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Sat May 30 16:09:48 PDT 1992 REDUCE 3.4.1, 15-Jul-92 ... 1: 1: 2: 2: 3: 3: Time: 17 ms 4: 4: comment factorizer test file; array a(20); factorize(x**2-1); {X - 1,X + 1} %To make sure factorizer is loaded; % If you want deterministic behavior, set randomseed* before each test. % global '(randomseed!*); % symbolic(randomseed!* := 300000); algebraic procedure test(prob,nfac); begin scalar basetime; p := for i:=1:nfac product a(i); Write "Problem number ",prob; symbolic (basetime := time()); symbolic prin2t list("The random seed is",randomseed!*); m := factorize p; symbolic (basetime := time() - basetime); symbolic lpri list("Time =",basetime); symbolic terpri(); q := for each j in m product j; if (length m=nfac) and (p=q) then return ok; write "This example failed:"; write m; return failed end; TEST % Wang test case 1; a(1) := x*y+z+10$ a(2) := x*z+y+30$ a(3) := x+y*z+20$ test(1,3); Problem number 1 (The random seed is 300000) Time = 153 OK % Wang test case 2; a(1) := x**3*z+x**3*y+z-11$ a(2) := x**2*z**2+x**2*y**2+y+90$ test(2,2); Problem number 2 (The random seed is 242633) Time = 255 OK % Wang test case 3; a(1) := x**3*y**2+x*z**4+x+z$ a(2) := x**3+x*y*z+y**2+y*z**3$ test(3,2); Problem number 3 (The random seed is 283219) Time = 170 OK % Wang test case 4; a(1) := x**2*z+y**4*z**2+5$ a(2) := x*y**3+z**2$ a(3) := -x**3*y+z**2+3$ a(4) := x**3*y**4+z**2$ test(4,4); Problem number 4 (The random seed is 385159) Time = 476 OK % Wang test case 5; a(1) := 3*u**2*x**3*y**4*z+x*z**2+y**2*z**2+19*y**2$ a(2) := u**2*y**4*z**2+x**2*z+5$ a(3) := u**2+x**3*y**4+z**2$ test(5,3); Problem number 5 (The random seed is 380938) Time = 748 OK % Wang test case 6; a(1) := w**4*x**5*y**6-w**4*z**3+w**2*x**3*y+x*y**2*z**2$ a(2) := w**4*z**6-w**3*x**3*y-w**2*x**2*y**2*z**2+x**5*z -x**4*y**2+y**2*z**3$ a(3) := -x**5*z**3+x**2*y**3+y*z$ test(6,3); Problem number 6 (The random seed is 178753) Time = 1938 OK % Wang test case 7; a(1) := x+y+z-2$ a(2) := x+y+z-2$ a(3) := x+y+z-3$ a(4) := x+y+z-3$ a(5) := x+y+z-3$ test(7,5); Problem number 7 (The random seed is 182507) Time = 357 OK % Wang test case 8; a(1) := -z**31-w**12*z**20+y**18-y**14+x**2*y**2+x**21+w**2$ a(2) := -15*y**2*z**16+29*w**4*x**12*z**3+21*x**3*z**2+3*w**15*y**20$ % Commented out, since it can take a long time. % TEST(8,2); % Wang test case 9; a(1) := 18*u**2*w**3*x*z**2+10*u**2*w*x*y**3+15*u*z**2+6*w**2*y**3*z**2$ a(2) := x$ a(3) := 25*u**2*w**3*y*z**4+32*u**2*w**4*y**4*z**3- 48*u**2*x**2*y**3*z**3-2*u**2*w*x**2*y**2+44*u*w*x*y**4*z**4- 8*u*w*x**3*z**4+4*w**2*x+11*w**2*x**3*y+12*y**3*z**2$ a(4) := z$ a(5) := z$ a(6) := u$ a(7) := u$ a(8) := u$ a(9) := u$ test(9,9); Problem number 9 (The random seed is 123858) Time = 2176 OK % Wang test case 10; a(1) := 