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Implement Vertex algebras and related algebraic structures #29610

Open heluani opened 4 years ago

heluani commented 4 years ago

This ticket implements (super) vertex algebras, (super) Poisson vertex algebras and (super) Lie conformal algebras

Summary of implemented structures

Examples from the documentation:

The documentation can be found in the compiled reference manuals. A copy can be found in the following links. The main usage examples are in:

http://potuz.net/reference/algebras/sage/algebras/vertex_algebras/vertex_algebra.html

And the tree of classes with more examples can be found in the pages

http://potuz.net/reference/algebras/vertex_algebras/vertex_algebras.html http://potuz.net/reference/algebras/lie_conformal_algebras/lie_conformal_algebras.html http://potuz.net/reference/algebras/poisson_vertex_algebras/poisson_vertex_algebras.html

The following is a typical example from the documentation (which was essentially what drove me to write this patch as it was used in https://arxiv.org/abs/2005.10769:

    sage: V = VirasoroVertexAlgebra(QQ,1/2); V.inject_variables()
    Defining L
    sage: L*L
    L_-2L_-2|0>
    sage: (L*L).T()
    2*L_-3L_-2|0> + L_-5|0>
    sage: L.bracket(L*L)
    {0: 2*L_-3L_-2|0> + L_-5|0>,
     1: 4*L_-2L_-2|0>,
     2: 3*L_-3|0>,
     3: 17/2*L_-2|0>,
     5: 3/2*|0>}
    sage: V.find_singular(6)
    (L_-2L_-2L_-2|0> + 93/64*L_-3L_-3|0> - 33/8*L_-4L_-2|0> - 27/16*L_-6|0>,)
    sage: I = V.ideal(_); I
    ideal of The Virasoro vertex algebra of central charge 1/2 over Rational Field generated by (L_-2L_-2L_-2|0> + 93/64*L_-3L_-3|0> - 33/8*L_-4L_-2|0> - 27/16*L_-6|0>,)
    sage: Q = V.quotient(I); Q
    Quotient of The Virasoro vertex algebra of central charge 1/2 over Rational Field by the ideal generated by (L_-2L_-2L_-2|0> + 93/64*L_-3L_-3|0> - 33/8*L_-4L_-2|0> - 27/16*L_-6|0>,)
    sage: Q.retract(L*(L*L))
    -93/64*L_-3L_-3|0> + 33/8*L_-4L_-2|0> + 27/16*L_-6|0>
    sage: P = Q.arc_algebra(); P
    Quotient of The classical limit of The Virasoro vertex algebra of central charge 1/2 over Rational Field by the ideal generated by (L_2^3,)
    sage: R = Q.classical_limit(); R
    The classical limit of Quotient of The Virasoro vertex algebra of central charge 1/2 over Rational Field by the ideal generated by (L_-2L_-2L_-2|0> + 93/64*L_-3L_-3|0> - 33/8*L_-4L_-2|0> - 27/16*L_-6|0>,)
    sage: P.hilbert_series(10)
    1 + q^2 + q^3 + 2*q^4 + 2*q^5 + 3*q^6 + 3*q^7 + 5*q^8 + 6*q^9 + O(q^10)
    sage: R.hilbert_series(10)
    1 + q^2 + q^3 + 2*q^4 + 2*q^5 + 3*q^6 + 3*q^7 + 5*q^8 + 5*q^9 + O(q^10)
    sage: f = R.arc_algebra_cover; f
    Ring morphism:
      From: Quotient of The classical limit of The Virasoro vertex algebra of central charge 1/2 over Rational Field by the ideal generated by (L_2^3,)
      To:   The classical limit of Quotient of The Virasoro vertex algebra of central charge 1/2 over Rational Field by the ideal generated by (L_-2L_-2L_-2|0> + 93/64*L_-3L_-3|0> - 33/8*L_-4L_-2|0> - 27/16*L_-6|0>,)
      Defn: L_2 |--> L_2
    sage: f.kernel(9)
    Free module generated by {0} over Rational Field
    sage: _.an_element().lift()
    2*L_4*L_3*L_2 + 1/3*L_5*L_2^2

Random Comments

I am happy to help breaking the ticket if this will facilitate reviewing it. But on the other hand if you look at the list of examples it is clear that most of the doctesting and examples will break.

