Function to test for algebraic dependence of polynomials

[araichev]

Added a function to sage/rings/polynomial/multi_polynomial_sequence.py to return an irreducible annihilating polynomial for the polynomials in self, if those polynomials are algebraically dependent. Otherwise it returns 0.

[malb]

• Shouldn't self be self, i.e. not typeset as mathematics?
• It would be good to show what the algebraic dependency is, i.e. what the polynomial means, by evaluating it in the doctest.
• "NOTES:" should ".. note::" IIRC
• it would be nice to have a more verbatim commit message, such that reading the logs makes sense
• wouldn't it be better to return *all* elements of the elimination ideal?

[malb]

erm, the first line should read: `self` and ``self``.

[malb]

Oh, and isn't it "algebraic dependency"?

[araichev]

Thanks for your help, Martin. I'm a newbie developer, so please bear with me. I incorporated your corrections.

• I evaluated the annihilating polynomials at self in the doctest to get 0. Is that what you mean?
• I think 'dependence' is the more conventional math noun: 'algebraic independence' and 'algebraic dependence'.
• Yes, it would be better to return the entire elimination ideal (did it now), which is what i meant to do initially but got sidetracked into making a tailored version for my bigger project.

[malb]

Replying to araichev:

Thanks for your help, Martin. I'm a newbie developer, so please bear with me. I incorporated your corrections.

NP at all.

• I evaluated the annihilating polynomials at self in the doctest to get 0. Is that what you mean?

yes, thanks.

• I think 'dependence' is the more conventional math noun: 'algebraic independence' and 'algebraic dependence'.

Okay, convinced :)

• Yes, it would be better to return the entire elimination ideal (did it now), which is what i meant to do initially but got sidetracked into making a tailored version for my bigger project.

Positive review.

[jdemeyer]

Your patch has two erroneous lines on top:

Detected SAGE64 flag
Building Sage on OS X in 64-bit mode

Please let me know which version of Sage you used to make this patch. Could you try upgrading to ​sage-4.7.1.alpha2, export the patch again and let me know whether the issue persists (it should be fixed)? In any case, the patch needs to be updated.

[araichev]

Hi jdemeyer:

I used Sage 4.7 to make the patch. I took your advice and upgraded to sage-4.7.1.alpha2 and retested the patch. The two erroneous lines disappeared. The new patch is up.

Thanks.