Opened 6 years ago

Closed 6 years ago

# improved PolynomialSequence

Reported by: Owned by: malb major sage-6.4 commutative algebra sd59 mmarco Martin Albrecht Jakob Kroeker N/A 1b208b5 (Commits) 1b208b5a2d4722637f82b14ef92ab46d4ab4d0e9

This now works:

sage: sr = mq.SR(1,1,2,4, gf2=True)
sage: F,s = sr.polynomial_system()
sage: I = F.ideal()
sage: I.random_element(degree=3) # new: return some funny distribution, #11850
k100*k102*x102 + k100*k102*x110 + ...

sage: I.random_element(degree=3, compute_gb=True, terms=True) # new: uniformly random up to degree 3
k100*k101*w112 + k100*k102*k110 + k100*k102*w102 + k100*k103*w111 + ...

sage: F.is_groebner() # new: PolynomialSequence.is_groebner, cf. #10856
False

sage: F.maximal_degree() # new: PolynomialSequence.maximal_degree, cf.
2

sage: gb = F.groebner_basis(algorithm='magma') # new: this used to fail
sage: gb.is_groebner()
True

sage: gb.maximal_degree()
1

sage: M = Sequence([f.lm() for f in F]) # new: this used to fail cf. #10680
sage: M.maximal_degree()
2

sage: F.reduced() # new: interreduced_basis() moved to Sequence
Polynomial Sequence with 60 Polynomials in 36 Variables


This ticket replaces #11850, #10856, #10680

### comment:1 Changed 6 years ago by malb

• Branch set to u/malb/t16585_mpolynomial_sequence
• Cc mmarco added
• Commit set to fef7d3bf43c0a2222fa9ddaf2809fd74603577fd
• Description modified (diff)
• Status changed from new to needs_review

### comment:2 Changed 6 years ago by malb

Anyone up for reviewing this?

### comment:3 Changed 6 years ago by jdemeyer

This obviously needs to be merged with the latest development version.

Apart from that, this ticket seems to do a lot of things (not only fixing several independent bugs, but also refactoring code), so it could be seen as a patch bomb which is a bad thing. Since this patch touches Magma-related stuff, only people who have Magma could review this.

### comment:4 Changed 6 years ago by git

• Commit changed from fef7d3bf43c0a2222fa9ddaf2809fd74603577fd to 6e9ef02bae16c9ec564b901d2a573bcb8f65ee6d

Branch pushed to git repo; I updated commit sha1. New commits:

 ​6e9ef02 Merge branch 'develop' of trac.sagemath.org:sage into u/malb/t16585_mpolynomial_sequence

### comment:5 Changed 6 years ago by vbraun_spam

• Milestone changed from sage-6.3 to sage-6.4

### comment:6 Changed 6 years ago by jakobkroeker

• Reviewers set to Jakob Kroeker
• Status changed from needs_review to needs_work

First remark:

in the commit 1b7927cb54bb2943ad2ae1a43c8e3befdf6703b6 in file src/sage/rings/polynomial/multi_polynomial_ideal.py at line 4139 I think it should be if d >= 0 instead of if d > 0

Second remark:

in the commit fffdbe0c8f9a248b3436d9c846bcd7b04a036d88 you introduce option terms=True to choose maximum number of terms. I don't like it, because the option is not self-descriptive, but try to convince me.

Third remark: in 81c951fa9d428816a44dd8855d5a00ec4c3cf2b3

you change the default option 'choose_degree=False' Changing default options is dangerous since it may break existing code. Please give reasons why this change is still ok

commits

3b6c11a13eb300f0a2bf6acb56d7b9001b03e1f8

c2a8506eed5d9db0106b38d1c643f503d19ab54a 37fb67cce683927cd248b518602e81a2e33ac134

looks ok for me

I will continue the review tomorrow evening.

Jakob

### comment:7 Changed 6 years ago by jakobkroeker

Ok, here the missing review comments:

############################################################################## 1. "make sure we use the polynomial ring as ring not the monoid", in file ./src/sage/rings/polynomial/multi_polynomial_sequence.py

I think there is a failing example, if the input below is legal:

R.<x,y,z> = PolynomialRing(QQ)
I = Ideal(5000*x*R,y*x+5) #error
# Ring is Monoid of ideals of Multivariate Polynomial Ring in x, y, z over Rational Field =>error:
# R must be a commutative ring


update: something is fishy with the next failing example:

1. what was K ?
2. how to reproduce "not a constant polynomial" error

second failing example (different error):

R.<x,y,z> = PolynomialRing(QQ)
I = Ideal(5000*x*K+y*x,y*x+5)
# TypeError: not a constant polynomial


####################################################### 2. in commit 9ee750ef52d6d6ba43254a07ffbf9cea1160315f snippet:

+ try:
+ c = K.characteristic()
+ except NotImplementedError:
+ c = 0


Why is c set to zero? At least this should be documented. Is it not possible to have a different characteristic in case of an NotImplementedError?? Do you have an example which hits this issue?

