Ugurgozutok

Yasemin Sagiroglu

20 Reputation

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4 years, 156 days
Karadeniz Technical University

MaplePrimes Activity


These are replies submitted by Ugurgozutok

@vv Thank you for your answer and interest, i will try it.

@vv Actually, i have two homogeneous polynomials, say f(x,y) and g(x,y). These polynomials have four constant unknowns, say a,b,c,d, which i have to find. I know theoretically that g(x,y) is a factor of f(x,y). So the resultant of these polynomials with respect to {x,y} has to be identically zero. Then i will use this resultant to find the constants a,b,c,d. This works with one variable but i dont know how to do it in two variables. I thought that maple may have a multivariate resultant option or something. Sorry for my English. 

@vv Dear vv,

I wonder that is it possible to extend your procedure to polynomials in two variables. I tried but I couldnt get a complete result.

@vv Here is the entire problem. I want to find the equivalence of two algebraic space curves using differential invariants. After if the curves are equivalent then the invariants of the curves are equal. From this equality, we obtain two polynomials that have two variables and a parameter. Therefore, polynomials are identically zero if and only if the curves are equivalent. In the case of symmetries, the second curve is the image of a möbius transformation (a*t+b/c*t+d where a,b,c,d in R and a*d-b*c<>0) under the first curve. So our curves are just real curves, our polynomials have real coefficients. Here we have two problems: Theoretically, we handle these problems, but with maple, I need fast, practical and simple codes to solve these problems.

First problem: We must find the Gcd of these polynomials, but since polynomials have a parameter (d, from the denominator of the möbius transformation), the Gcd returns 1. So we have to find this parameter first this is my first question in mapleprimes. The theory says that if an equivalence exists, these polynomials have at least 1 common factor. So I asked how to solve that parameter such that the polynomial has at least 1 trivial factor. I think this time I explain the problem.

Second problem: If our curve has a parameter value t_0 which makes denominators of some components of the curve vanish, both of our polynomials have the factor (t-t_0)^n for some natural number n. This common factor is useless, also when I calculate Gcd, it takes so long with these unwanted factors. When I divide both of the polynomials by these unwanted common factors, the Gcd calculation takes much faster. This is my second question. Is there any simple code to exclude these unwanted factors from the Gcd calculation automatically. I saw a similar problem in Sage and a simple code in the preamble solves this. If it will help, I can give my codes to you and others.

@Carl Love Also in my case when I calculate Gcd(p,q) and Gcd(p/f,q/f), first tooks approx 9 sec while latter tooks 2 sec. If you want I can give you examples.

@Kitonum Dear kitonum, this solution is good for my problem but I know this solution and I already use this. But this method require detecting unwanted factors, so I already write a procedure to detect these factors. I want to do that, I want maple do that automatically. I saw examples in sage that do this just defining the number field in the header of the code. Thank you for your answer.

@Carl Love Dear Carl, thank you again. I think I couldnt explain the problem well. It due to my english. Problem is that If I dont exclude unwanted factors, then evaluation of Gcd takes more time. If I divide polynomials by unwanted factors it is faster. So you are right: A and B return at same time. I want maple do the evaluation when t<>-2 automatically. I dont want to divide polynomials before gcd or after gcd. I can give you examples about this situations. I know that sage can do this. İn the header of the code you can select number field, after that gcd returns without unwanted factors. I dont know I could explain.

@Carl Love Dear Carl, thank you for your answer and interest. Your method worked fine, and solved my problem partially. For my polynomials, calculations took 7-10 secons, this timing is slover than I imagine. I have to improve it. And the most important problem is that d may not be an integer and I have to find all ds. So this brute force stuff could not solve my problem. But I really appreciate your effort. The polynomials that I deal with must be identically 0, with this condition, I have to find d with a fast method. But I could not figure it out.

@vv Dear vv, thank you for your answer and interest. Actually, in my case, my polynomials may have high degrees, real coefficients and may not be linear in d. Also, d may not be integer. So this brute force stuff could not solve my problem. But I really appreciate your effort. The polynomials that I deal with must be identically 0, with this condition, I have to find d with a fast method. But I could not figure it out.

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