Immediate Goals

What is not implemented

These require other techniques.

What is obviously wrong

I suppose I'll start adding things to this list shortly, but some things are now clearly wrong:

Depends on #30007 Depends on #30032 Depends on #30043

CC: @tscrim @heluani @dwbump

Component: algebra

Keywords: vertex algebras, lie conformal algebras

Author: Reimundo Heluani

Branch/Commit: u/heluani/vertex_algebras @ b578a35

Issue created by migration from https:https://user-images.githubusercontent.com/56448218/216875706-81af88ae-b4e3-493b-86a6-87337f21688a.jpg/29610

The latter should be https://trac.sagemath.org/ticket/29610

fchapoton commented 4 years ago
comment:1

The problem with such a huge ticket is that you will have even harder times to find a reviewer.

Small comment:

+EXAMPLES::
+
+- We construct the algebra of functions of the arc space of the *fat origin of
+  the line* `\mathbb{A}^1` over the rationals and compute it's graded
+  dimension::

This is not correct, only lines with indented content should end with ::

More generally you should build the doc and look at it.

heluani commented 4 years ago

Attachment: ticket.jpg

image built doc

heluani commented 4 years ago
comment:2

Thanks. Regarding the comment it looks good in my built copy of the doc (modulo the "it's" that should be "its"):

fchapoton commented 4 years ago
comment:4

The suggestion from comment:1 must be followed, please.

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from 0128ed3 to ae30dae

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

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

a33b8c0Fixing failures and allowing echelon_form to handle oo-dim modules.
748961fFixing doctests and making `_vector_` and from_vector methods more consistent.
c96e1d8Implemented EnergyPartitionTuples
71a567cQuotients are CombinatorialFreeModules
a02ec39Refactored Poisson Vertex Algebras
766ce98Implemented the cover morphism from the singular support
721ca0ffix Lie Conformal Algebras doctests
755740eLCAs inherit from CombinatorialFreeModule
61d5cccRemoved graded_algebra_with_derivation
ae30daeDocumentation of Lie Conformal Algebra
tscrim commented 4 years ago
comment:6

I am very much interested in getting this into Sage, and it is a very good project.

Like Frédéric, I think it would be better if you can split this into at least a few separate tickets. For example, the basic framework that can handle generic data can go in one and then some of the more specific examples can in another (or at most one specific implementation if there is no generic data possible that you can use for your doctests).

Something else from a quick browse through your code, it looks like at this point your framework of ABCs for Lie conformal algebras is better to be lifted to the respective categories.

I think another good thing to have is a catalog object as a common entry point for the different specific examples.

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

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

e82f103Documentation of Vertex Algebras
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from ae30dae to e82f103

heluani commented 4 years ago
comment:8

Replying to @tscrim:

I am very much interested in getting this into Sage, and it is a very good project.

Like Frédéric, I think it would be better if you can split this into at least a few separate tickets. For example, the basic framework that can handle generic data can go in one and then some of the more specific examples can in another (or at most one specific implementation if there is no generic data possible that you can use for your doctests).

Something else from a quick browse through your code, it looks like at this point your framework of ABCs for Lie conformal algebras is better to be lifted to the respective categories.

I think another good thing to have is a catalog object as a common entry point for the different specific examples.

Thanks for the comments, I'll finish documenting what I have now, following Chapoton's comments on the documentation (I refactored the whole with basis thing to use CombinatorialFreeModules and added plenty of examples of super algebras) and then I'll ask for help into how to break this. I have some ideas, but they all lead to breakage of doctesting, which I put a lot of effort into having plenty of them.

I should be ready to ask for reviewers in the next few days. I am happy with the functionality as it is now, the biggest problem is the speed of arithmetics when working with classical limits of quotients of vertex algebras. I will move the main computations to cython in a following ticket, but I am afraid that it may even be my choice of recursion instead of brutally computing commutators of Lie algebra modes.

