It's fairly stable (when I'm lazy as sysadmin):

[[email protected] was]$ date Fri Aug 10 14:23:08 EDT 2001 [[email protected] was]$ uptime 2:23pm up 98 days, 4:54, 3 users, load average: 3.26, 3.32, 3.16

SOME MODULAR SYMBOLS BENCHMARKS William A. Stein 1 October 2000 It is difficult or impossible to make correct general comparisons between computers with vastly different architectures. However, it is very easy to make specific and correct but possibly misleading comparisons. In this short note, we do just that. At present, my primary high-powered computer use involves memory and processor intensive modular symbols computations in Magma. Thus I chose some representative computations, and ran them on each of four Magma-equipped computers. I also compare the list prices of the four computers. The computers are as follows: miro Sun Ultra 450E Quad w/ 4GB RAM (miro.maths.usyd.edu.au) Magma V2.7-2 shimura Dual 450Mhz Celeron w/ 512MB RAM (shimura.math.berkeley.edu) Magma V2.7-1 z505 Sony Z505HE Laptop, 1 PIII 450, 192MB RAM Magma V2.7-1 modular Dual PIII 933 w/ 2GB RAM (modular at harvard) Magma V2.7-1 Contents: 0. List price 1. Computing "S_2(Gamma_0(512))" 2. q-expansions 3. Characteristic Polynomial over Q 4. Modular symbols over finite fields 0. List price miro $77477 shimura $ 2200 (est., some assembly required) z505 $ 2500 modular $ 5000 (some assembly required) modular(2) Modular, but with Magma V2.8 instead of V2.7. V2.8 has lots of changes, which sometimes make things faster, and sometimes *slower* (but less buggy!). Note: The list price for a Dual processor SUN Enterprise E450 w/ 2GB RAM is $44,447.00. See http://store.sun.com/webconfig/BuildConfig.jhtml;$sessionid$4S2XVZYAAB2UBAMTA1ESPJT5AAAACJ1K 1. Computing "S_2(Gamma_0(512))" > time M:=NewformDecomposition(CuspidalSubspace(ModularSymbols(512,2))); miro 35.390 shimura 36.000 z505 30.000 modular 14.669 modular(2) 19.730 2. q-expansions Continuing from (3) above: > time f:=qEigenform(M[1],997); miro 40.630 shimura 36.270 z505 36.490 modular 18.789 modular(2) 9.750 3. Characteristic Polynomial over Q > M:=ModularSymbols(5,50,+1);T:=HeckeOperator(M,11);time f:=CharacteristicPolynomial(T); miro 43.919 shimura 36.900 z505 39.359 modular 18.249 modular(2) 13.020 4. Modular symbols over finite fields > NextPrime(20000); 20011 > time M:=ModularSymbols(20011,2,GF(2003),+1); miro 42.740 shimura 32.210 z505 Segmentation fault (uses 313MB, swaps heavily, dies) modular 15.779 modular(2) 16.700 > time T2:=HeckeOperator(M,2); miro 50.860 shimura 51.189 z505 -- modular 24.949 modular(2) 20.370 > time f:=CharacteristicPolynomial(T2); miro 511.860 shimura 349.040 z505 -- modular 189.200 modular(2) 185.590 5. Bonus: Hard drive access speed [[email protected] was]# /sbin/hdparm -t /dev/hda /dev/hda: Timing buffered disk reads: 64 MB in ... seconds = ... miro N/A (but probably fast, since it's ULTRA SCSI) shimura 12.36 MB/sec z505 12.33 MB/sec modular 35.56 MB/sec (60GB IBM GXP-75 Deskstar) 6. Bonus 2: Timings comparison with a mystery Alpha box. This is an email from Helena Verrill: OK, the machine gram.math.ku.dk, which is a 600Mhz DEC alpha, the machine for running computing stuff like magma, we have: Anyway, I'll start the same computation, on both gram and your modular computer... time M80:=ModularSymbols(80,8); modular: gram: Time: 25.980 Time: 46.366 modular(2) 40.350 s (the following finds space of trasportable symbols for W_N trick with matrix [1,0;80,1]. Returns the space and it's dimension) time V1,d1:=FINDSUBSPACE(M80,[1,0,80,1]); modular: gram: Time: 0.509 Time: 0.933 (the following finds union of above subspaces for all matrices [*,*;*,d]. Returns space and it's dimension) (37 is the first prime where this function returns the full space of cuspidal symbols) time W37,d37:=VVV(M80,37); modular: gram: Time: 305.699 Time: 390.850 Well, the above is not so great without the stats of gram to give it more meaning; but it does seem modular is about 2 times as fast as gram. That's quite a lot! though not 2 times as fast on the last function - I wonder why? another couple of examples: time V2,d2:=FINDSUBSPACE(M80,mat(80*6,37)); modular: gram: Time: 1.329 Time: 2.050 time M90:=ModularSymbols(90,6); modular: gram: Time: 9.819 Time: 22.233 modular(2): 19.380 time M90c:=CuspidalSubspace(M90); modular: gram: Time: 0.149 Time: 0.533 time VVV(M90,29); modular: gram: Time: 230.569 Time: 278.033