Back to Forum  View unanswered posts  View active topics
Topic review  How to define an Rorder S where S denotes a matrix algebra? 
Author 
Message 


Post subject: 
Re: How to define an Rorder S where S denotes a matrix algebra? 


Hi,
thank you very much for your answer. I should have added some definitions, sorry.
Let R be a Noetherian integral domain with quotient field K.
Let mod(R) denote the category of all finitely generated Rmodules.
The torsionfree modules E of mod(R) are called Rlattices. They form a subcategory lat(R).
A nonzero Ralgebra S in lat(R) is called Rorder.
Unfortunately, I am completely new to the computer algebra system Singular.
I wonder, if it is possible to do calculations with (e.g.) the previously mentioned onedimensional Rorder S in Singular.
I was unable to find examples, but then I noticed the forum.
Kind regards, Bernhard
Hi,
thank you very much for your answer. I should have added some definitions, sorry.
Let R be a Noetherian integral domain with quotient field K.
Let mod(R) denote the category of all finitely generated Rmodules.
The torsionfree modules E of mod(R) are called Rlattices. They form a subcategory lat(R).
A nonzero Ralgebra S in lat(R) is called Rorder.
Unfortunately, I am completely new to the computer algebra system Singular.
I wonder, if it is possible to do calculations with (e.g.) the previously mentioned onedimensional Rorder S in Singular.
I was unable to find examples, but then I noticed the forum.
Kind regards, Bernhard




Posted: Sat Jun 17, 2017 8:28 pm 





Post subject: 
Re: How to define an Rorder S where S denotes a matrix algebra? 


I do not understand that order: Is it an admissible order on the set of monomials of R? If it is, it can be represented by an integer matrix (according to lemma by Robbiano). If not, it is not usable in the context of Groebner/Standard bases.
I do not understand that order: Is it an admissible order on the set of monomials of R? If it is, it can be represented by an integer matrix (according to lemma by Robbiano). If not, it is not usable in the context of Groebner/Standard bases.




Posted: Sat Jun 17, 2017 6:31 pm 





Post subject: 
How to define an Rorder S where S denotes a matrix algebra? 


Dear Singular Forum,
I have the following question:
Let IC denote the complex numbers.
Set R:=IC[[x]] (power series ring) and denote the onedimensional Rorder [[R, xR, xR],[x^2R, R, x^2R],[x^3R, x^3R, R]] (the latter shall be a matrix) by S.
Unforunately, I was even unable to define this Rorder S in Singular, since I only found examples of matrices with fixed entries.
So, my question is:
Is it possible to define and to do calculations with this special Rorder S in Singular?
Thanks in advance fo the help.
Dear Singular Forum,
I have the following question:
Let IC denote the complex numbers.
Set R:=IC[[x]] (power series ring) and denote the onedimensional Rorder [[R, xR, xR],[x^2R, R, x^2R],[x^3R, x^3R, R]] (the latter shall be a matrix) by S.
Unforunately, I was even unable to define this Rorder S in Singular, since I only found examples of matrices with fixed entries.
So, my question is:
Is it possible to define and to do calculations with this special Rorder S in Singular?
Thanks in advance fo the help.




Posted: Mon Jun 12, 2017 12:28 am 





It is currently Fri Jan 19, 2018 3:51 pm

