram/links/invariants.py", line 599, in spherogram.links.invariants.Link.braid_word
Failed example:
    Link('K6a2').braid_word(as_sage_braid=True)
Expected:
    (s0^-1*s1)^2*s0^-2
Got:
    s0^-1*(s0^-1*s1)^2*s0^-1
**********************************************************************

[culler]

Why are the monomials written in that strange way, instead of combining powers of the same variable and using a fixed ordering of the variables?

(s0^-1s1)^2s0^-2 -> s0^-4s1^2 s0^-1(s0^-1s1)^2s0^-1 -> s0^-4*s1^2

[NathanDunfield]

Those aren't monomials but rather words in the standard Artin generators for the braid group.

[culler]

No, github, I did not want to itialicize parts of my formulas

(s0^-1*s1)^2*s0^-2 -> s0^-4*s1^2

s0^-1*(s0^-1*s1)^2*s0^-1 -> s0^-4*s1^2

[culler]

Oh. I thought that was supposed to be an Alexander polynomial. I needed to scroll further to the right to see the rest of that long line. Sorry. Should have realized that you can't use s as a variable in an Alexander polynomial. Also should have realized that I was marking down. Maybe this is not the best medium for a discussion of this topic?

[NathanDunfield]

The old and new words are conjugate, so they have the same braid closure and hence both are correct answers. My first guess is that the deterministic order of dictionary keys in Python 3.6 onwards is the cause for this and the same for the alexander_matrix one.

The K.alexander_polynomial(norm=False) is more confusing, I'd guess some change in Sage means the code no longer correctly removes any "excess monomial" from the final answer.

[NathanDunfield]

Fixed in https://github.com/3-manifolds/Spherogram/commit/d7acde1fee96b2283229fd5de38cb99db9a67b31 .