#################################################################### 3. refactored (lib)Singular GB code, in commit e60f83a9e1584a899e8c79171ce177474b9fed06 in src/sage/rings/polynomial/multi_polynomial_ideal_libsingular.pyx , line 114, ff.sage_ideal_to_singular_ideal Is there a corresponding test for a conversion from "or a list of generators"? If not, could you add one?

Same commit, in file 'src/sage/rings/polynomial/polynomial_singular_interface.py renaming singular_default to singular; why? At other places there are singular_default usages. Is there a difference?

#################################################################### 4. Same commit, It seems that reduce examples show no examples for explicitly reducing leading coefficient, Could you add an example or a test which hits "ret.append(f.lc()**(-1)*f)"?

#################################################################### 5. Sequence has no 'reduced' function Is that ok? Example:

R.<x> = PolynomialRing(QQ)
F = Sequence([x,x+1])
F.reduced() # fails


#################################################################### 6. commit a88b44703751c13e451252ca2da671679077711e (fix Magma interface broken when moving decorators around):

Could you explain what may get wrong and add an example?

Last edited 6 years ago by jakobkroeker (previous) (diff)

### comment:8 Changed 6 years ago by git

• Commit changed from 6e9ef02bae16c9ec564b901d2a573bcb8f65ee6d to c0241972230aec8d6ca71dffeca933df5ef9b963

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

 ​80d9973 add option terms=True for random element in multivariate polynomial rings + bugfix ​81cf80a PolynomialSequence.is_groebner ​e1acc1c MPolynomialIdeal.random_element ​ac26dd8 BooleanPolynomialRing.random_element(terms=True) ​5d6f994 don't use choose_degree=True as it biases the distribution ​3f47a64 fix Magma interface broken when moving decorators around ​ae4110c moved interreduced_basis to sequence also for Boolean polynomials ​0fa7a24 MPolynomialIdeal.random_element bugfix ​563baf0 Change terms=True to terms=Infinity ​c024197 Merge branch 'develop' of trac.sagemath.org:sage into u/malb/t16585_mpolynomial_sequence

### comment:9 Changed 6 years ago by malb

Hi Jakob, thanks for your review. I started addressing the issues you identified.

in file src/sage/rings/polynomial/multi_polynomial_ideal.py at line 4139 I think it should be if d >= 0 instead of if d > 0

Fixed: 0fa7a24

you introduce option terms=True to choose maximum number of terms. I don't like it, because the option is not self-descriptive, but try to convince me.

I agree, so I changed it. I changed the True to Infinity and changed the behaviour such that when requesting more terms than exist the number is silently reduced to the maximum number of available terms: 563baf0

PS: Because I am stupid, though, I rebased instead of merged. Hence, I believe you'll have to check out the code again, i.e. you can't just git pull again in your current branch. Sorry for that!

### comment:10 Changed 6 years ago by jakobkroeker

you can't just git pull again in your current branch I believe you'll have to check out the code again

Thanks for the hint! Its likely that otherwise I would get confused by the merge conflicts.

### comment:11 Changed 6 years ago by git

• Commit changed from c0241972230aec8d6ca71dffeca933df5ef9b963 to 620322d9c80b1b30e71ce89d09e5ee42e079163d

Branch pushed to git repo; I updated commit sha1. New commits:

 ​667dde3 Merge branch 'develop' into u/malb/t16585_mpolynomial_sequence ​dfe5ed0 Merge branch 'develop' into u/malb/t16585_mpolynomial_sequence ​3d4e7f7 Add test for conversion to singular ideals from ideals and sequences ​adeffda Document why we can assume c = 0 ​36fce47 Add test for reduction of leading coefficients ​620322d Add another test for reduction of leading coefficients

### comment:12 Changed 6 years ago by malb

• Status changed from needs_work to needs_review

you change the default option 'choose_degree=False' Changing default options is dangerous since it may break existing code. Please give reasons why this change is still ok

It changes the behaviour of a random sampler so the output is not deterministic anyway. Also, choose_degree=Truedoes not return what I’d expect from a random sampler: something uniform if possible. Mod p the new default lives up to this expectation if we consider uniform to mean: uniform of a given degree.