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Branch pushed to git repo; I updated commit sha1. This was a forced push. Last 10 new commits:

6b99cc8Implemented EnergyPartitionTuples
e9c589aQuotients are CombinatorialFreeModules
e8f1ae6Refactored Poisson Vertex Algebras
e32a2cbImplemented the cover morphism from the singular support
b7b207dfix Lie Conformal Algebras doctests
e32d2ccLCAs inherit from CombinatorialFreeModule
737bdefRemoved graded_algebra_with_derivation
07ec01eDocumentation of Lie Conformal Algebra
19700ebDocumentation of Vertex Algebras
b7379b6Documented Poisson Vertex Algebras
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from e82f103 to b7379b6

heluani commented 4 years ago

Description changed:

--- 
+++ 
@@ -1,131 +1,162 @@
-This ticket implements **vertex algebras**, **Poisson vertex algebras**, **Lie conformal algebras** and related algebraic structures. 
+This ticket implements **(super) vertex algebras**, **(super) Poisson vertex algebras** and **(super) Lie conformal algebras** 

 ## Summary of implemented structures
 - Lie conformal algebras: 
-   - category of such and their subcategories (graded, finitely generated, etc)
-   - Freely and finitely generated Lie conformal algebras and central extensions of those. 
-   - H-graded Lie conformal algebras.
+   - category of such and their subcategories (graded, finitely generated, super, etc)
+   - construction of central extensions of freely generated Lie conformal algebras from the brackets of the generators.
+
 - Vertex algebras:
     - category of such and their subcategories as above.
     - Universal enveloping vertex algebras of Lie conformal algebras.
     - canonical embedding from a Lie conformal algebra to its universal enveloping algebra. 
     - Vertex algebra ideals of graded vertex algebras, generated by primary vectors. 
-    - Quotients of vertex algebras by vertex algebra ideals. 
-    - Li filtration and associated graded. 
+    - Quotients of universal enveloping vertex algebras by vertex algebra ideals. 
+
 - Poisson vertex algebras:
     - category of such and their subcategories as above.
     - classical limits of universal enveloping vertex algebras and their quotients by primary vectors. 
-- Graded commutative algebras with a derivation (it's a pity that `dca` has very different meanings in the literature and has already been taken in Sage)
-    - Affine arc algebras (differential polynomial algebra). Possibly weighted and using different `TermOrders`. 
-    - differential ideals 
-    - quotients of Affine arc algebras by their differential ideals.
-   
-
+    - arc algebras of universal enveloping vertex algebras and their quotients (the algebra of functions on the arc space of the associated scheme to a vertex algebra)
+    - The canonical surjective morphism from the arc algebra to the singular support of a vertex algebra.
+    - Ideals of freely generated poisson vertex algebras (this includes for example differential ideals of differential polynomial algebras)
+    - Quotients of freely generated poisson vertex algebras by their ideals.
+- The following examples are implemented:
+     - Abelian Lie conformal and vertex algebras 
+     - Affine Lie conformal and vertex algebras
+     - Bosonic Ghosts Lie conformal algebras
+     - Fermionic Ghosts Lie conformal algebras
+     - Free Bosons Lie Conformal and vertex Algebras
+     - Free Fermions Lie Conformal and vertex Algebras
+     - N=2 Super Lie Conformal and vertex Algebra
+     - Neveu-Schwarz super Lie conformal and vertex algebra
+     - Virasoro Lie conformal and vertex algebra
+     - Weyl Lie conformal and vertex algebra

 ## Examples from the documentation:

-The base class for all vertex algebras is `VertexAlgebra`. 
-All subclasses are called through its method `__classcall_private__`.
-We provide some convenience functions to define named vertex algebras
-like `VirasoroVertexAlgebra` and `AffineVertexAlgebra`
+The documentation can be found in the compiled reference manuals. A copy can be found in the following links. The main usage examples are in:

-- We create the Universal Virasoro Vertex algebra at central charge `c=1/2` and perform some basic computations:
+http://potuz.net/reference/algebras/sage/algebras/vertex_algebras/vertex_algebra.html
+
+And the tree of classes with more examples can be found in the pages
+
+http://potuz.net/reference/algebras/vertex_algebras/vertex_algebras.html
+http://potuz.net/reference/algebras/lie_conformal_algebras/lie_conformal_algebras.html
+http://potuz.net/reference/algebras/poisson_vertex_algebras/poisson_vertex_algebras.html
+
+The following is a typical example from the documentation (which was essentially what drove me to write this patch as it was used in https://arxiv.org/abs/2005.10769:
+
+- We create the Universal Virasoro Vertex algebra of central charge c=1/2 and perform some basic computations:

-sage: V = VirasoroVertexAlgebra(QQ,1/2); V.injectvariables() -Defining L -sage: L*L -L-2L-2|0> -sage: (LL).T() -2L-3L-2|0>+L-5|0> -sage: sorted(L.bracket(LL).items()) -[(0, 2L-3L-2|0>+L_-5|0>),

-- We compute it's irreducible quotient: +- The result above indicates that Q is not classically free:

-sage: V.find_singular(6)    [L_-2L_-2L_-2|0>-33/8*L_-4L_-2|0>+93/64*L_-3L_-3|0>-27/16*L_-6|0>]
-sage: v = _[0]; I = V.ideal(v)
-sage: I
-ideal of The Virasoro vertex algebra at central charge 1/2 generated by (L_-2L_-2L_-2|0>-33/8*L_-4L_-2|0>+93/64*L_-3L_-3|0>-27/16*L_-6|0>,)
-sage: Q = V.quotient(I)
-sage: Q
-Quotient of The Virasoro vertex algebra at central charge 1/2 by the ideal generated by (L_-2L_-2L_-2|0>-33/8*L_-4L_-2|0>+93/64*L_-3L_-3|0>-27/16*L_-6|0>,)
-sage: Q.retract(L*L*L)
-65/8*L_-4L_-2|0>+35/64*L_-3L_-3|0>+35/16*L_-6|0>
+    sage: f = R.arc_algebra_cover; f
+    Ring morphism:
+      From: Quotient of The classical limit of The Virasoro vertex algebra of central charge 1/2 over Rational Field by the ideal generated by (L_2^3,)
+      To:   The classical limit of Quotient of The Virasoro vertex algebra of central charge 1/2 over Rational Field by the ideal generated by (L_-2L_-2L_-2|0> + 93/64*L_-3L_-3|0> - 33/8*L_-4L_-2|0> - 27/16*L_-6|0>,)
+      Defn: L_2 |--> L_2
+    sage: f.kernel(9)
+    Free module generated by {0} over Rational Field
+    sage: _.an_element().lift()
+    2*L_4*L_3*L_2 + 1/3*L_5*L_2^2

-- We construct the universal Affine vertex algebra for sl_3 at level 2 and perform some basic computations: + +## Random Comments + +- This ticket fails one of the first Guidelines for opening tickets:

-- We construct the universal affine vertex algebra for sl_2 at level3 and check that a vector is singular: +I couldn't think of a better way to write them. and this is not that bad. But when you go to rational gradings, say the N=1 super vertex algebra, you start seeing things like

-sage: V = AffineVertexAlgebra(QQ,'A1',3)
-sage: V.gens()
-(E(alpha[1])_-1|0>, E(alphacheck[1])_-1|0>, E(-alpha[1])_-1|0>)
-sage: e = V.gen(0)
-sage: e*(e*(e*e))
-E(alpha[1])_-1E(alpha[1])_-1E(alpha[1])_-1E(alpha[1])_-1|0>
-sage: (e*(e*(e*e))).is_singular()
-True
+3*G_-3/2|0>

-- We construct the classical limit of V and check that the multiplication is associative in this limit while not in V: +Still not entirely awful as there can't be any confusion (as far as I can see). The worst situation is the Poisson case where that would render

-sage: P = V.classical_limit()
-sage: P
-The Poisson vertex algebra quasi-classical limit of The universal affine vertex algebra of CartanType ['A', 1] at level 3
-sage: f = V.gen(2)
-sage: e*(e*f) == (e*e)*f
-False
-sage: e=P(e); e.parent()
-The Poisson vertex algebra quasi-classical limit of The universal affine vertex algebra of CartanType ['A', 1] at level 3
-sage: f=P(f)
-sage: e*(e*f) == (e*e)*f
-True
+3*G_3/2

+And that /2 is quite bad. It is not ambiguous with

-## Comments

-- This ticket fails one of the first Guidelines for opening tickets:

heluani commented 4 years ago
comment:12

Replying to @tscrim:

I am very much interested in getting this into Sage, and it is a very good project.

