Opened 12 years ago

Closed 12 years ago

# Function to test for algebraic dependence of polynomials

Reported by: Owned by: araichev AlexGhitza major sage-4.7.2 algebra algebraic dependence polynomials malb sage-4.7.2.alpha0 Alex Raichev Martin Albrecht N/A

### Description

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.

### comment:1 Changed 12 years ago by araichev

Status: new → needs_review

### comment:3 Changed 12 years ago by malb

Reviewers: → Martin Albrecht needs_review → needs_work → documentation
• 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?

### comment:4 Changed 12 years ago by malb

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

### comment:5 Changed 12 years ago by malb

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

### comment:6 follow-up:  7 Changed 12 years ago by araichev

Status: needs_work → needs_review

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.

### comment:7 in reply to:  6 Changed 12 years ago by malb

Status: needs_review → positive_review

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.

### comment:8 Changed 12 years ago by jdemeyer

Milestone: sage-4.7.1 → sage-4.7.2 documentation

### comment:9 Changed 12 years ago by jdemeyer

Status: positive_review → needs_work

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.

### comment:10 Changed 12 years ago by araichev

Status: needs_work → needs_review

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.

### comment:11 Changed 12 years ago by jdemeyer

Status: needs_review → positive_review

### comment:12 Changed 12 years ago by jdemeyer

Merged in: → sage-4.7.2.alpha0 → fixed positive_review → closed
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