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Old 2011-09-07, 19:00   #1
Jun 2011

716 Posts
Default question to murphys Q2 value

i want to test some polynomials with ggnfs and compute their quality with the murphy value Q2. The definition of Q2 is:

Q2:= int(from 0 to pi) rho[(alpha(F1)+log F1(-Acos(t),Bsin(t)))/log L1] * rho[(alpha(F2)+log F2(-Acos(t),Bsin(t)))/log L2] dt

rho is the dickman funtion. I didnt find threads in this forum to the Q2 value.
My questions are:
1) Is there an easy way to compute Q2? Any implementations in maple/matlab/pari?
2) Where can i find A,B after using ggnfs/msieve?

i computed the dickman function by numerical integration and the computation of alpha should also work. but after using ggnfs/msieve i cant find A and B. For example i tested pp40*pp41 with ggnfs and msieve and got:

Number: testzahl2
N = 100000000000000000000000000000000000001039999999999999999999999999999999999997943 (81 digits)
Divisors found:
r1=9999999999999999999999999999999999999983 (pp40)
r2=10000000000000000000000000000000000000121 (pp41)
Version: Msieve v. 1.48
Total time: 0.20 hours.
Factorization parameters were as follows:
n: 100000000000000000000000000000000000001039999999999999999999999999999999999997943
Y0: -15591583604619784232
Y1: 5229783359
c0: -109864692158220730521
c1: -3507793033389192474
c2: 41762546876374
c3: 449858979
c4: 1692
skew: 100469.73
type: gnfs
Factor base limits: 350000/500000
Large primes per side: 3
Large prime bits: 24/24
Sieved algebraic special-q in [0, 0)
Total raw relations: 978897
Relations: 41204 relations
Pruned matrix : 31182 x 31409
Polynomial selection time: 0.07 hours.
Total sieving time: 0.12 hours.
Total relation processing time: 0.01 hours.
Matrix solve time: 0.00 hours.
time per square root: 0.00 hours.
Prototype def-par.txt line would be: gnfs,80,4,52,1500,0.005,0.3,220,15,10000,400,350000,500000,24,24,37,37,1.7,1.7,10000
total time: 0.20 hours.
Intel64 Family 6 Model 23 Stepping 7, GenuineIntel

Where can i find A and B in this file? I dont see it. Is there another file i can find A and B?
I hope someone understands my problem ^^
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Old 2011-09-07, 19:33   #2
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Old 2011-09-08, 00:41   #3
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Oct 2004

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A and B are treated as constants in your formula for the Murphy E score. The Murphy score computation in GGNFS and Msieve (the latter is deliberately chosen to produce comparable scores to the former) is given the polynomial skew S, chooses the sieving area (always 1e16), and sets A to sqrt(sieve_area * S) and B to sqrt(sieve_area / S). So A and B are still constants, but they depend on the skew of the sieving region. All the implementations out there compute the integral numerically (most use the midpoint rule, msieve uses a full numerical integrator).

Murphy's dissertation originally did not account for the actual length of the rays emanating from the origin. Even the current code does not increase the size of the sieve interval or the value of L1 and L2 for larger problems.
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