Exploring the Galois Universe
Japanese
How to Explore
Let's use gcc and
gmp!
1 Download
real quadratic(64-bit)bcn64.c
img quadratic (64-bit)bcm64.c
real quadratic (32-bit)bcn32.c
img quadratic (32-bit)bcm32.c
2 Edit
Change pn1, pn2 and fn as you like. p should be less than 160 million (64-bit cpu).
Prime-(Mem+Swap): 10M-1.5G, 20M-3G, 40M-6G, 80M-12G, 160M-15G.
f0 and 2*deg*gap should be less than 2^31 (32-bit cpu).
3 Compile and Execute
# gcc -O2 -m64 -o bcn64 bcn64.c -L /usr/local/lib/ -lgmp
# limit stacksize unlimited (or ***M)
# nohup ./bcn64 &
# gcc -O2 -o bcn32 bcn32.c -L /usr/local/lib/ -lgmp
# limit stacksize unlimited (or ***M)
# nohup ./bcn32 &
DATA
|f|<200, p<500,000 (I explored up to 500,000.)
http://hiro2.pm.tokushima-u.ac.jp/~hiroki/data/real/????/bcn*.txt
????=000-005, 005-010, 010-015, ..., 495-500
http://hiro2.pm.tokushima-u.ac.jp/~hiroki/data/img/????/bcn*.txt
????=000-010, 010-015, 015-020, ..., 495-500
bcn*.txt
bcn1.txt: exceptional pairs
bcn2.txt: p divides discriminant
bcn3.txt: irregular pairs
[prime, index, discriminant, (root/prime) mod p, type]
f=1,5,8, p<6,000,000 (I explored up to 8,000,000.)
real1
real5
real8
[prime, index, discriminant, type]
f=-3, -4, -7, -8, p<6,000,000 (I explored up to 8,000,000.)
img3
img4
img7
img8
Exceptional (They are dedicated to Euler.)
379
34301 and 157229
real1e
real5e
real8e (34301, 157229)
img3e
img4e (379)
img7e
img8e
Excel file
Check by Gauss sums
programs
Euler is the first explorer.
Partially supported by Grant-in-Aid
for Young Scientists, (No. 16740019),
the Ministry of Education, Culture,
Sports, Science and Technology of Japan.
Partially supported by JSPS KAKENHI Grant Number 21540018, 25400013 and 17K05176.
Reg: 2005, June
Title: Exploring the Galois Universe
Method:webpage
Content:
http://hiro2.pm.tokushima-u.ac.jp/~hiroki/major/galois1-e.html
EP: 379
Index