Opened 11 years ago
Last modified 2 years ago
#10501 closed task
Deprecate adjoint in favor of adjugate — at Version 15
Reported by:  rbeezer  Owned by:  jason, was 

Priority:  minor  Milestone:  sage8.7 
Component:  linear algebra  Keywords:  notation, linear algebra, adjugate, matrices, determinants 
Cc:  was, mvngu, kohel, tornaria, mjo  Merged in:  
Authors:  Kwankyu Lee  Reviewers:  
Report Upstream:  N/A  Work issues:  
Branch:  u/klee/10501 (Commits, GitHub, GitLab)  Commit:  0669f64d384d8b42838d590a41a6bf9fcb115979 
Dependencies:  Stopgaps: 
Description (last modified by )
Matrix methods named adjoint
and _adjoint
are renamed adjugate
and _adjugate
and replacements are added that raise deprecation warnings.
This is part of the program at #10465.
Change History (16)
Changed 11 years ago by
comment:1 Changed 11 years ago by
 Cc was mvngu kohel tornaria added
 Status changed from new to needs_review
comment:2 followup: ↓ 3 Changed 11 years ago by
 Status changed from needs_review to needs_work
I already stated some objections to this on the mailing list, but I'll repeat:
On deprecating "adjoint" meaning "matrix of cofactors"
 it's standard terminology and has meant this in sage for long
 "adjugate" is newer and (IMO) less standard terminology  in particular it has no obvious translations
On using "adjoint" meaning "conjugate transpose"
 "conjugate transpose" is easy to say, and it's really what is meant
 the "adjoint operator" for a matrix seems illdefined, because a matrix is not an operator but only a representation of an operator in some basis.
Moreover, if there are two colliding usages of the name "adjoint", I would find it more reasonable to keep the usage that is already traditional in Sage.
The usage of "adjoint" is ubiquitous in relation to quadratic forms afaict (and, as John Cremona pointed out, is where the term originates with Gauss on ternary quadratic forms)
Reference for "Adjoint of a matrix":
Bourbaki, Elements, book 2, chapter III, section 11, exercise 9:
The adjoint of a square matrix X of order n over A is the matrix X = (det (A'")) of minors of A" of order n — 1.
(Note that the term also shows at the index of terminology of the book)
PS: searching for
"The adjoint of a square matrix" bourbaki
in books.google.com, yields the above passage.
comment:3 in reply to: ↑ 2 Changed 11 years ago by
Replying to tornaria:
Hi Gonzalo,
I certainly read your postings to the mailing list carefully and appreciated the points you raised. However, I had not realized you were so opposed to the change.
After some discussion, I asked 'Is there any objection to deprecating the current .adjoint() function (which returns a matrix of cofactors) and renaming it as the "adjugate"?'
It was not meant to be an official vote, but I got +1 replies from Grout, Cremona, Loeffler and Stein. Dima P and Karl Crisman had earlier voiced support. There were no objections stated once I asked the question carefully. So I have been proceeding on the assumption that there was strong support.
I do not believe I changed any of the names of the commands for quadratic forms, though I can see that causing confusion if the adjoint of a matrix becomes the conjugate transpose.
I have written a patch (#10471) with the conjugate_transpose()
, which I find a really clumsy command, but workable in the interim. William has suggested a more general adjoint
function, which I would need to think about some more, but maybe that does not help with any of your objections (sounds like maybe that is worse in your view).
I have twice now taught a "matrix analysis" course and it seems to me that adjoint gets used regularly (but maybe not consistently) for the conjugate transpose. I am in the middle of making a major push to add significant amount of Sage code to my introductory linear algebra text, which is going very nicely. But I need to also fix my "complex inner product" since I defined it with the conjugation on the "wrong" half. So I would really like to keep Sage, my text, and the word "adjoint" all consistent with each other when I get to that point in a few weeks.
Do you have some suggestions for a way forward?
Thanks, Rob
comment:4 Changed 9 years ago by
 Cc mjo added
+1 from me. I hit this today, and just checked a handful of books:
 Atkinson, An Introduction to Numerical Analysis, 1989. Section 7.1.
 Axler, Linear Algebra Done Right, 1997. Ch. 6.
 Marcus & Minc, Introduction to Linear Algebra, 1988. Section 1.4.
 Meyer, Matrix Analysis and Applied Linear Algebra, 2000. Section 3.2.
 Rudin, Functional Analysis, 1991. Chapter 4.
 Shilov, Linear Algebra, 1977. Section 7.6.
All of which use the "new" meaning. In the interest of fairness, I also found,
 Edwards, Elementary Linear Algebra, 2000. Section 3.4.
