Dear All,
It seems that FreeAlgebraElement is missing some accessors:
It is very easy to create elements:
sage: sage: A.=FreeAlgebra(ZZ,3)
sage: bla = -x+3*y*z
sage: bla
-x + 3*y*z
but I can't find any way to get some information on an element (except for
printing it of cour
Dear William,
> FreeAlgebraElement was written in 2005, and nobody has worked on it since.
> Maybe now it is your turn.
Or my student's :). That was my intention ! The obvious question is now the
naming convention. It seems to me that we should stick as close as possible to
polynomials:
s
Dear William,
> > Or my student's :). That was my intention ! The obvious question is now the
> > naming convention. It seems to me that we should stick as close as possible
> > to
> > polynomials:
> >
> > sage: ring = ZZ['x1,x2']
> > sage: x1 = ring.gens()[0] # why x1 is not defin
Dear David,
> I think the polynomial ring model should translate well
> to the non-commutative free algebras. In addition to
> access, specifying a (non-commutative) monomial
> ordering would be desirable. Generalizing these
> orderings is the only challenge in the generalization
> from f
Dear all,
When I try to connect (either by a browser or by mercurial) to
http://combinat.sagemath.org/ I get an error:
Proxy Error
The proxy server received an invalid response from an upstream server.
The proxy server could not handle the request GET /.
Reason: DNS lookup failure for: c
Hi sage developers,
I need to play with polynomials on various kind of coefficients. So I tried
the following:
--
| Sage Version 4.1.1, Release Date: 2009-08-14 |
| Type notebook() for the GUI, and li
Dear All,
Here is the full content of the file linear.py... I particularly like the
second comment (2006-12) from William :-). I was just wondering if there is a
reason to keep this file other than anyone didi take care of removing it...
Cheers,
Florent
"""
Linear Groups
AUTHORS:
- W
Sorry I mixed-up Module with Bi-module
So that you certainly have two other categories RightModule and LeftModule.
Here I see two possibilities:
1 - Restrict Module to the commutative case and create RightModule and
LeftModule and define:
Module(R) := Bimodule(R,R)
BiModule
Hi there,
> > Is there any real reason to use "Modules(R)" as "Bimodules(R,R)"
> > beyond the comfort of not changing the names? If not, I'd strongly
> > suggest forgetting the name "Modules" for noncommutative rings or
> > default it to left modules.
>
> Oh, interesting that you say that
Hi,
> > Minh, William and I just had a short conversation on #sage-devel about COQ
> > ( http://en.wikipedia.org/wiki/Coq ), then about SAT Solvers in Sage...
I just want to mention that on the contrary to what has been said on irc, the
primary goal of Coq is not to automatically prove t
Dear all,
I'm looking for a good name for the following concept:
In several place in Sage, we need to build a set (ie a parent) which will
generated some objects whose parents are actually a different set. Some
examples:
- I want to model the enumerated set of non negative integer or prim
Hi there,
I'm writing a parent whose elements contain an attribute called value which is
an Integer. I'd like to have a coercion to the integer. So I wrote the
following in the __init__ method of my parent
mor = Hom(self, IntegerRing())(lambda z: z.value)
mor.register_as_co
Dear Robert,
> There isn't without modifying the Integer's __init__ method itself.
> However, for integers you can implement the _integer_ method (which
> won't provide coercion, but will provide conversion).
This is exactly what I needed ! Thanks.
Florent
--~--~-~--~~---
Hi there,
I'm having trouble with coercion in sage 4.2...
The following (reduced) example works with sage 4.1.2 and breaks with sage
4.2. Here is the error:
File "", line 1, in
bla = Essai(); bla###line 11:
sage: bla = Essai(); bla
File "/home/averell/.sage/tmp/wr
Dear David,
[...]
> For this reason, I don't think CategoryWithBasis (or more
> generally CategoryWith[Free]Generators) is a natural
> category -- unless the generators are structures intended
> to be preserved, as is the case with a category of pointed
> sets.
