Re: [sage-combinat-devel] Re: About Free Algebras, infinite Words and equality

2014-01-05 Thread Darij Grinberg
Hi Nathann, You are right. Infinite words don't belong into an algebra; you cannot multiply them. Barring hack reasons, the change is correct. Best regards, Darij On Sun, Jan 5, 2014 at 3:32 PM, Nathann Cohen nathann.co...@gmail.com wrote: Or possibly : you know that your algebras can

Re: [sage-combinat-devel] Re: About Free Algebras, infinite Words and equality

2014-01-05 Thread Nathann Cohen
You are right. Infinite words don't belong into an algebra; you cannot multiply them. Barring hack reasons, the change is correct. HMmm... And what do you think of Shuffle Algebras on infinite words ? Is this one correct or not ? It looks okay to me.. But if you tell me that it is not

Re: [sage-combinat-devel] Re: About Free Algebras, infinite Words and equality

2014-01-05 Thread Nathann Cohen
Okay, I just created an element manually instead of calling an_element(). Nathann On 5 January 2014 15:59, Nathann Cohen nathann.co...@gmail.com wrote: You are right. Infinite words don't belong into an algebra; you cannot multiply them. Barring hack reasons, the change is correct.

Re: [sage-combinat-devel] Re: About Free Algebras, infinite Words and equality

2014-01-05 Thread Darij Grinberg
Oops, I've just realized that you *can* multiply infinite words, though I'm not sure if this has ever been used. (No, you cannot take their shuffle product.) On Sun, Jan 5, 2014 at 4:29 PM, Nathann Cohen nathann.co...@gmail.com wrote: Okay, I just created an element manually instead of calling

Re: [sage-combinat-devel] Re: About Free Algebras, infinite Words and equality

2014-01-05 Thread Vincent Delecroix
How do you define multiplication ?! If it is concatenation then uv = u... 2014/1/5, Darij Grinberg darijgrinb...@gmail.com: Oops, I've just realized that you *can* multiply infinite words, though I'm not sure if this has ever been used. (No, you cannot take their shuffle product.) On Sun,

Re: [sage-combinat-devel] Re: About Free Algebras, infinite Words and equality

2014-01-05 Thread Darij Grinberg
On Sun, Jan 5, 2014 at 5:54 PM, Vincent Delecroix 20100.delecr...@gmail.com wrote: How do you define multiplication ?! If it is concatenation then uv = u... Yes, but it's associative, so it works... (Except I don't expect it to have much of a use.) -- You received this message because you are

Re: [sage-combinat-devel] Re: About Free Algebras, infinite Words and equality

2014-01-05 Thread Christian Stump
Yes, but it's associative, so it works... (Except I don't expect it to have much of a use.) can you be more specific? How is the product uv defined? I see that you have a shuffle product defined, but I don't see that you have concatenation... Thanks, Christian -- You received this message

Re: [sage-combinat-devel] Re: About Free Algebras, infinite Words and equality

2014-01-05 Thread Nathann Cohen
H... I just had Nicolas on the phone who told me that both can be changed to finite words only. Aand he had Florent around to confirm. I also think that the concatenation product is not well defined. And I actually wrote that in the patch already :-/ On the other hand I did not

Re: [sage-combinat-devel] Re: About Free Algebras, infinite Words and equality

2014-01-05 Thread Vincent Delecroix
Concatenation product is well defined but not well implemented in Sage. If u is infinite then uv = u for any (finite or infinite) word v. It is not a free monoid anymore. That being said, you can build the algebra on finite words, the one on infinite words (which is really stupid) and the one on

Re: [sage-combinat-devel] Re: About Free Algebras, infinite Words and equality

2014-01-05 Thread Nathann Cohen
The shuffle algebra is not well defined on infinite words (the product becomes an infinite sum). So please turn infinite=False in both situations. Okay... So I will edit #12867 again :-P Nathann -- You received this message because you are subscribed to the Google

Re: [sage-combinat-devel] Re: About Free Algebras, infinite Words and equality

2014-01-05 Thread Nathann Cohen
I just edited ticket #12867. Thank you for your help :-) Nathann -- You received this message because you are subscribed to the Google Groups sage-combinat-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to

Re: [sage-combinat-devel] Re: About Free Algebras, infinite Words and equality

2014-01-05 Thread Vincent Delecroix
Thank you for your work !! 2014/1/5, Nathann Cohen nathann.co...@gmail.com: I just edited ticket #12867. Thank you for your help :-) Nathann -- You received this message because you are subscribed to the Google Groups sage-combinat-devel group. To unsubscribe from this group and stop