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| Trying to ascertain if Singular can fulfill my needs https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=1830 |
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| Author: | Randall R [ Thu May 13, 2010 5:48 am ] |
| Post subject: | Trying to ascertain if Singular can fulfill my needs |
I am working with algebraic points on the unit sphere S2 in R3. I need to find the minimal polynomials for the algebraic numbers. Can Singular handle this? Currently I am using algdep() command in GP-Pari to attempt to find the polynomials, but running into trouble, for example with 10,018 digits, I still cannot successfully recover the coefficients of a 72nd degree polynomial. If you have worked on algebraic points on the unit sphere, please let me know how well Singular works. Thanks |
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| Author: | steenpass [ Fri May 14, 2010 2:53 pm ] |
| Post subject: | Re: Trying to ascertain if Singular can fulfill my needs |
Thank you for your interest in Singular. What does the data of the given algebraic points consist of? For example, I could think of algebraic points given as - rational coordinates - rational coordinates with some roots occurring - floating point coordinates - ... Regards, Andreas |
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| Author: | Randall [ Sat May 15, 2010 3:39 am ] |
| Post subject: | Re: Trying to ascertain if Singular can fulfill my needs |
Actually algebraic numbers can be coordinates on the unit sphere. While we think of just quadratic numbers, here's an example: [R(7*x^2 + 66*x + 23), R(49*x^4 + 3936*x^2 - 3456), 0] R means a root of the polynomial. These polynomials are VERY interesting because one of their roots are on the unit sphere. Notice that the 2nd polynomial seems to be a polynomial in x^2. This happens because the polynomial has a square root. I can cite other examples, but I need something to enable me to find the characteristic polynomial of the determinant of a Sylvester matrix. I hope Singular can handle this. Randall |
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| Author: | Randall [ Sun May 16, 2010 12:40 am ] |
| Post subject: | Re: Trying to ascertain if Singular can fulfill my needs |
Okay, Singular is running faster than the current stable version of GP-Pari, when it comes to factoring large degree polynomials. I have a 864th degree polynomial which Singular factored into 3 ideals, in almost record time. (about 5 seconds or so). This took at least 2 or 3 minutes on GP-Pari. Now... how do do the PolCompositum command which takes two polynomials and finds the polynomial whose roots are the same as the input two. |
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| Author: | steenpass [ Mon May 17, 2010 11:26 am ] |
| Post subject: | Re: Trying to ascertain if Singular can fulfill my needs |
You are probably searching for the commands primitive() and primitive_extra() from the library primitiv.lib (see http://www.singular.uni-kl.de/Manual/3- ... htm#SEC938). Regards, Andreas |
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