As Nicolas already explained
Hi Vincent,
> I'm just in trouble with the behavior of sqrt(n) when n is an integer,
> because of the following:
> {{{
> sage: x = sqrt(2)
> sage: x in RR
> True
> sage: x > 1 # a boolean expected
> x > 1 # a symbolic expression obtained
> }}}
>
> It could be avoided by forcing the
Hi
> > IMHO, Sage should be aiming to be more like the professional maths package,
> > not
> > itunes or Firefox.
>
> What are they like? My main experience with deprecation in the Ma's
> is with Maple and Magma.
>
>- Maple -- has an idiotic, confusing and contradictory mix of upper
Dear William,
> This is completely orthogonal to the real question, which is about
> design. You've replaced the question of whether or not sqrt(2) > 1
> should be *simplified* automatically, by the question of how to do
> such simplifications. How to do them, is a black box that can cha
Hi there,
> And another example, where I (would like to) follow the example of the
> constructor for multivariate polynomials:
>
> sage: FreeGroup('x', 10)
> Expected:
> Free Group on the Set {x0, x1, x2, x3, x4, x5, x6, x7, x8, x9}
> Got:
> Free Group on the Set {x8, x9, x2, x
Hi Alex,
By the way, I think this is a good moment to advertise for a very good idea
Nicolas had a few years ago, that is to implement and use the very common and
basic notion of family:
A Family is an associative container which models a family
`(f_i)_{i in I}`. Then, f[i]
Hi
> I think the design problem comes from the fact the "category of
> enumerated sets" is not real "category" from the mathematical point of
> view, although you can embed it inside the category of totally ordered
> sets with the "enumeration order", that point of view might solve some
> o
Hi there !
I've four different implementations of the same function that I compared for
timing. Is there any policy in sage for keeping somewhere the timing
comparison and the slow version in case something is re-optimized in Python ?
I mean : on different machines and different versions of p
Hi William,
> Nick -- please please keep pushing this stuff!! It's really important
> to people that this all get in promptly. I would like to see as much
> as possible that the combinat branch get merged back into mainline
> sage.
You're not the only one !!! Here is the status of our b
Hi Nicolas,
> On Tue, Nov 10, 2009 at 05:23:28PM +0100, Nicolas Thiéry wrote:
> > > While browsing the code I realized that the files "entire_rings" and
> > > "ordered_sets" are still there. Didn't we agree in a name change? From
> > > sage one calls the right Domains() rather than EntireR
Hi there,
Here are some random suggestion about sphinx doc rendering.
Disclaimer: I've no idea how much these are doable in sphinx.
One thing that I dislike in the current doc rendering is that the method are
reordered in alphabetical order. It's good for reference but usually in the
sour
Hi,
> > As an online document, I think the cost for repetition is almost
> > nothing, and is greatly outweighed by the benefit of having these
> > inherited functions explicitly listed.
>
> We can also *list* them without listing their docstrings. I.e., a
> list (with links) to the docs o
Hi,
> 1. These references used to be local to the docstring they appear in.
> As soon as we ReST-ify them, they become global in the reference
> manual. Therefore if there is already a reference labeled [ABC],
> Sphinx will rightfully complain. That's easy to fix, just use a
> different l
Hi,
> I always have to include in my graphs functions some part of code to deal
> with the fact that for undirected graphs edges can be returned as (u,v) or
> as (v,u), which my code does not like Isn't there a Sage a type of
> variable which is both immutable and not ordered ?
>
> I'd
Hi !
With the forthcoming bunch of sage-combinat patches, to test a parent we call
sage: TestSuite(P).run()
which by default returns nothing if everything is ok and raise an
AssertionError
if not. There is also a verbose mode
sage: TestSuite(P).run(verbose=True)
Hi there,
I really like to see the following questions answered and the answer
implemented in sage. There has been already at least 5 or 6 discussion on
sage-devel about improving the doc... few of them are conclusive. I think we
should push this discussion to its end...