Which uses the cofactor definition.
comment:5 followup: ↓ 6 Changed 9 years ago by
Hmm. Given two completely different uses of the word "adjoint" in this situation, I wonder if the right solution is to avoid it completely (with a deprecation warning for a while). If we use the "new" meaning, there will still be people who type A.adjoint()
expecting the old meaning, and vice versa. Something like A.conjugate_transpose()
can be found by tab completion; is that good enough? Is A.adjugate()
the right name for the other version?
comment:6 in reply to: ↑ 5 ; followup: ↓ 7 Changed 9 years ago by
Replying to jhpalmieri:
Hmm. Given two completely different uses of the word "adjoint" in this situation, I wonder if the right solution is to avoid it completely (with a deprecation warning for a while). If we use the "new" meaning, there will still be people who type
A.adjoint()
expecting the old meaning, and vice versa. Something likeA.conjugate_transpose()
can be found by tab completion; is that good enough? IsA.adjugate()
the right name for the other version?
Did someone seriously implement m.conjugate_transpose()
as a shortcut for m.conjugate().transpose()
? =)
I never thought to look for another method, I just did the operations individually.
From what I understand, the terms "adjoint" and "adjunct" come from higher algebra, most of which is over my head. If that's the case, books written after e.g. category theory became popular will probably gravitate towards the new terminology. Although it does suck to have to deprecate adjoint
, give it a new name, and then give something else the old name.
Most of us have access to math departments; maybe we could do a survey of people working in linear algebra? If the result is overwhelming, rename it.
comment:7 in reply to: ↑ 6 ; followup: ↓ 8 Changed 9 years ago by
Replying to mjo:
Did someone seriously implement
m.conjugate_transpose()
as a shortcut form.conjugate().transpose()
? =)
Yep, that was me. ;) But the BDFL suggested it. Required reading:
https://groups.google.com/forum/?fromgroups=#!topic/sagedevel/YjImMWVVwo4
You will see a lot of support for changes. You'll see one conscientious objector. I dropped it. If someone else wants to carry the torch, I'll have their back.
Rob
comment:8 in reply to: ↑ 7 ; followup: ↓ 9 Changed 9 years ago by
Did someone seriously implement
m.conjugate_transpose()
as a shortcut form.conjugate().transpose()
? =)
It's not as bad as you think, because tabcompletion doesn't work on m.conjugate()
, though it would be awesome if Sage could magically know that...
Rob, so what does the latest version of your book do?
comment:9 in reply to: ↑ 8 Changed 9 years ago by
Replying to kcrisman:
Rob, so what does the latest version of your book do?
conjugatetranspose has always been called "adjoint," in line with my experience teaching numerical linear algebra. I even have my inner product conjugating the correct vector now. ;)
See: http://linear.ups.edu/html/sectionMO.html#subsectionAM
I almost never have need to reference the matrix of cofactors (proposed as adjugate here), but do use it one exercise about building a matrix inverse this way.
See: Exercise PDM.T20 in http://linear.ups.edu/html/sectionPDM.html
Rob
comment:10 Changed 8 years ago by
 Milestone changed from sage5.11 to sage5.12
comment:11 Changed 8 years ago by
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comment:12 Changed 7 years ago by
 Milestone changed from sage6.2 to sage6.3
comment:13 Changed 7 years ago by
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comment:14 Changed 3 years ago by
 Branch set to u/klee/10501
 Commit set to 0669f64d384d8b42838d590a41a6bf9fcb115979
 Milestone changed from sage6.4 to sage8.4
 Priority changed from major to minor
 Status changed from needs_work to needs_review
I want to revive this ticket. So here is the needed patch.
One thing not found in Rob's original patch is alias adjoint_classical
of adjugate
. The alias is used in quadratic form code in Sage.
New commits:
0669f64  Deprecate adjoint for adjugate and adjoint_classical

comment:15 Changed 3 years ago by
 Description modified (diff)
Three files caused doctest errors on a full run with only the necessary changes in sage/matrix. I've made changes in these other places to fix those failures, and the affected files now pass their tests. I'm running the full suite right now.
I've cc'ed folks who I think might be able to doublecheck that no complications have crept in. If you want to sneak a quick look at the patch, here's a quick guide:
Minh, David: sage/crypto/classical.py, inverse_key() for a Hill Cryptosystem
Gonzalo: sage/quadratic_forms/quadratic_form_ternary_Tornaria.py, adjoints of a form
William: sage/quadratic_forms/quadratic_form.py, adjoint_primitive()