(OLD) DATA FOR TABLES OF NUMBER FIELDS OF DEGREE 8 AND SIGNATURE (2,3)
These are the numerical data needed for verify the classification made in "The minimum discriminant of number fields of degree 8 and signature (2,3)".
Some instructions on how to manage the data:
- The main parameters are a1, N and the parity of p(1). The possible choices are
a1=0, N=1
a1=-1, N=1
a1=-2, N=1
a1=-3, N=1,7,8
a1=-4, N=1,7,8,9
For every choice of (a1,N), we have to choose a8 between N and -N and p(1) to be odd or even. This leads to 40 cases that must be verified.
Each case is uniquely defined by the value of a1, a8 and the parity of p(1).
- Once the choice of the parameters has been made, the program starts by running the corrispondent Matlab_Program in MATLAB: this program is saved in .txt format.
The result is saved in a .mat file.
- Next the data are translated in PARI/GP: this is done by means of the program Translation (saved in .txt format) which must be run in MATLAB.
For computational reasons, the matrix of polynomials v saved in the .mat file (containing from 8*10^6 to 25*10^6 polynomials) is translated not in one but in many .gp files, each one defining a matrix v with around one milion of polynomials. Thus Translation need to be applied to many submatrices u1,..,uk such that their sum is the original v.
- Each .gp file must be loaded in PARI/GP and examined via the program "Discriminant": the polynomials surviving the test must be gathered in a vector (this is done in the Results file corresponding to the examined case).
WARNING: Do not open the .gp files directly in a text editor, because they are very heavy. Use PARI/GP.
- All the vectors containing the polynomials survived are collected in a unique vector pol. This is done in the program Results.gp (which can be opened with no risk). The program also classifies the number fields via isomorphism classes, leading to the appearance of the 56 number fields.
Discriminant
Program for inspection of discriminants in PARI/GP.
Translation
Program for conversion of .mat files in .gp files
Results
This is the .gp file containing all the polynomials found. There are only polynomials with N=1; almost each of them is with p(1) odd.
Results_even
Here are the few polynomials with N=1 and p(1) even survived to the tests.
Results_upper_N
This file is empty because no polynomials with N>1 passed the tests.
N=1, p(1) odd
a1=0, a8=1
data_a10_a81_odd.mat
data_a10_a81_odd_01.gp
data_a10_a81_odd_02.gp
data_a10_a81_odd_03.gp
data_a10_a81_odd_04.gp
data_a10_a81_odd_05.gp
data_a10_a81_odd_06.gp
data_a10_a81_odd_07.gp
data_a10_a81_odd_08.gp
Matlab Program_a10_a81_odd.txt
Results_a10_a81_odd.txt
a1=0, a8=-1
data_a10_a8-1_odd.mat
data_a10_a8-1_odd_01.gp
data_a10_a8-1_odd_02.gp
data_a10_a8-1_odd_03.gp
data_a10_a8-1_odd_04.gp
data_a10_a8-1_odd_05.gp
data_a10_a8-1_odd_06.gp
data_a10_a8-1_odd_07.gp
data_a10_a8-1_odd_08.gp
data_a10_a8-1_odd_09.gp
Matlab Program_a10_a8-1_odd.txt
Results_a10_a8-1_odd.txt