Though I'm far from
Dear Tzango,
> Is there any particular reason why when one tries to iterate over
> IntegerVectors(k,n) one gets the vectors represented as lists and not
> tuples? The only difference between the two that I can think of is
> that lists are mutable and tuples aren't. I cannot see why being
> m
> We definitely should allow to specify any constructor for list-like
> objects (list, tuple, vector). Depending on the context, you may want
> the result to be hashable, to have further properties (like being a
> vector and doing linear algebra), that is mutable, ...
>
> Now what should be the def
Hi there,
> It would be nice if we could do something like:
>
> sage: f(x,0)=e^x
>
> sage: f(x,t)=x*t
>
>
> or
>
> sage: f(0)=0
> sage: f(x)=sin(x)/x
>
> Is there an elegant way to have multiple definitions like this in pynac,
> or definitions with specific conditions on the arguments
Hi !
> I just created the following ticket :
> http://trac.sagemath.org/sage_trac/ticket/7492
>
> which is about the decomposition of a doubly stochastic matrix as a
> convex sum of permutationsm also called the Birkhoff–von Neumann
> Theorem ( more information on the Trac ticket ). I could
Hi,
I'd like to generate all partially ordered sets of a given cardinality upto
isomorphisms... They are in bijection with aclyclic, transitively reduced
directed graphs. Does anyone have an idea how to do that ? I can't manage to
get this with nauty.
Cheers,
Florent
--
To post to this g
Hi Jason,
> > I'd like to generate all partially ordered sets of a given cardinality upto
> > isomorphisms... They are in bijection with aclyclic, transitively reduced
> > directed graphs. Does anyone have an idea how to do that ? I can't manage to
> > get this with nauty.
>
>
> I'm sure t
Hi There,
> > During the review of http://trac.sagemath.org/sage_trac/ticket/7364,
> > Florent Hivert mentionned it could be a great idea to add a
> > "complexity" note in all of our algorithms, and some informations
> > about optimality if known ( or eve
> > My (obvious) suggestion is to add at the end of a function doc (close to
> > reference) a section e.g.:
> >
> > ALGORITHM:
> >
> > - modified merge sort algorithm. The complexity ``O(n * ln(n))`` is
> > optimal however it has a bad constant time factor. We therefore use a
> > naive
Hi there,
> Regarding deprecation, we already hashed this out in a previous thread
> quite some time ago.
>
> * Use the official deprecation(...) function when deprecating a function.
>
> * We can tell precisely what is deprecated and when by simply
> looking at the source code and usi
Hi Jason
> > Speaking about deprecation, I posted a patch #7515 which does two things:
> >
> > 1 - Add an option called ``version`` do deprecation where you can put the
> > information on since which version of sage this thing was deprecated:
> >
> > sage: def bar():
> > ..
> > Speaking about deprecation, I posted a patch #7515 which does two things:
> >
> > 1 - Add an option called ``version`` do deprecation where you can put the
> > information on since which version of sage this thing was deprecated:
> >
> > sage: def bar():
> > ... sage.misc.misc.
> >> Of course, when writing code, we have no idea what date the next
> >> release
> >> would be, and sometimes are mistaken about the release that the patch
> >> will be included in as well. How should we take care of this
> >> patch-updating problem?
> >
> > I've been lazy to raise this proble
Hi There,
On Mon, Nov 23, 2009 at 03:41:46PM -0600, Jason Grout wrote:
> mark mcclure wrote:
> > On Nov 23, 3:30 pm, William Stein wrote:
> >> That is true. In fact, I hope in the proposal to not insult or snub
> >> non-free commercial software either.
> >
> > But William, just two days a
Hi William,
> > In the operation, several friend there lost their job (actually this in not
> > Mathworks fault and probably the result of Sciface being bought by
> > Mathworks is
> > that some of them keep their job)...
