ASKSAGE: Sage Q&A Forum - Individual question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Thu, 10 Oct 2013 22:24:07 -0500Subtraction of two non-homogenous monomial in a non-commutative ringhttp://ask.sagemath.org/question/10595/subtraction-of-two-non-homogenous-monomial-in-a-non-commutative-ring/Hi every one,
I have a problem for subtracting two non-homogenous monomial "xyyx-xyx" in
a unital associative free algebra with two generators x&y.
The error which is appeared is "ArithmaticError : can only subtract the
elements of the same degree".
I will apreciate some one who tell me what is the soloution.
Thanks
AbdolrasoulMon, 07 Oct 2013 04:11:34 -0500http://ask.sagemath.org/question/10595/subtraction-of-two-non-homogenous-monomial-in-a-non-commutative-ring/Comment by Abdolrasoul Baharifard for <p>Hi every one,</p>
<p>I have a problem for subtracting two non-homogenous monomial "xyyx-xyx" in
a unital associative free algebra with two generators x&y.</p>
<p>The error which is appeared is "ArithmaticError : can only subtract the
elements of the same degree".</p>
<p>I will apreciate some one who tell me what is the soloution.</p>
<p>Thanks</p>
<p>Abdolrasoul</p>
http://ask.sagemath.org/question/10595/subtraction-of-two-non-homogenous-monomial-in-a-non-commutative-ring/?comment=15523#post-id-15523Actually the problem is here:
F.<x,y> = FreeAlgebra(QQ, implementation='letterplace')
I=F*[x*y*x-2x*y]*F
J=F.quo(I)
And the eroor is :
ArithmaticError : can only subtract the elements of the same degree"
Mon, 07 Oct 2013 09:26:39 -0500http://ask.sagemath.org/question/10595/subtraction-of-two-non-homogenous-monomial-in-a-non-commutative-ring/?comment=15523#post-id-15523Answer by Luca for <p>Hi every one,</p>
<p>I have a problem for subtracting two non-homogenous monomial "xyyx-xyx" in
a unital associative free algebra with two generators x&y.</p>
<p>The error which is appeared is "ArithmaticError : can only subtract the
elements of the same degree".</p>
<p>I will apreciate some one who tell me what is the soloution.</p>
<p>Thanks</p>
<p>Abdolrasoul</p>
http://ask.sagemath.org/question/10595/subtraction-of-two-non-homogenous-monomial-in-a-non-commutative-ring/?answer=15526#post-id-15526The docstring of `FreeAlgebra` says
> By http://trac.sagemath.org/7797, we provide a different
> implementation of free algebras, based on Singular's "letterplace
> rings". Our letterplace wrapper allows for chosing positive
> integral degree weights for the generators of the free algebra.
> However, only (weighted) homogenous elements are supported. Of
> course, isomorphic algebras in different implementations are not
> identical:
If you drop the `implementation='letterplace'` option, the `ArithmeticError` disappears:
sage: F.<x,y> = FreeAlgebra(QQ)
sage: x*y*x + 2*x*y
2*x*y + x*y*x
Tue, 08 Oct 2013 04:03:43 -0500http://ask.sagemath.org/question/10595/subtraction-of-two-non-homogenous-monomial-in-a-non-commutative-ring/?answer=15526#post-id-15526Comment by Luca for <p>The docstring of <code>FreeAlgebra</code> says</p>
<blockquote>
<p>By <a href="http://trac.sagemath.org/7797">http://trac.sagemath.org/7797</a>, we provide a different
implementation of free algebras, based on Singular's "letterplace
rings". Our letterplace wrapper allows for chosing positive
integral degree weights for the generators of the free algebra.
However, only (weighted) homogenous elements are supported. Of
course, isomorphic algebras in different implementations are not
identical:</p>
</blockquote>
<p>If you drop the <code>implementation='letterplace'</code> option, the <code>ArithmeticError</code> disappears:</p>
<pre><code>sage: F.<x,y> = FreeAlgebra(QQ)
sage: x*y*x + 2*x*y
2*x*y + x*y*x
</code></pre>
http://ask.sagemath.org/question/10595/subtraction-of-two-non-homogenous-monomial-in-a-non-commutative-ring/?comment=16937#post-id-16937See the example in the documentation by typing `F.quo?`Thu, 10 Oct 2013 22:24:07 -0500http://ask.sagemath.org/question/10595/subtraction-of-two-non-homogenous-monomial-in-a-non-commutative-ring/?comment=16937#post-id-16937Comment by Luca for <p>The docstring of <code>FreeAlgebra</code> says</p>
<blockquote>
<p>By <a href="http://trac.sagemath.org/7797">http://trac.sagemath.org/7797</a>, we provide a different
implementation of free algebras, based on Singular's "letterplace
rings". Our letterplace wrapper allows for chosing positive
integral degree weights for the generators of the free algebra.