a1=-1, a8=1
data_a1-1_a81_odd.mat
data_a1-1_a81_odd_01.gp
data_a1-1_a81_odd_02.gp
data_a1-1_a81_odd_03.gp
data_a1-1_a81_odd_04.gp
data_a1-1_a81_odd_05.gp
data_a1-1_a81_odd_06.gp
data_a1-1_a81_odd_07.gp
data_a1-1_a81_odd_08.gp
data_a1-1_a81_odd_09.gp
data_a1-1_a81_odd_10.gp
data_a1-1_a81_odd_11.gp
data_a1-1_a81_odd_12.gp
data_a1-1_a81_odd_13.gp
data_a1-1_a81_odd_14.gp
data_a1-1_a81_odd_15.gp
Matlab Program_a1-1_a81_odd.txt
Results_a1-1_a81_odd.txt
a1=-1, a8=-1
data_a1-1_a8-1_odd.mat
data_a1-1_a8-1_odd_01.gp
data_a1-1_a8-1_odd_02.gp
data_a1-1_a8-1_odd_03.gp
data_a1-1_a8-1_odd_04.gp
data_a1-1_a8-1_odd_05.gp
data_a1-1_a8-1_odd_06.gp
data_a1-1_a8-1_odd_07.gp
data_a1-1_a8-1_odd_08.gp
data_a1-1_a8-1_odd_09.gp
data_a1-1_a8-1_odd_10.gp
data_a1-1_a8-1_odd_11.gp
data_a1-1_a8-1_odd_12.gp
data_a1-1_a8-1_odd_13.gp
data_a1-1_a8-1_odd_14.gp
data_a1-1_a8-1_odd_15.gp
data_a1-1_a8-1_odd_16.gp
Matlab Program_a1-1_a8-1_odd.txt
Results_a1-1_a8-1_odd.txt
a1=-2, a8=1
data_a1-2_a81_odd.mat
data_a1-2_a81_odd_01.gp
data_a1-2_a81_odd_02.gp
data_a1-2_a81_odd_03.gp
data_a1-2_a81_odd_04.gp
data_a1-2_a81_odd_05.gp
data_a1-2_a81_odd_06.gp
data_a1-2_a81_odd_07.gp
data_a1-2_a81_odd_08.gp
data_a1-2_a81_odd_09.gp
data_a1-2_a81_odd_10.gp
data_a1-2_a81_odd_11.gp
data_a1-2_a81_odd_12.gp
data_a1-2_a81_odd_13.gp
data_a1-2_a81_odd_14.gp
data_a1-2_a81_odd_15.gp
data_a1-2_a81_odd_16.gp
data_a1-2_a81_odd_17.gp
data_a1-2_a81_odd_18.gp
data_a1-2_a81_odd_19.gp
data_a1-2_a81_odd_20.gp
Matlab Program_a1-2_a81_odd.txt
Results_a1-2_a81_odd.txt
a1=-2, a8=-1
data_a1-2_a8-1_odd.mat
data_a1-2_a8-1_odd_01.gp
data_a1-2_a8-1_odd_02.gp
data_a1-2_a8-1_odd_03.gp
data_a1-2_a8-1_odd_04.gp
data_a1-2_a8-1_odd_05.gp
data_a1-2_a8-1_odd_06.gp
data_a1-2_a8-1_odd_07.gp
data_a1-2_a8-1_odd_08.gp
data_a1-2_a8-1_odd_09.gp
data_a1-2_a8-1_odd_10.gp
data_a1-2_a8-1_odd_11.gp
data_a1-2_a8-1_odd_12.gp
data_a1-2_a8-1_odd_13.gp
data_a1-2_a8-1_odd_14.gp
data_a1-2_a8-1_odd_15.gp
data_a1-2_a8-1_odd_16.gp
data_a1-2_a8-1_odd_17.gp
data_a1-2_a8-1_odd_18.gp
data_a1-2_a8-1_odd_19.gp
data_a1-2_a8-1_odd_20.gp
data_a1-2_a8-1_odd_21.gp
Matlab Program_a1-2_a8-1_odd.txt
Results_a1-2_a8-1_odd.txt
a1=-3, a8=1
data_a1-3_a81_odd.mat
data_a1-3_a81_odd_01.gp
data_a1-3_a81_odd_02.gp
data_a1-3_a81_odd_03.gp
data_a1-3_a81_odd_04.gp
data_a1-3_a81_odd_05.gp
data_a1-3_a81_odd_06.gp
data_a1-3_a81_odd_07.gp
data_a1-3_a81_odd_08.gp
data_a1-3_a81_odd_09.gp
data_a1-3_a81_odd_10.gp
data_a1-3_a81_odd_11.gp
data_a1-3_a81_odd_12.gp
data_a1-3_a81_odd_13.gp
data_a1-3_a81_odd_14.gp
data_a1-3_a81_odd_15.gp
data_a1-3_a81_odd_16.gp
data_a1-3_a81_odd_17.gp
data_a1-3_a81_odd_18.gp
data_a1-3_a81_odd_19.gp
data_a1-3_a81_odd_20.gp
Matlab Program_a1-3_a81_odd.txt
Results_a1-3_a81_odd.txt
a1=-3, a8=-1
data_a1-3_a8-1_odd.mat
data_a1-3_a8-1_odd_01.gp
data_a1-3_a8-1_odd_02.gp
data_a1-3_a8-1_odd_03.gp
data_a1-3_a8-1_odd_04.gp
data_a1-3_a8-1_odd_05.gp
data_a1-3_a8-1_odd_06.gp
data_a1-3_a8-1_odd_07.gp
data_a1-3_a8-1_odd_08.gp