> >
> > I'm not sure anyone in this sharks market will care a cent abo
On Wed, Nov 25, 2009 at 03:20:38AM -0800, Michel wrote:
> --
> | Sage Version 4.2, Release Date: 2009-10-24 |
> | Type notebook() for the GUI, and license() for information.|
> --
[...]
> This looks like an after-effect of ticket #6441. Sebastian Pancratz
> wrote some very fast code to compute determinants over general
> commutative rings, which proceeds by computing the characteristic
> polynomial first. When doing this for symbolic matrices it needs to
> choose a variable
> [...]
>
> > This looks like an after-effect of ticket #6441. Sebastian Pancratz
> > wrote some very fast code to compute determinants over general
> > commutative rings, which proceeds by computing the characteristic
> > polynomial first. When doing this for symbolic matrices it needs to
> > cho
Hi Michel,
> On Nov 25, 1:15 pm, Michel wrote:
> > Too bad. I really need those determinants. Will
> >
> > sage -upgrade
> >
> > magically put things right for me?
>
> Probably. I can confirm that in 4.2.1 the problem does not occur.
>
> > I feel hesitant to spend another day compiling sa
Hi there,
On Wed, Nov 25, 2009 at 09:38:23PM -0800, William Stein wrote:
> On Wed, Nov 25, 2009 at 7:26 PM, John H Palmieri
> wrote:
> > In ring.pyx, there is code like this:
> >
> > if proof:
> > return NotImplementedError
> > else:
> > return False
> >
Hi Nathann,
> For Linear Programming, I need to create plenty of symbolic variables
> which I use to represent linear functions To do it, I use the
> class InfinitePolynomialRing which lets me create them easily ( and it
> is really needed, as my colleagues often have to create Linear
> Pro
Hi Simon,
On Thu, Nov 26, 2009 at 01:16:09AM -0800, Simon King wrote:
> > On Nov 26, 2009, at 12:35 AM, Florent Hivert wrote:
> [...]
> > I think this makes perfect sense...I'm actually surprised it's not
> > implemented that way already.
>
> That&
Hi there,
I'll use the excuse that I'm now writing on a laptop in a train for not having
searched if this as already been discussed...
Is there a limitation somewhere (apart of course the available free time of
the developers) which prevent us from improving the following ugly printing ?
s
> On Thu, Nov 26, 2009 at 06:54:43AM -0800, Nathann Cohen wrote:
> > Actually, I use these polynomials to emulate what your
> > CombinatorialFreeModule does on a much larger basis : everything that
> > is hashable ;-)
> >
> > I want to be able to index my variables with sets, with edges, with
> >
> > On Thu, Nov 26, 2009 at 08:30:53AM -0800, YannLC wrote:
> >> Just a toy implementation as a very thin layer over dict (at least it
> >> should be fast)
> >
> > That's precisely what CombinatorialFreeModule elements are :-)
> >
> > Further optimizations to it are most welcome (For example, I am
> > Could you elaborate ? What's makes you skeptical ?
>
> Two things, mostly. The huge amount of code that wasn't being merged
> -- that appears to now be merged :) And the whole categories/generic
> code effort: while I support the ends, I'm worried that the system
> will become so slow
Hi Jason !
> The patch is already done and waiting on trac for several months:
>
> http://trac.sagemath.org/sage_trac/ticket/1918
Excellent !
> You just have to update a bunch of doctests and review the patch!
I was ready to do that, unfortunately, that not the problem here. There seems
Hi William Cauchois
> Original author of the patch here. I took some time to look at this
> today and found that the doctesting bug was due to reading the value
> of sys.stdout only once in install(); during doctesting, sys.stdout is
> reset some time after install() is called, presumably to
> I volunteer for combinatorics if Mike wants to get out of it.
>
> Alternatively, would it make sense to make sage-combinat the owner,
> meaning in practice we would share the work between Florent, Mike,
> myself, for a better 24/24 7/7 service?
