simplifying expressions
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S G
Apr 21, 2011, 1:56:22 PM4/21/11
to Macaulay2
I have asked this on math.stackexchange. Just wanted to see if I can
get some direct help here.
I have a polynomial ring R=k[x,y,z...] and a given ideal I (defined by
given generators) and several polynomials f1,f2,... in the ring. I
also have several other elements of R given as polynomials in
f1,f2,... and x,y,z.... I wish to determine whether these elements lie
in the ideal or not. I do not have exact expressions for f1,f2,... but
I know certain relations that hold between these and the
indeterminates. Now, my problem is computational. I wish to simplify
the expressions I have to a more manageable form where I am able to
"see" the membership. So I was wondering whether there are any
softwares that will allow me to automate this. Essentially I would
like to feed the relations to the software, and it should simplify the
expression as much as possible using these relations. So far I have
tried Maple and Matlab, but both of those require too much manual
intervention. For example the expression I have may have a term like
f1(x+f1) and I have a relation f21=f2+f3. Then I would like the term
simplified to xf1+f2+f3. Can I use Macaulay2 to do this?
get some direct help here.
I have a polynomial ring R=k[x,y,z...] and a given ideal I (defined by
given generators) and several polynomials f1,f2,... in the ring. I
also have several other elements of R given as polynomials in
f1,f2,... and x,y,z.... I wish to determine whether these elements lie
in the ideal or not. I do not have exact expressions for f1,f2,... but
I know certain relations that hold between these and the
indeterminates. Now, my problem is computational. I wish to simplify
the expressions I have to a more manageable form where I am able to
"see" the membership. So I was wondering whether there are any
softwares that will allow me to automate this. Essentially I would
like to feed the relations to the software, and it should simplify the
expression as much as possible using these relations. So far I have
tried Maple and Matlab, but both of those require too much manual
intervention. For example the expression I have may have a term like
f1(x+f1) and I have a relation f21=f2+f3. Then I would like the term
simplified to xf1+f2+f3. Can I use Macaulay2 to do this?
Douglas Leonard
Apr 21, 2011, 3:28:16 PM4/21/11
to maca...@googlegroups.com
You already got one correct answer on math.stackexchange using Macsyma,
where your question was typed correctly.
where your question was typed correctly.
In Macaulay2, for this particular problem over the rationals,
A=QQ[f1,f2,f3];
(f1*(x+f1)) % (f1^2-f2-f3)
produces the normal form of (f1*(x+f1)) modulo the ideal generated by
f1^2-f2-f3.
>>> S G <locallyi...@gmail.com> 04/21/11 1:29 PM >>>
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S G
Apr 21, 2011, 4:52:25 PM4/21/11
to Macaulay2
Hi Douglas,
Thanks for the response. I don't have access to Macsyma. Your
solution works for me when I have only one relation. What can be done
when there are several relations (I have 6). I tried writing the
quantity following the % symbol as a list of these relations separated
by commas and enclosed in paranthesis, but this gives an error. Thanks
again for your quick response.
On Apr 21, 3:28 pm, "Douglas Leonard" <leon...@auburn.edu> wrote:
> You already got one correct answer on math.stackexchange using Macsyma,
> where your question was typed correctly.
>
> In Macaulay2, for this particular problem over the rationals,
>
> A=QQ[f1,f2,f3];
> (f1*(x+f1)) % (f1^2-f2-f3)
>
> produces the normal form of (f1*(x+f1)) modulo the ideal generated by
> f1^2-f2-f3.
>
> >>> S G <locallyintegra...@gmail.com> 04/21/11 1:29 PM >>>
Thanks for the response. I don't have access to Macsyma. Your
solution works for me when I have only one relation. What can be done
when there are several relations (I have 6). I tried writing the
quantity following the % symbol as a list of these relations separated
by commas and enclosed in paranthesis, but this gives an error. Thanks
again for your quick response.
On Apr 21, 3:28 pm, "Douglas Leonard" <leon...@auburn.edu> wrote:
> You already got one correct answer on math.stackexchange using Macsyma,
> where your question was typed correctly.
>
> In Macaulay2, for this particular problem over the rationals,
>
> A=QQ[f1,f2,f3];
> (f1*(x+f1)) % (f1^2-f2-f3)
>
> produces the normal form of (f1*(x+f1)) modulo the ideal generated by
> f1^2-f2-f3.
>
S G
Apr 21, 2011, 5:19:48 PM4/21/11
to Macaulay2
OK. I got it. I just needed to write the word "ideal" before the
paranthesis.
Thanks for your help.
paranthesis.
Thanks for your help.
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