"make sure we use the polynomial ring as ring not the monoid", in file ./src/sage/rings/polynomial/multi_polynomial_sequence.py

I think there is a failing example, if the input below is legal:

sage: R.<x,y,z> = PolynomialRing(QQ)
sage: I = Ideal(5000*x*R,y*x+5) #error
# Ring is Monoid of ideals of Multivariate Polynomial Ring in x, y, z over Rational Field =>error:
# R must be a commutative ring


I don’t think this is connected. I’m getting the same error with sage 6.4.1. Also, The business of monoid vs ring only occurs when PolyBoRi? implements the ring.

a second failing example (different error):

sage: R.<x,y,z> = PolynomialRing(QQ)
sage: I = Ideal(5000*x*K+y*x,y*x+5)
# TypeError: not a constant polynomial


See above.

Why is c set to zero? At least this should be documented. Is it not possible to have a different characteristic in case of an NotImplementedError??? Do you have an example which hits this issue?

I added a comment:

# We assume that our ring has characteristic zero if it does not implement a # characteristic(). For example, generic quotient rings do not have a characteristic() # method implemented. It is okay to set c = 0 here because we're only using the # characteristic to pick a more specialized implementation for c = 2.

in src/sage/rings/polynomial/multi_polynomial_ideal_libsingular.pyx , line 114, ff.sage_ideal_to_singular_ideal Is there a corresponding test for a conversion from "or a list of generators"? If not, could you add one?

I added a test.

in file 'src/sage/rings/polynomial/polynomial_singular_interface.py renaming singular_default to singular; why? At other places there are singular_default usages. Is there a difference?

There is no need to rename singular to singular_default so I dropped it. It makes no difference either way.

It seems that reduce examples show no examples for explicitly reducing leading coefficient, Could you add an example or a test which hits "ret.append(f.lc()(-1)*f)"?

Sequence has no 'reduced' function Is that ok? Example:

I think this is fine as Sequence is not only for polynomials but for anything. However, reduced() only seems to make sense for polynomials.

(fix Magma interface broken when moving decorators around): Could you explain what may get wrong and add an example?

Unfortunately, I forgot. I could investigate if you insist.

### comment:13 Changed 6 years ago by malb

PS: Thanks again for your comments and sorry for taking so long to reply!

### comment:14 Changed 6 years ago by jakobkroeker

Thanks again for your comments and sorry for taking so long to reply!

You are welcome!

PS: I'm currently busy so I can't promise to look at the patch earlier than next Thursday

### comment:15 Changed 6 years ago by jakobkroeker

• Branch changed from u/malb/t16585_mpolynomial_sequence to u/jakobkroeker/t16585_mpolynomial_sequence.rebased
• Commit changed from 620322d9c80b1b30e71ce89d09e5ee42e079163d to 68c684cb7ddea420460ac12797f59b2ba6457b37
• Status changed from needs_review to positive_review

positive review.

I rebased the commits on recent develop branch

and ran all the tests again.

### comment:16 Changed 6 years ago by vbraun

• Status changed from positive_review to needs_work

Breaks PDF docs:

! Package inputenc Error: Unicode char \u8:ᵢ not set up for use with LaTeX.

See the inputenc package documentation for explanation.
Type  H <return>  for immediate help.
...

l.22080 ...element in this ideal as $r = \sum hᵢ ·fᵢ$.
?


### comment:17 Changed 6 years ago by git

• Commit changed from 68c684cb7ddea420460ac12797f59b2ba6457b37 to 1b208b5a2d4722637f82b14ef92ab46d4ab4d0e9

Branch pushed to git repo; I updated commit sha1. New commits:

 ​1b208b5 removed unicode char from documentation

### comment:18 Changed 6 years ago by malb

• Status changed from needs_work to positive_review

./sage --docbuild reference pdf went through without errors with Jakob's fix.

### comment:19 Changed 6 years ago by jakobkroeker

• Status changed from positive_review to needs_work

the reference builds, but building all pdf documentation fails

./sage --nodotsage --docbuild all pdf


### comment:20 Changed 6 years ago by malb

What is the error message?

### comment:21 Changed 6 years ago by jakobkroeker

What is the error message?

the failure was likely related to incremental docbuild (I didn' keep the error message)

Running 'make doc-clean' first did the trick ( the docbuild succeeds with warnings)

1. Can you confirm that './sage --nodotsage --docbuild all pdf' succeeds?
1. Did I forget to review some other important aspects ? I must admit that there is a hint in the review checklist http://www.sagemath.org/doc/developer/trac.html?highlight=review to test if the reference manual builds or not.

### comment:22 Changed 6 years ago by malb

• Status changed from needs_work to positive_review

I can confirm than make doc-pdf` succeeds. I think this should be all :).

### comment:23 Changed 6 years ago by vbraun

• Branch changed from u/jakobkroeker/t16585_mpolynomial_sequence.rebased to 1b208b5a2d4722637f82b14ef92ab46d4ab4d0e9
• Resolution set to fixed
• Status changed from positive_review to closed
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