2021-08-31 03:11:28 +0200 received badge ● Popular Question (source) 2021-05-15 21:25:39 +0200 received badge ● Popular Question (source) 2021-05-13 13:23:06 +0200 edited question Reduction of the coefficients of a polynomial using the LLL algorithm Reduction of the coefficients of a polynomial using the LLL algorithm Given the two polynomials in two variables x and y 2021-05-13 13:00:16 +0200 commented answer Reduction of the coefficients of a polynomial in sage @Max Alekseyev I asked here https://ask.sagemath.org/question/57105/reduction-of-the-coefficients-of-a-polynomial-using- 2021-05-13 12:56:59 +0200 asked a question Reduction of the coefficients of a polynomial using the LLL algorithm Reduction of the coefficients of a polynomial using the LLL algorithm Given the two polynomials in two variables x and y 2021-05-12 21:12:03 +0200 commented answer Reduction of the coefficients of a polynomial in sage @Max Alekseyev thank you. It will take years to implement but I will make it. I am a beginner. 2021-05-12 10:56:46 +0200 commented answer Reduction of the coefficients of a polynomial in sage @Max Alekseyev in the wikipedia you showed me, in the "Implementations" section it says that it is implemented in sage " 2021-05-11 19:39:03 +0200 commented answer Reduction of the coefficients of a polynomial in sage @Max Alekseyev I posted a free paper for you right now here https://mersenneforum.org/showthread.php?p=578212#post578212 2021-05-11 18:27:28 +0200 commented answer Reduction of the coefficients of a polynomial in sage @Max Alekseyev Thanks for everything. One last question, if possible: What is the computational cost of using LLL to fi 2021-05-11 16:55:29 +0200 commented answer Reduction of the coefficients of a polynomial in sage @Max Alekseyev What is the computational complexity over j and N? Maybe that's my problem. My computer does not output 2021-05-11 12:44:18 +0200 commented answer Reduction of the coefficients of a polynomial in sage @Max Alekseyev for j = 100 Where am I wrong? from sage.modules.free_module_integer import IntegerLattice def mnTSW(N,a 2021-05-11 12:19:59 +0200 marked best answer Reduction of the coefficients of a polynomial in sage Given the two polynomials in two variables x and y A(y,x)=((a1)*y+(a2))*((a3)*x+(a4)) B(y,x)=((b4)-(b3)*x)*((b2)-(b1)*y)  both congruent to zero mod a semiprimal number N Is there a method in sage to reduce , the coefficients in x and y smaller than sqrt (N) and the coefficient in xy smaller than 64, of their linear combination of the same degree of polynomials A and B by exploiting the congruence? Example given the two polynomials in two variables x and y A(y,x)=(25*y+11)*(27*x+1) B(y,x)=(65-8*x)*(67-8*y)  both congruent to zero mod 1763 I had thought of finding m and n such that m*(a1)*(a3)+n*(b1)*(b3) = N*t +T m*(a1)*(a4)-n*(b1)*(b4) = N*s + S m*(a2)*(a3)-n*(b2)*(b3) = N*w + W T <= 64 S <= sqrt(N) W <= sqrt(N)  2021-05-11 12:13:18 +0200 commented answer Reduction of the coefficients of a polynomial in sage @Max Alekseyev for j = 100 Where am I wrong? from sage.modules.free_module_integer import IntegerLattice def mnTSW(N,a 2021-05-11 12:09:32 +0200 commented answer Reduction of the coefficients of a polynomial in sage @Max Alekseyev for j = 100 Where am I wrong? from sage.modules.free_module_integer import IntegerLattice def mnTSW(N,a 2021-05-11 09:28:00 +0200 received badge ● Enthusiast 2021-05-10 18:33:01 +0200 commented answer Reduction of the coefficients of a polynomial in sage @Max Alekseyev and if you wanted 64 0 and W> 0 How 2021-05-10 12:24:36 +0200 commented answer Reduction of the coefficients of a polynomial in sage @Max Alekseyev and if you wanted 64 0 and W> 0 How 2021-05-10 12:24:07 +0200 commented answer Reduction of the coefficients of a polynomial in sage @Max Alekseyev and if you wanted 64 0 and W> 0 How 2021-05-10 12:23:47 +0200 commented answer Reduction of the coefficients of a polynomial in sage Max Alekseyev and if you wanted 64