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Make minimal polynomial of I irreducible #14382

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Merged
smichr merged 2 commits into from
Mar 13, 2018
Merged

Make minimal polynomial of I irreducible #14382

smichr merged 2 commits into from
Mar 13, 2018

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@jksuom
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@jksuom jksuom commented Mar 4, 2018

Currently, the minimal polynomial of I is hard-coded x**2 + 1
over all domains. This PR returns x - I over domains that
contain I.

Current master:
>>> minimal_polynomial(I, x, domain=QQ.algebraic_field(I))
x**2 + 1

This PR:
>>> minimal_polynomial(I, x, domain=QQ.algebraic_field(I))
x - I

@jksuom
Make minimal polynomial of I irreducible
2b02333 
Currently, the minimal polynomial of I is hard-coded `x**2 + 1`
over all domains. This PR returns `x - I` over domains that
contain I.

Current master:
>>> minimal_polynomial(I, x, domain=QQ.algebraic_field(I))
x**2 + 1

This PR:
>>> minimal_polynomial(I, x, domain=QQ.algebraic_field(I))
x - I
normalhuman
normalhuman reviewed Mar 4, 2018
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sympy/polys/tests/test_numberfields.py
# minimal polynomial of I
assert minimal_polynomial(I, x, domain=QQ.algebraic_field(I)) == x - I
K = QQ.algebraic_field(I*(sqrt(2) + 1))
assert minimal_polynomial(I, x, domain=K) == x - I
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@normalhuman normalhuman Mar 4, 2018

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Both of these tests result in x - I. Is the other possibility, the minimal polynomial being x**2 + 1 , tested anywhere?

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@jksuom jksuom Mar 4, 2018

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I didn't think it was necessary but maybe it could be included. Perhaps this would suffice?

>>> minimal_polynomial(I, x, domain=QQ)
x**2 + 1

Or this?

>>> minimal_polynomial(I, x, domain='QQ(y)')
x**2 + 1

@skirpichev
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skirpichev commented Mar 5, 2018 •
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I suspect, there are plenty of such hardcoded surprises...

In [11]: minimal_polynomial(exp(I*pi/3), x, domain=QQ.algebraic_field(sqrt(3)*I))
Out[11]: 
 2        
x  - x + 1

In [12]: factor(_, extension=sqrt(3)*I)
Out[12]: 
⎛          ___  ⎞ ⎛          ___  ⎞
⎜    1   ╲╱ 3 ⋅ⅈ⎟ ⎜    1   ╲╱ 3 ⋅ⅈ⎟
⎜x - ─ - ───────⎟⋅⎜x - ─ + ───────⎟
⎝    2      2   ⎠ ⎝    2      2   ⎠

More systematic workaround may be using compose=False algorithm (currently, it doesn't support anything except Q) for algebraic extensions.

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jksuom commented Mar 5, 2018

That is disappointing. There is a whole range of private methods like _minpoly_exp(ex, x) that ignore the dom argument.

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skirpichev commented Mar 5, 2018

As a variant, you could "sanitize" output of minpoly helpers: factorize one over specified dom (if it's badly supported) and select appropriate factor with _choose_factor().

@smichr
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smichr commented Mar 13, 2018

That is disappointing. There is a whole range of private methods

Is that a blocker for this PR or should we let that be a new issue?

@jksuom
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jksuom commented Mar 13, 2018

No, I think those other cases could be taken care of elsewhere. They are concerned with algebraic values of transcendental functions, and it seems that they are currently not considered in number field computations. I was the only one I have encountered so far.

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skirpichev commented Mar 13, 2018

That's a damn simple problem, with a clear solution, explained above. Why just not fix it?

@jksuom
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jksuom commented Mar 13, 2018

Why just not fix it?

Well, why not. (Maybe not all simple problems should be handed over to beginners...)

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smichr commented Mar 13, 2018

I will open a new issue. Feel free to edit it if I have misrepresented the issue. As the change here is minimal I will commit this.

@smichr smichr merged commit cdd5a23 into sympy:master Mar 13, 2018
@smichr smichr mentioned this pull request Mar 13, 2018
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@jksuom jksuom deleted the minpoly-of-I branch March 13, 2018 13:12
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