Most of you know lots more about computer algebra than I do. I'm interested in finding ALL solutions over the complex numbers of the following five equations: {1 + 1/b + c + b/d + e/c + d/f + f/e == 0, 1 + b + 1/c + d/b + c/e + e/f + f/d == 0, 1 + c/b + 1/d + d/e + e + b/f + f/c == 0, 1 + b/c + d + 1/e + e/d + c/f + f/b == 0, 1 + c/d + d/c + b/e + e/b + 1/f + f == 0} Here's what I already know: There exist solutions where all the variables are 6th roots of 1. There exist solutions where all the variables are 7th roots of 1. Numerically I can find solutions different from either of the above to very many digits. When I use Reduce or GroebnerBasis in Mma7 I quickly run out of memory. Any suggestions? Veit
Veit, I gave this to SAGE (which actually uses the Groeber Basis stuff in SINGULAR) and it fairly quickly calculated a Groebner Basis, and showed that the dimension of the ideal is 3. Right now I'm waiting for it to produce a primary decomposition which should shed some light on the matter. Victor On Tue, Aug 23, 2011 at 1:29 PM, Veit Elser <ve10@cornell.edu> wrote:
Most of you know lots more about computer algebra than I do. I'm interested in finding ALL solutions over the complex numbers of the following five equations:
{1 + 1/b + c + b/d + e/c + d/f + f/e == 0, 1 + b + 1/c + d/b + c/e + e/f + f/d == 0, 1 + c/b + 1/d + d/e + e + b/f + f/c == 0, 1 + b/c + d + 1/e + e/d + c/f + f/b == 0, 1 + c/d + d/c + b/e + e/b + 1/f + f == 0}
Here's what I already know:
There exist solutions where all the variables are 6th roots of 1.
There exist solutions where all the variables are 7th roots of 1.
Numerically I can find solutions different from either of the above to very many digits.
When I use Reduce or GroebnerBasis in Mma7 I quickly run out of memory. Any suggestions?
Veit
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The fact that there's been no update yet leads me to speculate that either your basis is very complicated or that your machine became a casualty of the earthquake. Veit On Aug 23, 2011, at 3:00 PM, Victor Miller wrote:
Veit, I gave this to SAGE (which actually uses the Groeber Basis stuff in SINGULAR) and it fairly quickly calculated a Groebner Basis, and showed that the dimension of the ideal is 3. Right now I'm waiting for it to produce a primary decomposition which should shed some light on the matter.
Victor
On Tue, Aug 23, 2011 at 1:29 PM, Veit Elser <ve10@cornell.edu> wrote:
Most of you know lots more about computer algebra than I do. I'm interested in finding ALL solutions over the complex numbers of the following five equations:
{1 + 1/b + c + b/d + e/c + d/f + f/e == 0, 1 + b + 1/c + d/b + c/e + e/f + f/d == 0, 1 + c/b + 1/d + d/e + e + b/f + f/c == 0, 1 + b/c + d + 1/e + e/d + c/f + f/b == 0, 1 + c/d + d/c + b/e + e/b + 1/f + f == 0}
Here's what I already know:
There exist solutions where all the variables are 6th roots of 1.
There exist solutions where all the variables are 7th roots of 1.
Numerically I can find solutions different from either of the above to very many digits.
When I use Reduce or GroebnerBasis in Mma7 I quickly run out of memory. Any suggestions?
Veit
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Veit, the Groebner basis has 106 polynomials in it. I was using the SAGE server sagenb.org which kept dying when I asked it to compute either the radical or the primary decomposition. I'll try on my home computer tonight. Victor Sent from my iPhone On Aug 23, 2011, at 4:44 PM, Veit Elser <ve10@cornell.edu> wrote:
The fact that there's been no update yet leads me to speculate that either your basis is very complicated or that your machine became a casualty of the earthquake.
Veit
On Aug 23, 2011, at 3:00 PM, Victor Miller wrote:
Veit, I gave this to SAGE (which actually uses the Groeber Basis stuff in SINGULAR) and it fairly quickly calculated a Groebner Basis, and showed that the dimension of the ideal is 3. Right now I'm waiting for it to produce a primary decomposition which should shed some light on the matter.
Victor
On Tue, Aug 23, 2011 at 1:29 PM, Veit Elser <ve10@cornell.edu> wrote:
Most of you know lots more about computer algebra than I do. I'm interested in finding ALL solutions over the complex numbers of the following five equations:
{1 + 1/b + c + b/d + e/c + d/f + f/e == 0, 1 + b + 1/c + d/b + c/e + e/f + f/d == 0, 1 + c/b + 1/d + d/e + e + b/f + f/c == 0, 1 + b/c + d + 1/e + e/d + c/f + f/b == 0, 1 + c/d + d/c + b/e + e/b + 1/f + f == 0}
Here's what I already know:
There exist solutions where all the variables are 6th roots of 1.