data_a1-3_a8-1_odd_09.gp
data_a1-3_a8-1_odd_10.gp
data_a1-3_a8-1_odd_11.gp
data_a1-3_a8-1_odd_12.gp
data_a1-3_a8-1_odd_13.gp
data_a1-3_a8-1_odd_14.gp
data_a1-3_a8-1_odd_15.gp
data_a1-3_a8-1_odd_16.gp
data_a1-3_a8-1_odd_17.gp
data_a1-3_a8-1_odd_18.gp
data_a1-3_a8-1_odd_19.gp
data_a1-3_a8-1_odd_20.gp
data_a1-3_a8-1_odd_21.gp
Matlab Program_a1-3_a8-1_odd.txt
Results_a1-3_a8-1_odd.txt
a1=-4, a8=1
data_a1-4_a81_odd.mat
data_a1-4_a81_odd_01.gp
data_a1-4_a81_odd_02.gp
data_a1-4_a81_odd_03.gp
data_a1-4_a81_odd_04.gp
data_a1-4_a81_odd_05.gp
data_a1-4_a81_odd_06.gp
data_a1-4_a81_odd_07.gp
data_a1-4_a81_odd_08.gp
data_a1-4_a81_odd_09.gp
data_a1-4_a81_odd_10.gp
data_a1-4_a81_odd_11.gp
data_a1-4_a81_odd_12.gp
data_a1-4_a81_odd_13.gp
data_a1-4_a81_odd_14.gp
data_a1-4_a81_odd_15.gp
data_a1-4_a81_odd_16.gp
data_a1-4_a81_odd_17.gp
data_a1-4_a81_odd_18.gp
data_a1-4_a81_odd_19.gp
data_a1-4_a81_odd_20.gp
data_a1-4_a81_odd_21.gp
data_a1-4_a81_odd_22.gp
data_a1-4_a81_odd_23.gp
data_a1-4_a81_odd_24.gp
data_a1-4_a81_odd_25.gp
Matlab Program_a1-4_a81_odd.txt
Results_a1-4_a81_odd.txt
a1=-4, a8=-1
data_a1-4_a8-1_odd.mat
data_a1-4_a8-1_odd_01.gp
data_a1-4_a8-1_odd_02.gp
data_a1-4_a8-1_odd_03.gp
data_a1-4_a8-1_odd_04.gp
data_a1-4_a8-1_odd_05.gp
data_a1-4_a8-1_odd_06.gp
data_a1-4_a8-1_odd_07.gp
data_a1-4_a8-1_odd_08.gp
data_a1-4_a8-1_odd_09.gp
data_a1-4_a8-1_odd_10.gp
data_a1-4_a8-1_odd_11.gp
data_a1-4_a8-1_odd_12.gp
data_a1-4_a8-1_odd_13.gp
data_a1-4_a8-1_odd_14.gp
data_a1-4_a8-1_odd_15.gp
data_a1-4_a8-1_odd_16.gp
data_a1-4_a8-1_odd_17.gp
data_a1-4_a8-1_odd_18.gp
data_a1-4_a8-1_odd_19.gp
data_a1-4_a8-1_odd_20.gp
data_a1-4_a8-1_odd_21.gp
data_a1-4_a8-1_odd_22.gp
data_a1-4_a8-1_odd_23.gp
data_a1-4_a8-1_odd_24.gp
data_a1-4_a8-1_odd_25.gp
data_a1-4_a8-1_odd_26.gp
data_a1-4_a8-1_odd_27.gp
Matlab Program_a1-4_a8-1_odd.txt
Results_a1-4_a8-1_odd.txt
N=1, p(1) even
a1=0, a8=1
data_a10_a81_even.mat
data_a10_a81_even.gp
Matlab Program_a10_a81_even.txt
a1=0, a8=-1
data_a10_a8-1_even.mat
data_a10_a8-1_even.gp
Matlab Program_a10_a8-1_even.txt
a1=-1, a8=1
data_a1-1_a81_even.mat
data_a1-1_a81_even.gp
Matlab Program_a1-1_a81_even.txt
a1=-1, a8=-1
data_a1-1_a8-1_even.mat
data_a1-1_a8-1_even.gp
Matlab Program_a1-1_a8-1_even.txt
a1=-2, a8=1
data_a1-2_a81_even.mat
data_a1-2_a81_even_01.gp
data_a1-2_a81_even_02.gp
Matlab Program_a1-2_a81_even.txt
a1=-2, a8=-1
data_a1-2_a8-1_even.mat
data_a1-2_a8-1_even_01.gp
data_a1-2_a8-1_even_02.gp
Matlab Program_a1-2_a8-1_even.txt
a1=-3, a8=1
data_a1-3_a81_even.mat
data_a1-3_a81_even.gp
Matlab Program_a1-3_a81_even.txt
a1=-3, a8=-1
data_a1-3_a8-1_even.mat
data_a1-3_a8-1_even.gp
Matlab Program_a1-3_a8-1_even.txt
a1=-4, a8=1
data_a1-4_a81_even.mat
data_a1-4_a81_even_01.gp
data_a1-4_a81_even_02.gp
Matlab Program_a1-4_a81_even.txt
a1=-4, a8=-1
data_a1-4_a8-1_even.mat
data_a1-4_a8-1_even_01.gp
data_a1-4_a8-1_even_02.gp
Matlab Program_a1-4_a8-1_even.txt
N=7, p(1) odd
N=7, p(1) even
N=8, p(1) odd
N=8, p(1) even
N=9, p(1) odd
N=9, p(1) even