Re: [sage-combinat-devel] Re: About Free Algebras, infinite Words and equality
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 break at any moment if you play with the wrong words, but you want to be able to define this anyway when you know what you are doing ?... Nathann On Sunday, January 5, 2014 3:30:40 PM UTC+1, Nathann Cohen wrote: Hello everybody !! Because of broken doctests in #12867, I find myself opening the file sage/categories/examples/algebras_with_basis.py, and about to do something potentially big. I am about to remplace this CombinatorialFreeModule.__init__(self, R, Words(alphabet), category = AlgebrasWithBasis(R)) By this: CombinatorialFreeModule.__init__(self, R, Words(alphabet, infinite=False), category = AlgebrasWithBasis(R)) And I would like to know what you think of it. Because I wondered : can you really define (in Sage) an algebra over (Finite+Infinite) Words, given that you cannot even check whether two infinite words are ... equal ? This is my problem. And if there is no reason to create (in Sage) an algebra over infiinite words, my problem is settled :-P Tell me what you think ! 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 sage-combinat-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-combinat-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/groups/opt_out. -- 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 sage-combinat-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-combinat-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/groups/opt_out.
Re: [sage-combinat-devel] Re: About Free Algebras, infinite Words and equality
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 for yet another reason it will make my debugging *much* easier :-P 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 sage-combinat-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-combinat-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/groups/opt_out.
Re: [sage-combinat-devel] Re: About Free Algebras, infinite Words and equality
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. 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 for yet another reason it will make my debugging *much* easier :-P Nathann -- You received this message because you are subscribed to a topic in the Google Groups sage-combinat-devel group. To unsubscribe from this topic, visit https://groups.google.com/d/topic/sage-combinat-devel/zdN44XJZu5s/unsubscribe . To unsubscribe from this group and all its topics, send an email to sage-combinat-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-combinat-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/groups/opt_out. -- 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 sage-combinat-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-combinat-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/groups/opt_out.
Re: [sage-combinat-devel] Re: About Free Algebras, infinite Words and equality
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 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. 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 for yet another reason it will make my debugging *much* easier :-P Nathann -- You received this message because you are subscribed to a topic in the Google Groups sage-combinat-devel group. To unsubscribe from this topic, visit https://groups.google.com/d/topic/sage-combinat-devel/zdN44XJZu5s/unsubscribe. To unsubscribe from this group and all its topics, send an email to sage-combinat-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-combinat-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/groups/opt_out. -- 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 sage-combinat-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-combinat-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/groups/opt_out. -- 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 sage-combinat-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-combinat-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/groups/opt_out.
Re: [sage-combinat-devel] Re: About Free Algebras, infinite Words and equality
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, Jan 5, 2014 at 4:29 PM, Nathann Cohen nathann.co...@gmail.com wrote: 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. 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 for yet another reason it will make my debugging *much* easier :-P Nathann -- You received this message because you are subscribed to a topic in the Google Groups sage-combinat-devel group. To unsubscribe from this topic, visit https://groups.google.com/d/topic/sage-combinat-devel/zdN44XJZu5s/unsubscribe. To unsubscribe from this group and all its topics, send an email to sage-combinat-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-combinat-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/groups/opt_out. -- 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 sage-combinat-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-combinat-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/groups/opt_out. -- 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 sage-combinat-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-combinat-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/groups/opt_out. -- 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 sage-combinat-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-combinat-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/groups/opt_out.
Re: [sage-combinat-devel] Re: About Free Algebras, infinite Words and equality
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 subscribed to the Google Groups sage-combinat-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-combinat-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-combinat-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/groups/opt_out.
Re: [sage-combinat-devel] Re: About Free Algebras, infinite Words and equality
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 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 sage-combinat-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-combinat-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/groups/opt_out.
Re: [sage-combinat-devel] Re: About Free Algebras, infinite Words and equality
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 touch the Shuffle Product. Well, tell me what you think ^^; Nathann On 5 January 2014 19:09, Darij Grinberg darijgrinb...@gmail.com wrote: Huh? I thought shuffle does not work (because ... sh ... would be a sum of infinitely many identical words), but uv is well-defined (and equals u when u is infinite)? On Sun, Jan 5, 2014 at 7:08 PM, Christian Stump christian.st...@gmail.com wrote: 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 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 sage-combinat-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-combinat-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/groups/opt_out. -- You received this message because you are subscribed to a topic in the Google Groups sage-combinat-devel group. To unsubscribe from this topic, visit https://groups.google.com/d/topic/sage-combinat-devel/zdN44XJZu5s/unsubscribe . To unsubscribe from this group and all its topics, send an email to sage-combinat-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-combinat-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/groups/opt_out. -- 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 sage-combinat-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-combinat-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/groups/opt_out.
Re: [sage-combinat-devel] Re: About Free Algebras, infinite Words and equality
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 all words. I guess only the first one matters. The shuffle algebra is not well defined on infinite words (the product becomes an infinite sum). So please turn infinite=False in both situations. Vincent 2014/1/5, Nathann Cohen nathann.co...@gmail.com: 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 touch the Shuffle Product. Well, tell me what you think ^^; Nathann On 5 January 2014 19:09, Darij Grinberg darijgrinb...@gmail.com wrote: Huh? I thought shuffle does not work (because ... sh ... would be a sum of infinitely many identical words), but uv is well-defined (and equals u when u is infinite)? On Sun, Jan 5, 2014 at 7:08 PM, Christian Stump christian.st...@gmail.com wrote: 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 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 sage-combinat-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-combinat-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/groups/opt_out. -- You received this message because you are subscribed to a topic in the Google Groups sage-combinat-devel group. To unsubscribe from this topic, visit https://groups.google.com/d/topic/sage-combinat-devel/zdN44XJZu5s/unsubscribe . To unsubscribe from this group and all its topics, send an email to sage-combinat-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-combinat-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/groups/opt_out. -- 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 sage-combinat-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-combinat-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/groups/opt_out. -- 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 sage-combinat-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-combinat-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/groups/opt_out.
Re: [sage-combinat-devel] Re: About Free Algebras, infinite Words and equality
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 Groups sage-combinat-devel group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-combinat-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-combinat-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/groups/opt_out.
Re: [sage-combinat-devel] Re: About Free Algebras, infinite Words and equality
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 sage-combinat-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-combinat-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/groups/opt_out.
Re: [sage-combinat-devel] Re: About Free Algebras, infinite Words and equality
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 receiving emails from it, send an email to sage-combinat-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-combinat-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/groups/opt_out. -- 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 sage-combinat-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-combinat-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-combinat-devel. For more options, visit https://groups.google.com/groups/opt_out.