There exist solutions where all the variables are 7th roots of 1.
Numerically I can find solutions different from either of the above to very many digits.
When I use Reduce or GroebnerBasis in Mma7 I quickly run out of memory. Any suggestions?
Veit
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Is there a cheap or free program for doing this sort of stuff ? Preferably for Intel Mac? I have looked but everything is *way* out of my price range even if I become a student or lecturer !! On 23 Aug 2011, at 21:55, Victor S. Miller wrote:
Veit, the Groebner basis has 106 polynomials in it. I was using the SAGE server sagenb.org which kept dying when I asked it to compute either the radical or the primary decomposition. I'll try on my home computer tonight.
Victor
Sent from my iPhone
On Aug 23, 2011, at 4:44 PM, Veit Elser <ve10@cornell.edu> wrote:
The fact that there's been no update yet leads me to speculate that either your basis is very complicated or that your machine became a casualty of the earthquake.
Veit
On Aug 23, 2011, at 3:00 PM, Victor Miller wrote:
Veit, I gave this to SAGE (which actually uses the Groeber Basis stuff in SINGULAR) and it fairly quickly calculated a Groebner Basis, and showed that the dimension of the ideal is 3. Right now I'm waiting for it to produce a primary decomposition which should shed some light on the matter.
Victor
On Tue, Aug 23, 2011 at 1:29 PM, Veit Elser <ve10@cornell.edu> wrote:
Most of you know lots more about computer algebra than I do. I'm interested in finding ALL solutions over the complex numbers of the following five equations:
{1 + 1/b + c + b/d + e/c + d/f + f/e == 0, 1 + b + 1/c + d/b + c/e + e/f + f/d == 0, 1 + c/b + 1/d + d/e + e + b/f + f/c == 0, 1 + b/c + d + 1/e + e/d + c/f + f/b == 0, 1 + c/d + d/c + b/e + e/b + 1/f + f == 0}
Here's what I already know:
There exist solutions where all the variables are 6th roots of 1.
There exist solutions where all the variables are 7th roots of 1.
Numerically I can find solutions different from either of the above to very many digits.
When I use Reduce or GroebnerBasis in Mma7 I quickly run out of memory. Any suggestions?
Veit
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Yes, SAGE: sagemath.org Sent from my iPhone On Aug 23, 2011, at 5:03 PM, David Makin <makinmagic@tiscali.co.uk> wrote:
Is there a cheap or free program for doing this sort of stuff ? Preferably for Intel Mac? I have looked but everything is *way* out of my price range even if I become a student or lecturer !!
On 23 Aug 2011, at 21:55, Victor S. Miller wrote:
Veit, the Groebner basis has 106 polynomials in it. I was using the SAGE server sagenb.org which kept dying when I asked it to compute either the radical or the primary decomposition. I'll try on my home computer tonight.
Victor
Sent from my iPhone
On Aug 23, 2011, at 4:44 PM, Veit Elser <ve10@cornell.edu> wrote:
The fact that there's been no update yet leads me to speculate that either your basis is very complicated or that your machine became a casualty of the earthquake.
Veit
On Aug 23, 2011, at 3:00 PM, Victor Miller wrote:
Veit, I gave this to SAGE (which actually uses the Groeber Basis stuff in SINGULAR) and it fairly quickly calculated a Groebner Basis, and showed that the dimension of the ideal is 3. Right now I'm waiting for it to produce a primary decomposition which should shed some light on the matter.
Victor
On Tue, Aug 23, 2011 at 1:29 PM, Veit Elser <ve10@cornell.edu> wrote:
Most of you know lots more about computer algebra than I do. I'm interested in finding ALL solutions over the complex numbers of the following five equations:
{1 + 1/b + c + b/d + e/c + d/f + f/e == 0, 1 + b + 1/c + d/b + c/e + e/f + f/d == 0, 1 + c/b + 1/d + d/e + e + b/f + f/c == 0, 1 + b/c + d + 1/e + e/d + c/f + f/b == 0, 1 + c/d + d/c + b/e + e/b + 1/f + f == 0}
Here's what I already know:
There exist solutions where all the variables are 6th roots of 1.
There exist solutions where all the variables are 7th roots of 1.
Numerically I can find solutions different from either of the above to very many digits.
When I use Reduce or GroebnerBasis in Mma7 I quickly run out of memory. Any suggestions?
Veit
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Thanks - that explains my confusion - the only program called "Sage" I knew of is a program for doing accounts/tax/vat etc. !! On 23 Aug 2011, at 22:08, Victor S. Miller wrote:
Yes, SAGE: sagemath.org
Sent from my iPhone
On Aug 23, 2011, at 5:03 PM, David Makin <makinmagic@tiscali.co.uk> wrote:
Is there a cheap or free program for doing this sort of stuff ? Preferably for Intel Mac? I have looked but everything is *way* out of my price range even if I become a student or lecturer !!