Does that mean that one of us has to move to Vladi
Hi everybody !
When inheriting from Element, copy does not copy the dictionary:
sage: from sage.structure.element import Element
sage: class Demo(Element): pass
:
sage: bla = Demo(parent = ZZ)
sage: bla.a = [1,2,3]
sage: blo = copy(bla)
sage: blo is bla
False
sage: blo.__dict__ is bla.
Just a stupid remark:
> Here's the latest list:
>
>algebraAlexGhitza
[...]
> graphicswas
> graph theoryrlm
> group_theoryjoyner
> interactitolkov
[...]
> website/wikischilly
Why group_theory vs g
Dear Javier,
> > sage: def conjugacy_class(g,G):
> > ... cc = Set([x*g*x^(-1) for x in G])
> > ... return cc
> >
> > this feels very pythonic and works just fine, but is terribly
> > inefficient since it requires a lot of computations and stores in
> > memory an array of the whol
> Yes, have a look at sage/groups/group.pyx. It has a FiniteGroup
> class, where I think you should put your main method (that's what
> Florent said as well, I think).
Yep ! This will probably needs some cleanup when we will merge categories with
the other generic stuff but I think this is the ri
sage-devel@googlegroups.com
> To unsubscribe from this group, send an email to
> sage-devel-unsubscr...@googlegroups.com
> For more options, visit this group at
> http://groups.google.com/group/sage-devel
> URL: http://www.sagemath.org
--
Florent Hivert
---
Il y a trois sortes
Hi Simon,
> Not a big surprise, I would say. I mean, think what "v in b" does, if
> b is a list that does not contain v, and what it does if b is a set.
> AFAIK, a set is internally represented by a sorted binary tree that,
> ideally, is balanced.
>
> So, in order to find out that v is NOT
Hi there,
On Tue, Dec 15, 2009 at 01:44:50PM +, Dr. David Kirkby wrote:
> I've noticed on several occasions people reporting issues when Sage includes
> a
> library which the system has. This causes conflicts with the linker, and can
> result in messages which sometimes include:
>
>
Hi there,
On Wed, Dec 16, 2009 at 04:05:49AM +1100, Minh Nguyen wrote:
> Hi folks,
>
> The SciPy 2009 proceedings [1] contain four papers that cite Sage. These are:
> [2] http://www.sagemath.org/library-publications.html
http://arxiv.org/abs/0912.2212
I don't know who's in charge
Dear All and probably mostly Robert Bradshaw,
I'm trying to complete Nicolas infrastructure for categories and I don't
understand the design of the standard mechanism for building elements. Mainly,
my problem is: for a parent P, are there precise specifications concerning the
respective
Dear All,
I'm preparing a patch which allows one to use generic_power (computing a^n)
for monoids and even semi groups. So I had to change the handling of
particular cases (a=0 or n=0). After this change all tests passes except for
one in matrix_mod2_dense:
**
Dear Martin Albrecht,
Thanks for your quick answer.
> > So my question is the following: is there a specific reason why this test
> > has been written ?
>
> I wrote that doctest, because that behaviour is consistent with other
> matrices.
>
> sage: A = random_matrix(GF(127),0,0)
Dear John Cremona,
> I certainly want to be able to create 0x0 matrices, and would insist
> that the determinant is 1. So it seems consistent to say that such a
> matrix is invertible; and then there isn't much choice for the
> inverse!
Agreed !!! The following current behavior is indeed
Sorry for the previous mail !!! I didn't paste everything I meant to.
> > I certainly want to be able to create 0x0 matrices, and would insist
> > that the determinant is 1. So it seems consistent to say that such a
> > matrix is invertible; and then there isn't much choice for the
> > inverse!
On Sat, Feb 07, 2009 at 03:22:51PM +, Martin Albrecht wrote:
>
> > One community question : suppose that this happen and that I don't
> > find the correct way to fix it (no one knows about strange data structure
> > :-)) is this ok to post a patch that test the problem and raise a doc error
>
Hi
> Yes, write code to workaround this case.