Hello I just posted the last of what I had n mind for a first draft and I am hoping to get some reviewers. I posted some views in sage-devel (which I suppose is better to discuss than trac) but I am happy to break this if this would help reviewers.

Before doing so I wanted to come back to some of your comments:

Something else from a quick browse through your code, it looks like at this point your framework of ABCs for Lie conformal algebras is better to be lifted to the respective categories.

I tried to put every method that was implementation independent in the category, is this what you mean? did I miss much?

I think another good thing to have is a catalog object as a common entry point for the different specific examples.

This I don't know what you mean? I tried to copy your model on LieAlgebras where there's one exposed class that you call to construct any other object through it's __classcall_private__ method. These are LieConformalAlgebra, VertexAlgebra and PoissonVertexAlgebra respectively now. The first is essentially the same as you LieAlgebra: you feed it structure constants and it constructs something. Is this what you mean by catalog?

mkoeppe commented 4 years ago
comment:13

I would suggest to split out the changes to src/sage/combinat/partition_tuple.py to a separate ticket, but I would suspect that there is no point in trying to break the other things into many tickets.

heluani commented 4 years ago
comment:14

Replying to @mkoeppe:

I would suggest to split out the changes to src/sage/combinat/partition_tuple.py to a separate ticket, but I would suspect that there is no point in trying to break the other things into many tickets.

Ah thanks, I opened #30007

heluani commented 4 years ago

Dependencies: #30007

heluani commented 4 years ago

Description changed:

--- 
+++ 
@@ -133,30 +133,39 @@
 These require other techniques. 

-### What is obviously wrong ==
+## What is obviously wrong

 I suppose I'll start adding things to this list shortly, but some things are now clearly wrong:

-- Printing of elements. A typical element of the Virasoro Vertex algebra now is printed as 
+- Printing of elements. A typical element of the Virasoro Vertex 
+  algebra now is printed as 

-```
-3*L_-3L_-3L_2|0> -2*L_2|0>
-```
+  ```
+  3*L_-3L_-3L_-2|0> -2*L_-2|0>
+  ```

-I couldn't think of a better way to write them. and this is not that bad. But when you go to rational gradings, say the N=1 super vertex algebra, you start seeing things like
+  I couldn't think of a better way to write them. and this is not 
+  that bad. But when you go to rational gradings, say the N=1 super 
+  vertex algebra, you start seeing things like

-```
-3*G_-3/2|0>
-```
+  ```
+  3*G_-3/2|0>
+  ```

-Still not entirely awful as there can't be any confusion (as far as I can see). The worst situation is the Poisson case where that would render
+  Still not entirely awful as there can't be any confusion (as far 
+  as I can see). The worst situation is the Poisson case where 
+  that would render

-```
-3*G_3/2
-```
-And that /2 is quite bad. It is not ambiguous with 
+  ```
+  3*G_3/2
+  ```
+  And that /2 is quite bad. It is not ambiguous with 

-```
-3/2*G_3
-```
-But is ugly. Still I couldn't find anything better. 
+  ```
+  3/2*G_3
+  ```
+  But is ugly. Still I couldn't find anything better. 
+- Speed: the biggest problem in computing on quotients and on their 
+  classical limits is the test that an element is in the ideal. 
+  There is no analog to `_divides_` in commutative rings. Currently 
+  what I am doing is to compute every element of the algebra acting on the generators of the ideal so that many vectors are counted several times due to relations. This I think is the bottleneck and surely can be improved.
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

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

8b6562bImplemented vector regular partition tuples
58e7553PartitionTuples allow componentwise regular value
192b9ecrebase #30007
5ee6f1bMerge branch 't/30007/public/vector_regular_partition_tuples' into t/29610/vertex_algebras
c5697ebUse RegularPartitionTuples_level
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from b7379b6 to c5697eb

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

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

d6ced88Implement `_an_element_` instead of an_element
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from c5697eb to d6ced88

