A problem with the "resultant" function
Gabriel Pires <[email protected]> Sat, 23 Jun 2012 21:08:12 -0300
| Newsgroups | gmane.comp.mathematics.axiom.user |
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| Message-ID | <CALnKcws4QbGrvAuAvr6_+fWZfzsWTxW8khVqx1ybqcj1cLJV-w@mail.gmail.com> |
--14dae9340cad8371ec04c32caa6d Content-Type: multipart/alternative; boundary=14dae9340cad8371e704c32caa6b --14dae9340cad8371e704c32caa6b Content-Type: text/plain; charset=ISO-8859-1 Good evening, I've been experiencing a hard time using the resultant function. The resultant between two univariative polynomials can be defined as the determinant of the Sylvester Matrix of said polynomials ( http://en.wikipedia.org/wiki/Sylvester_matrix). That being said, it should be always posible to find out the resultant of two polynomials. So, I've been trying to find out 2 polynomials, *f(x)* and *g(x)*, that satisfy: 1. f(x) should be of degree *n*, monic and irreducible over the integers. 2. g(x) should be of degree at most *n*, and its coefficients should vary from a determined range. 3. resultant(f, g) should be a prime number My algorithm should first choose an satisfying f(x) and then sample random g(x) that satisfies the second condition until it gets a prime resultant. I'm sending an input to show how I'm trying to achieve this, and hopefully, enlight about my problem. That being said, I'm having trouble trying to execute my algorithm as I end up with a message like "can't find a definition or applicable library (...) with arguments Polynomial Integer and Polynomial Integer". I'm sending a picture of the error as well. But, if I try to calculate the resultant of the same 2 polynomials, with the same types and all, I can do it, without a problem! The trickier part is that sometimes the input runs without a problem, and sometimes it doesn't. This problem is killing me as I can't figure out why I'm getting this. I'm sending both the .input with all needed and the screen with the error. If anyone needs any further information, you can ask, I'm about to go and define the Sylvester Matrix of them myself, but can't figure why it works sometimes... Best regards. --14dae9340cad8371e704c32caa6b Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable Good evening,<div><br></div><div>I've been experiencing a hard time usi= ng the resultant function.</div><div><br></div><div>The resultant between t= wo univariative polynomials can be defined as the determinant of the Sylves= ter Matrix of said polynomials (<a href=3D"http://en.wikipedia.org/wiki/Syl= vester_matrix">http://en.wikipedia.org/wiki/Sylvester_matrix</a>).</div> <div><br></div><div>That being said, it should be always posible to find ou= t the resultant of two polynomials.</div><div><br></div><div>So, I've b= een trying to find out 2 polynomials, <b>f(x)</b> and <b>g(x)</b>, that sat= isfy:</div> <div><br></div><div><ol><li>f(x) should be of degree <b>n</b>, monic and ir= reducible over the integers.</li><li>g(x) should be of degree at most <b>n<= /b>, and its coefficients should vary from a determined range.</li><li> resultant(f, g) should be a prime number</li></ol><div>My algorithm should = first choose an satisfying f(x) and then sample random g(x) that satisfies = the second condition until it gets a prime resultant.</div></div><div> <br> </div><div>I'm sending an input to show how I'm trying to achieve t= his, and hopefully, enlight about my problem.</div><div><br></div><div>That= being said, I'm having trouble trying to execute my algorithm as I end= up with a message like "can't find a definition or applicable lib= rary (...) with arguments Polynomial Integer and Polynomial Integer". = I'm sending a picture of the error as well.</div> <div><br></div><div>But, if I try to calculate the resultant of the same 2 = polynomials, with the same types and all, I can do it, without a problem!</= div><div><br></div><div>The trickier part is that sometimes the input runs = without a problem, and sometimes it doesn't.</div> <div><br></div><div>This problem is killing me as I can't figure out wh= y I'm getting this.</div><div><br></div><div>I'm sending both the .= input with all needed and the screen with the error.</div><div><br></div> <div>If anyone needs any further information, you can ask, I'm about to= go and define the Sylvester Matrix of them myself, but can't figure wh= y it works sometimes...</div><div><br></div><div>Best regards.</div> --14dae9340cad8371e704c32caa6b-- --14dae9340cad8371ec04c32caa6d Content-Type: application/octet-stream; name="problem.input" Content-Disposition: attachment; filename="problem.input" Content-Transfer-Encoding: base64 X-Attachment-Id: f_h3tczsb50 LS0gRnVuY3Rpb24gdGhhdCBjb252ZXJ0cyBhIExpc3QgSU5UIGNvbnRhaW5pbmcgY29lZmZpY2ll bnRzIHRvIGEgUE9MWSBJTlQNCmNvZWZUb1BvbGlub21pbyh2ZXRvciA6IExpc3QgSW50ZWdlcikg OiBQT0xZIElOVCA9PQ0KICAgIHBvbGkgOj0gMA0KICAgIGZvciBpIGluIDEuLiN2ZXRvciByZXBl YXQNCiAgICAgICAgcG9saSA6PSBwb2xpICsgdmV0b3IuaSAqIHheKGktMSkNCiAgICAgICAgDQog ICAgcG9saQ0KDQotLSBGdW5jdGlvbiB0aGF0IGdlbmVyYXRlcyBhIFBPTFkgSU5UIHdoaWNoIGlz 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