This is mostly done except that on some ring the 0x3 matrix is considered to
be invertible ! And also that the error messages are inconsistent: some raise
a ValueError some raise an ArithmeticError, some says "self must be a square
matrix" some
> For trying to invert a non-square matrix, I think the error should be
> a ValueError, since you're inputing an improper value so that the
> operation is meaningless.
>
> >From http://docs.python.org/library/exceptions.html
>
> exception ValueError
> Raised when a built-in operation or func
Dear William
> Maybe. I'm not convinced it's better. It's usually good when people
> write code, they do
>
> try:
> ...
> except (Specific, Tuple, Of, Exceptions):
> code
>
> and *never*
>
> try:
> ...
> except:
> ...
Yes... This was perfectly clear to me. And that's w
> > 3. Any singular matrix when inverted should raise a DivisionByZero Error.
> > In numpy case this probably means catching an exception to launch a
> > different one. Am I right ?
>
> You mean a ZeroDivisionError, right?
Sure !!! It's hard to use several languages at the same time :-).
Flor
Dear William,
Sorry to bother you again with those stupid error messages... You'll
probably think I'm a kind of lawyer after that :-) I still needs a
confirmation... We agreed that:
> 2. Any nx0 or 0xn (n != 0) matrix is not invertible and should raise a
>**ValueError** "matrix mus
Hi,
> ValueError derives from ArithmeticError, so if anybody wrote
>
>try: something...
>except ArithmeticError:
> ..
>
> and you change the ArithmeticError to ValueError, then their code will
> still work fine.
> So I think the impact of making this change isn't too bad.
G
Hi,
> Crap, you're right. It's not the case the ValueError derives from
> ArithmeticError.
>
> Thus, I now change my mind, and think you should *definitely* stick
> with ArithmeticError, for backwards compatibility, etc.
As you suggested in your previous e-mail, there is a last chance th
Dear All,
The patch is close to be ready to submission. However I'm not sure if the
two last answer was from this mail or another one.
> As you suggested in your previous e-mail, there is a last chance that can save
> us: what about creating a new exception say MatrixFormatErro
ays possible to test any symbolic
expression to be equal to zero or not. But at least for symbolic constant, It
should be feasible. Is there any problem to overload is_unit for
SymbolicConstant ?
Florent Hivert
---
Il y a trois sortes de gens dans le monde : ceux qui savent compter et
ceux qu
Dear all,
Due to some misunderstanding, we (ie the combinat team) are in the process
of late reviewing of some patch for a tentative integration into 3.3. The
patch #4371 is used in two other patch currently in review. This patch has
noting to do with combinatoric and is of overall inter
Sorry for the two e-mail
>Due to some misunderstanding, we (ie the combinat team) are in the process
> of late reviewing of some patch for a tentative integration into 3.3. The
> patch #4371 is used in two other patch currently in review. This patch has
> noting to do with combinatoric
> I'll review it.
Thanks.
Florent
--~--~-~--~~~---~--~~
To post to this group, send email to sage-devel@googlegroups.com
To unsubscribe from this group, send email to
sage-devel-unsubscr...@googlegroups.com
For more options, visit this group at http://groups.goo
Dear William,
> > Going further, I understand that it's not always possible to test any
> > symbolic
> > expression to be equal to zero or not. But at least for symbolic constant,
> > It
> > should be feasible. Is there any problem to overload is_unit for
> > SymbolicConstant ?
>
> It se
Dear all,
I'm writing to both sage-devel and sage-combinat-devel to make sure that this
discussion goes as fast as possible (try IRC !!!). Can someone ensure to
forward e-mail from one mailing list to the other if needed ?