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from d6ced88 to db1804c

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

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

db1804cCreated Catalog files of examples per reviewer request
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

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

c5233f6Fix category of 0-Regular partition tuples
23a7270Merge branch 'vector_regular_partition_tuples'
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from db1804c to 23a7270

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Branch pushed to git repo; I updated commit sha1. This was a forced push. Last 10 new commits:

91b2181Documentation of Lie Conformal Algebra
f9322dbDocumentation of Vertex Algebras
74b83a7Documented Poisson Vertex Algebras
6c5a923PartitionTuples allow componentwise regular value
d4ccd3brebase #30007
77bb0cdUse RegularPartitionTuples_level
94662ebImplement `_an_element_` instead of an_element
a52a5c1Created Catalog files of examples per reviewer request
f5711c8Fix category of 0-Regular partition tuples
1a2734eRebase onto #30032
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from 23a7270 to 1a2734e

heluani commented 4 years ago

Changed dependencies from #30007 to #30007, #30032

heluani commented 4 years ago

Last 10 new commits:

91b2181Documentation of Lie Conformal Algebra
f9322dbDocumentation of Vertex Algebras
74b83a7Documented Poisson Vertex Algebras
6c5a923PartitionTuples allow componentwise regular value
d4ccd3brebase #30007
77bb0cdUse RegularPartitionTuples_level
94662ebImplement `_an_element_` instead of an_element
a52a5c1Created Catalog files of examples per reviewer request
f5711c8Fix category of 0-Regular partition tuples
1a2734eRebase onto #30032
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from 1a2734e to 8a9671b

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

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

8a9671bBot complaints cleaning
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from 8a9671b to 840912d

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Branch pushed to git repo; I updated commit sha1. This was a forced push. Last 10 new commits:

fdde439Moved from FooVertexAlgebra to vertex_algebras.Foo
9237b52Moved from FooLieConformalAlgebra to lie_conformal_algebras.Foo
1036855Corrected bad sed on va examples
0795811Moved doctest to class level instead of __init__
db496e6Renamed LieConformalAlgebraWithGenerators
0070a0eRemoved uses of NN
7b21d66Removed abstract_method(optional=False)
e430b4dRemoved def WithBasis() from categories
49f397fown file for LieConformalAlgebras().Graded()
840912drebase onto #30043
heluani commented 4 years ago

Changed dependencies from #30007, #30032 to #30007, #30032, #30043

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

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

a432b8cBlocks bot complaints
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from 840912d to a432b8c

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from a432b8c to eb1d099

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

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

eb1d099Added missing docstrings
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

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

c6a0dc0Fixed a docstring
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from eb1d099 to c6a0dc0

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from c6a0dc0 to d6968ab

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Branch pushed to git repo; I updated commit sha1. This was a forced push. Last 10 new commits:

13d337aRemoved def WithBasis() from categories
ff9ce33own file for LieConformalAlgebras().Graded()
cb1483drebase onto #30043
c2ea9b0Blocks bot complaints
1f06001Added missing docstrings
08e4166Fixed a docstring
5e33e63Cleaned Category of Lie Conformal Algebras
4b1982ffinitely generated LCA -> finitelyfreelygeneratedLCA
8cbe6c0Correct pyflakes bot warnings
d6968abFix 1 docstring
fchapoton commented 4 years ago
comment:31

red branch => needs work

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from d6968ab to 1da1fdf

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Branch pushed to git repo; I updated commit sha1. This was a forced push. Last 10 new commits:

04da8fcAdded missing docstrings
24a05c6Fixed a docstring
e2568e1Cleaned Category of Lie Conformal Algebras
f2185c9finitely generated LCA -> finitelyfreelygeneratedLCA
38a051aCorrect pyflakes bot warnings
c2d1bd7Revert _test_jacobi to some_elements instead of all gens
b196e65Split category of vertex algebras
9bde444Rebase onto #30043
05a38e6Implemented ProtoVertexAlgebras
1da1fdfImplemented ProtoPoissonVertexAlgebras
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from 1da1fdf to 7601ead

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

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

7601eadMerge changes from #30007
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from 7601ead to b578a35

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

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

b578a35Move repr_lincomb import