ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 24 Jan 2017 15:53:09 +0100default order in FreeAlgebrahttps://ask.sagemath.org/question/36369/default-order-in-freealgebra/In this link : http://doc.sagemath.org/html/en/reference/algebras/sage/algebras/free_algebra.html I am interested in the method lie_polynomial(w), which takes word from a FreeMonoid as input and give the output, the corresponding Lie monomial. But All these things depends on the order in the FreeAlgebra elements. Theoretically this is the lex order induced from the order on the alphabets, but in sage, the order in FreeAlgebra is it same as lex or different order?
F = FreeAlgebra(QQ, 3, 'x,y,z')
M.<x,y,z> = FreeMonoid(3)
w = x*y*z
print F.lie_polynomial(w)
w = w.to_word()
w.lyndon_factorization()
This code giving me the output :
x*y*z - y*z*x
(xyz)
Since, w is Lyndon, the associated Lie monomial is [x [y z]] = xyz - xzy - yzx + zyx which is different from the above output, where am I making mistake. please tell.
The method of associating monomial to a word can be seen here : https://en.wikipedia.org/wiki/Free_Lie_algebra#Lyndon_basis
Edit :
There is a ticket regarding lie_polynomial( ) method. Please see here : https://trac.sagemath.org/ticket/22251
Thanks a lot once again.Tue, 24 Jan 2017 07:41:56 +0100https://ask.sagemath.org/question/36369/default-order-in-freealgebra/Comment by kcrisman for <p>In this link : <a href="http://doc.sagemath.org/html/en/reference/algebras/sage/algebras/free_algebra.html">http://doc.sagemath.org/html/en/refer...</a> I am interested in the method lie_polynomial(w), which takes word from a FreeMonoid as input and give the output, the corresponding Lie monomial. But All these things depends on the order in the FreeAlgebra elements. Theoretically this is the lex order induced from the order on the alphabets, but in sage, the order in FreeAlgebra is it same as lex or different order?</p>
<pre><code>F = FreeAlgebra(QQ, 3, 'x,y,z')
M.<x,y,z> = FreeMonoid(3)
w = x*y*z
print F.lie_polynomial(w)
w = w.to_word()
w.lyndon_factorization()
</code></pre>
<p>This code giving me the output :</p>
<pre><code>x*y*z - y*z*x
(xyz)
</code></pre>
<p>Since, w is Lyndon, the associated Lie monomial is [x [y z]] = xyz - xzy - yzx + zyx which is different from the above output, where am I making mistake. please tell.</p>
<p>The method of associating monomial to a word can be seen here : <a href="https://en.wikipedia.org/wiki/Free_Lie_algebra#Lyndon_basis">https://en.wikipedia.org/wiki/Free_Li...</a></p>
<p>Edit :
There is a ticket regarding lie_polynomial( ) method. Please see here : <a href="https://trac.sagemath.org/ticket/22251">https://trac.sagemath.org/ticket/22251</a> </p>
<p>Thanks a lot once again.</p>
https://ask.sagemath.org/question/36369/default-order-in-freealgebra/?comment=36375#post-id-36375See also http://math.stackexchange.com/questions/2111600/default-order-in-freealgebra-in-sageTue, 24 Jan 2017 15:53:09 +0100https://ask.sagemath.org/question/36369/default-order-in-freealgebra/?comment=36375#post-id-36375