I'm writing from my train to Rouen hoping to be able to plug my lap
Dear Sage and Sage-Combinat developers,
First of all, I'm sorry for the slightly of topic e-mail I sent this
morning. I didn't understand from the discussion that the issue we had in mind
was not to pickle and un-pickle an object in the *current* sage version, but
to un-pickle a object whic
izes : 38 bits physical, 48 bits virtual
power management:
massena-~ $ gcc --version
gcc (GCC) 4.1.1 (Gentoo 4.1.1-r3)
--
Florent Hivert
---
Il y a trois sortes de gens dans le monde : ceux qui savent compter et
ceux qui ne savent pas.
There are three kinds of people in the world:
Dear All,
Michael suggested on irc to put here some hint about things to look at when
checking ReST doc. Here are some thing that I have seen lost in sage-combinat:
- comparison sign outside maths < > and also in arrows where
the ascii art -> and <- become -;
- exponent outisde math ^
Dear All,
We working in combinat have a problem of naming convention which is likely to
concern everyone in sage. As you can guess, in combinatorics we like to count
sets an iterate through them. So we designed some objects called for now
CombinatorialClass which represent a finite or count
Dear Sebastien and Vincent,
> I like more something like this (_len_). We should also impose that
> the cardinality must be a SAGE Integer or +Infinity and this should be
> integrate in the core of SAGE.
>
> 2009/2/26, Sébastien Labbé :
> > Couldn't we define something like :
> >
> > def _
Dear William
> I like s.cardinality() since that's what I've used often already all
> over in Sage.
> Do
>
> sage: search_src('cardinality')
>
Arglll !!! I had this idea and issued an
tomahawk-*ge-combinat/sage $ grep def\ cardinality\( **/*.py* | wc
11 35 533
which was a
Dear Carl,
> How about s.size()?
>
> I don't particularly like s.card(), because the abbreviation is too
> opaque -- it would be nice if somebody seeing the method for the first
> time has a good chance of guessing what it means.
Sure ! That was my first motivation for asking widely this
Hi Vincent Delecroix,
> There is a difference at the interpreter level, look at :
> sage: timeit('len(l)')
> 625 loops, best of 3: 229 ns per loop
> sage: timeit('l.__len__()')
> 625 loops, best of 3: 442 ns per loop
>
> I don't know exactly why. Perhaps the len() do not have to parse the
Dear David,
> Natural numbers are missing, but it is not clear that one
> implementation
> will suit all intended uses:
>
>1) as a poset with i <= i+j (extended by other cardinalities);
>2) as a poset with i <= i*j;
>3) as an additive abelian monoid;
>4) as a multiplicative
Dear Kiran
> Just to make life complicated, have a look at
>
> http://en.wikipedia.org/wiki/Positive_number
>
> and then
>
> http://fr.wikipedia.org/wiki/Nombre_positif
>
> Yes, it seems that "positive" means >0 in English and ">=0" in French.
> (I suppose "nonnegative" means >=0
> So do natural numbers in France always include the zero?
Sure !!! Peano rulez !!!
That's makes me wondering if sage really improves me mathematical creativity !
Let me see some of my recent work:
Ticket #5256: coherent handling of trivial matrices
# Check that the empty 0x0 matrix is i
> BTW, NonNegative- and PostiveIntegers were implemented by David Roe
> as part of the Coercion branch, but never ended up getting merged
> over (partially due to lack of doctests).
Thanks for the info. But now the obvious question is what should I do here ? I
can't find any trace of this in
Hi Jason,
> > We had removed it from our list of alternatives, because we will be
> > using the concept of "size" elsewhere in combinatorics (the size of a
> > tree, of a permutation, and more generally of a combinatorial object),
> > and we could run into a conflict later on. However, we d
Dear all,
The big cleanup of combinat is moving forward. I'd like again to have a wide
vote about some names... One of our central concept in combinatorics is:
finite or countable set together with a canonical enumeration of its
elements; the related operations are:
cardinality, __it
1 - 100 of 482 matches
Mail list logo