However, only (weighted) homogenous elements are supported. Of
course, isomorphic algebras in different implementations are not
identical:</p>
</blockquote>
<p>If you drop the <code>implementation='letterplace'</code> option, the <code>ArithmeticError</code> disappears:</p>
<pre><code>sage: F.<x,y> = FreeAlgebra(QQ)
sage: x*y*x + 2*x*y
2*x*y + x*y*x
</code></pre>
http://ask.sagemath.org/question/10595/subtraction-of-two-non-homogenous-monomial-in-a-non-commutative-ring/?comment=16948#post-id-16948Please use comments instead of "your answer".
Maybe I am misunderstanding something, but how is the free algebra over `QQ` not unital?Tue, 08 Oct 2013 10:03:33 -0500http://ask.sagemath.org/question/10595/subtraction-of-two-non-homogenous-monomial-in-a-non-commutative-ring/?comment=16948#post-id-16948Comment by Abdolrasoul Baharifard for <p>The docstring of <code>FreeAlgebra</code> says</p>
<blockquote>
<p>By <a href="http://trac.sagemath.org/7797">http://trac.sagemath.org/7797</a>, we provide a different
implementation of free algebras, based on Singular's "letterplace
rings". Our letterplace wrapper allows for chosing positive
integral degree weights for the generators of the free algebra.
However, only (weighted) homogenous elements are supported. Of
course, isomorphic algebras in different implementations are not
identical:</p>
</blockquote>
<p>If you drop the <code>implementation='letterplace'</code> option, the <code>ArithmeticError</code> disappears:</p>
<pre><code>sage: F.<x,y> = FreeAlgebra(QQ)
sage: x*y*x + 2*x*y
2*x*y + x*y*x
</code></pre>
http://ask.sagemath.org/question/10595/subtraction-of-two-non-homogenous-monomial-in-a-non-commutative-ring/?comment=16944#post-id-16944Maybe I miss understood the definition of free algebra. When I put F.<x,y>=FreeAlgebra(QQ) "Sage" write me "Free Algebra en two generators x,y"" and when I write F.<x,y>=FreeAlgebra(QQ, implementation='letterplace') it gives me "Unital associative free algebra with two generators", but I think the both is the same, yes? Now, my problem is to construct a quotient of this algebra ba a non-homogenous ideal. Do you know, how can I do that?Wed, 09 Oct 2013 06:27:15 -0500http://ask.sagemath.org/question/10595/subtraction-of-two-non-homogenous-monomial-in-a-non-commutative-ring/?comment=16944#post-id-16944Comment by Abdolrasoul Baharifard for <p>The docstring of <code>FreeAlgebra</code> says</p>
<blockquote>
<p>By <a href="http://trac.sagemath.org/7797">http://trac.sagemath.org/7797</a>, we provide a different
implementation of free algebras, based on Singular's "letterplace
rings". Our letterplace wrapper allows for chosing positive
integral degree weights for the generators of the free algebra.
However, only (weighted) homogenous elements are supported. Of
course, isomorphic algebras in different implementations are not
identical:</p>
</blockquote>
<p>If you drop the <code>implementation='letterplace'</code> option, the <code>ArithmeticError</code> disappears:</p>
<pre><code>sage: F.<x,y> = FreeAlgebra(QQ)
sage: x*y*x + 2*x*y
2*x*y + x*y*x
</code></pre>
http://ask.sagemath.org/question/10595/subtraction-of-two-non-homogenous-monomial-in-a-non-commutative-ring/?comment=15527#post-id-15527But I need an unital associative free algebra and if I drop the "implementation=
'letterplace", it just give me free algebra.Tue, 08 Oct 2013 08:39:01 -0500http://ask.sagemath.org/question/10595/subtraction-of-two-non-homogenous-monomial-in-a-non-commutative-ring/?comment=15527#post-id-15527