catalog of sequences in SageMath

[dkrenn]

similar to

    graphs.some_graph

or to

    codes.some_code

(and similar), I propose to introduce

    sequences.some_sequence

which should provide a unified access point to all possible sequences in SageMath. For example, there is fibonacci_sequence in sage.combinat.combinat, binary_recurring_sequence (somewhere in combinat) and various other code.

This will use homogenous sequences (#19896), which them-self use lazy lists.

See also the meta-ticket #16107.

---

Old: See the discussion on sage-devel

Depends on #19896

CC: @mantepse

Component: combinatorics

Author: Daniel Krenn

Branch/Commit: u/dkrenn/sequences/base @ b0bb4fa

Issue created by migration from https://trac.sagemath.org/ticket/18565

[dkrenn]

Description changed:

--- 
+++ 
@@ -18,3 +18,4 @@
 One motivation for creating this, is to include here many sequences, which can be calculated term-by-term (from the previously calculated ones, i.e., recursively) or where the first N terms can be calculated at once efficiently.
 Nevertheless, it can also provide an interface to sequences, where each term can be calculated explicitly (without dealing with the previous ones).
 
+See the discussion on [sage-devel](https://groups.google.com/forum/#!topic/sage-devel/L-wSCu4fXe8)

[videlec]

comment:2

Hello Daniel,

Could you define what you mean by sequence. Is it sequence of numbers? Rational numbers? Real numbers? An element of an infinite cartesian power? Because there also are

sage: words.FibonacciWord('ab')
word: abaababaabaababaababaabaababaabaababaaba...

which is an infinite sequence of elements in {a,b}.

Vincent

[dkrenn]

comment:3

Dear Vincent,

Replying to @videlec:

Could you define what you mean by sequence. Is it sequence of numbers? Rational numbers? Real numbers? An element of an infinite cartesian power? Because there also are

sage: words.FibonacciWord('ab')
word: abaababaabaababaababaabaababaabaababaaba...

which is an infinite sequence of elements in {a,b}.

What I head in mind is a sequence of numbers (usually intergers, rationals, maybe reals). But of course words are very much related to it. So any ideas/suggestions are very welcome.

[videlec]

comment:4

Replying to @dkrenn:

Replying to @videlec:

Could you define what you mean by sequence. Is it sequence of numbers? Rational numbers? Real numbers? An element of an infinite cartesian power? Because there also are

sage: words.FibonacciWord('ab')
word: abaababaabaababaababaabaababaabaababaaba...

which is an infinite sequence of elements in {a,b}.

What I head in mind is a sequence of numbers (usually intergers, rationals, maybe reals). But of course words are very much related to it. So any ideas/suggestions are very welcome.

Then you are more restrictive than wikipedia in which a sequence is even allowed to be finite. I do not have suggestion beyond having precise specifications. You can perhaps even be explicit in the names by using number_sequences.* or sequences.numbers.*? But those two looks a bit too much.

Vincent

[videlec]

comment:5

And you also have orthogonal polynomials, orbit of a dynamical system, permutations (i.e. image of the letters), ... Depending on who you are talking to a sequence can be many things!

[nathanncohen]

comment:6

What about 'integer sequences', like for Sloane? Words are already stored in word.<tab>

[dkrenn]

comment:7

Replying to @videlec:

Replying to @dkrenn:

Replying to @videlec:

Could you define what you mean by sequence. Is it sequence of numbers? Rational numbers? Real numbers? An element of an infinite cartesian power?

What I head in mind is a sequence of numbers (usually intergers, rationals, maybe reals). [...]

Then you are more restrictive than wikipedia in which a sequence is even allowed to be finite.

I am happy to make it as general as needed.

I do not have suggestion beyond having precise specifications.

Like: Finite and infinite sequences where the elements can be any sage objects (but all of the same type/parent)?

Best,

Daniel

[dkrenn]

comment:8

Replying to @nathanncohen:

What about 'integer sequences', like for Sloane? Words are already stored in word.<tab>

Ok. Do you think here of a parametrisation (parameter ZZ for integer sequences; like the base for some parent)? I ask, because maybe someone wants to have a sequence of rationals (e.g. Bernoulli numbers) or polynomials (again e.g. Bernoulli). This would then be similar to words with an infinite alphabet...

[nathanncohen]

comment:9

Ok. Do you think here of a parametrisation (parameter ZZ for integer sequences; like the base for some parent)?

No idea. But I do not think that it is related to what this ticket is about. It seems that you want to create a catalog of some sorts, and we just have to figure out a sensible name for it. I do not think that there is any reason to define any kind of interface for the object that it contains.

I also expect that you will find in the (many) combinat class something which can already handle sequences. In this case, it would be better to use it rather than build a new one.

Nathann

[mantepse]

comment:11

Let me try to summarize the two apparently orthogonal issues here:

• provide an interface for playing with sequences. My favorite ticket attempting this is lazy_list from various input data #16137, together with Meta ticket: unified sequence/lazy list objects #16107. This is for sequences indexed by natural numbers, although possibly finite. If I recall correctly, a generalization might be provided by Family.

• provide a catalogue of named ("famous") sequences. I believe that lazy_list from various input data #16137 should be general enough to be able to deal with just about any sequence. Is there any need to restrict to a certain type of sequence?

If the scope of this ticket is the second item, there is no conflict. However, a backend would need to be chosen...

[dkrenn]

Description changed:

--- 
+++ 
@@ -15,7 +15,9 @@
 ```
 which should provide a unified access point to all possible sequences in SageMath. For example, there is `fibonacci_sequence` in `sage.combinat.combinat`, `binary_recurring_sequence` (somewhere in combinat) and various other code.
 
-One motivation for creating this, is to include here many sequences, which can be calculated term-by-term (from the previously calculated ones, i.e., recursively) or where the first N terms can be calculated at once efficiently.
-Nevertheless, it can also provide an interface to sequences, where each term can be calculated explicitly (without dealing with the previous ones).
+This will use homogenous sequences (#19896), which them-self use lazy lists.
 
-See the discussion on [sage-devel](https://groups.google.com/forum/#!topic/sage-devel/L-wSCu4fXe8)
+See also the meta-ticket #16107.
+
+---
+Old: See the discussion on [sage-devel](https://groups.google.com/forum/#!topic/sage-devel/L-wSCu4fXe8)