On 23 Aug 2011, at 21:55, Victor S. Miller wrote:
Veit, the Groebner basis has 106 polynomials in it. I was using the SAGE server sagenb.org which kept dying when I asked it to compute either the radical or the primary decomposition. I'll try on my home computer tonight.
Victor
Sent from my iPhone
On Aug 23, 2011, at 4:44 PM, Veit Elser <ve10@cornell.edu> wrote:
The fact that there's been no update yet leads me to speculate that either your basis is very complicated or that your machine became a casualty of the earthquake.
Veit
On Aug 23, 2011, at 3:00 PM, Victor Miller wrote:
Veit, I gave this to SAGE (which actually uses the Groeber Basis stuff in SINGULAR) and it fairly quickly calculated a Groebner Basis, and showed that the dimension of the ideal is 3. Right now I'm waiting for it to produce a primary decomposition which should shed some light on the matter.
Victor
On Tue, Aug 23, 2011 at 1:29 PM, Veit Elser <ve10@cornell.edu> wrote:
Most of you know lots more about computer algebra than I do. I'm interested in finding ALL solutions over the complex numbers of the following five equations:
{1 + 1/b + c + b/d + e/c + d/f + f/e == 0, 1 + b + 1/c + d/b + c/e + e/f + f/d == 0, 1 + c/b + 1/d + d/e + e + b/f + f/c == 0, 1 + b/c + d + 1/e + e/d + c/f + f/b == 0, 1 + c/d + d/c + b/e + e/b + 1/f + f == 0}
Here's what I already know:
There exist solutions where all the variables are 6th roots of 1.
There exist solutions where all the variables are 7th roots of 1.
Numerically I can find solutions different from either of the above to very many digits.
When I use Reduce or GroebnerBasis in Mma7 I quickly run out of memory. Any suggestions?
Veit
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http://en.wikipedia.org/wiki/Comparison_of_computer_algebra_systems On Tue, Aug 23, 2011 at 2:03 PM, David Makin <makinmagic@tiscali.co.uk> wrote:
Is there a cheap or free program for doing this sort of stuff ? Preferably for Intel Mac? I have looked but everything is *way* out of my price range even if I become a student or lecturer !!
On 23 Aug 2011, at 21:55, Victor S. Miller wrote:
Veit, the Groebner basis has 106 polynomials in it. I was using the SAGE server sagenb.org which kept dying when I asked it to compute either the radical or the primary decomposition. I'll try on my home computer tonight.
Victor
Sent from my iPhone
On Aug 23, 2011, at 4:44 PM, Veit Elser <ve10@cornell.edu> wrote:
The fact that there's been no update yet leads me to speculate that either your basis is very complicated or that your machine became a casualty of the earthquake.
Veit
On Aug 23, 2011, at 3:00 PM, Victor Miller wrote:
Veit, I gave this to SAGE (which actually uses the Groeber Basis stuff in SINGULAR) and it fairly quickly calculated a Groebner Basis, and showed that the dimension of the ideal is 3. Right now I'm waiting for it to produce a primary decomposition which should shed some light on the matter.
Victor
On Tue, Aug 23, 2011 at 1:29 PM, Veit Elser <ve10@cornell.edu> wrote:
Most of you know lots more about computer algebra than I do. I'm interested in finding ALL solutions over the complex numbers of the following five equations:
{1 + 1/b + c + b/d + e/c + d/f + f/e == 0, 1 + b + 1/c + d/b + c/e + e/f + f/d == 0, 1 + c/b + 1/d + d/e + e + b/f + f/c == 0, 1 + b/c + d + 1/e + e/d + c/f + f/b == 0, 1 + c/d + d/c + b/e + e/b + 1/f + f == 0}
Here's what I already know:
There exist solutions where all the variables are 6th roots of 1.
There exist solutions where all the variables are 7th roots of 1.
Numerically I can find solutions different from either of the above to very many digits.
When I use Reduce or GroebnerBasis in Mma7 I quickly run out of memory. Any suggestions?
Veit
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-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
Thanks, that pretty much confirms Sage as the only real option ;) The dmg is now sitting in my downloads - I hope I have enough time to try it out sometime next month !! On 24 Aug 2011, at 00:58, Mike Stay wrote:
http://en.wikipedia.org/wiki/Comparison_of_computer_algebra_systems
On Tue, Aug 23, 2011 at 2:03 PM, David Makin <makinmagic@tiscali.co.uk> wrote:
Is there a cheap or free program for doing this sort of stuff ? Preferably for Intel Mac? I have looked but everything is *way* out of my price range even if I become a student or lecturer !!
participants (5)
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David Makin -
Mike Stay -
Veit Elser -
Victor Miller -
Victor S. Miller