31*u**2*x*z+35*w**2*y**2+40*w*x**2+6*x*y$ a(2) := 42*u**2*w**2*y**2+47*u**2*w**2*z+22*u**2*w**2+9*u**2*w*x**2+21 *u**2*w*x*y*z+37*u**2*y**2*z+u**2*w**2*x*y**2*z**2+8*u**2*w**2 *z**2+24*u**2*w*x*y**2*z**2+24*u**2*x**2*y*z**2+12*u**2*x*y**2 *z**2+13*u*w**2*x**2*y**2+27*u*w**2*x**2*y+39*u*w*x*z+43*u* x**2*y+44*u*w**2* z**2+37*w**2*x*y+29*w**2*y**2+31*w**2*y*z**2 +12*w*x**2*y*z+43*w*x*y*z**2+22*x*y**2+23*x*y*z+24*x*y+41*y**2 *z$ test(10,2); Problem number 10 (The random seed is 298745) Time = 1241 OK % Wang test case 11; a(1) := -36*u**2*w**3*x*y*z**3-31*u**2*w**3*y**2+20*u**2*w**2*x**2*y**2 *z**2-36*u**2*w*x*y**3*z+46*u**2*w*x+9*u**2*y**2-36*u*w**2*y**3 +9*u*w*y**3-5*u*w*x**2*y**3+48*u*w*x**3*y**2*z+23*u*w*x**3*y**2 -43*u*x**3*y**3*z**3-46*u*x**3*y**2+29*w**3*x*y**3*z**2- 14*w**3*x**3*y**3*z**2-45*x**3-8*x*y**2$ a(2) := 13*u**3*w**2*x*y*z**3-4*u*x*y**2-w**3*z**3-47*x*y$ a(3) := x$ a(4) := y$ test(11,4); Problem number 11 (The random seed is 271044) Time = 2142 OK % Wang test case 12; a(1) := x+y+z-3$ a(2) := x+y+z-3$ a(3) := x+y+z-3$ test(12,3); Problem number 12 (The random seed is 309235) Time = 68 OK % Wang test case 13; a(1) := 2*w*z+45*x**3-9*y**3-y**2+3*z**3$ a(2) := w**2*z**3-w**2+47*x*y$ test(13,2); Problem number 13 (The random seed is 337962) Time = 204 OK % Wang test case 14; a(1) := 18*x**4*y**5+41*x**4*y**2-37*x**4+26*x**3*y**4+38*x**2*y**4-29* x**2*y**3-22*y**5$ a(2) := 33*x**5*y**6-22*x**4+35*x**3*y+11*y**2$ test(14,2); Problem number 14 (The random seed is 255258) Time = 1411 OK % Wang test case 15; a(1) := 12*w**2*x*y*z**3-w**2*z**3+w**2-29*x-3*x*y**2$ a(2) := 14*w**2*y**2+2*w*z+18*x**3*y-8*x*y**2-y**2+3*z**3$ a(3) := z$ a(4) := z$ a(5) := y$ a(6) := y$ a(7) := y$ a(8) := x$ a(9) := x$ a(10) := x$ a(11) := x$ a(12) := x$ a(13) := x$ test(15,13); Problem number 15 (The random seed is 122339) Time = 408 OK % Test 16 - the 40th degree polynomial that comes from % SIGSAM problem number 7; a(1) := 8192*y**10+20480*y**9+58368*y**8-161792*y**7+198656*y**6+ 199680*y**5-414848*y**4-4160*y**3+171816*y**2-48556*y+469$ a(2) := 8192*y**10+12288*y**9+66560*y**8-22528*y**7-138240*y**6+ 572928*y**5-90496*y**4-356032*y**3+113032*y**2+23420*y-8179$ a(3) := 4096*y**10+8192*y**9+1600*y**8-20608*y**7+20032*y**6+87360*y**5- 105904*y**4+18544*y**3+11888*y**2-3416*y+1$ a(4) := 4096*y**10+8192*y**9-3008*y**8-30848*y**7+21056*y**6+146496* y**5-221360*y**4+1232*y**3+144464*y**2-78488*y+11993$ test(16,4); Problem number 16 (The random seed is 93784) Time = 12937 OK % Test 17 - taken from Erich Kaltofen's thesis. This polynomial % splits mod all possible primes p; a(1) := x**25-25*x**20-3500*x**15-57500*x**10+21875*x**5-3125$ test(17,1); Problem number 17 (The random seed is 266680) Time = 1972 OK % Test 18 - another 'hard-to-factorize' univariate; a(1) := x**18+9*x**17+45*x**16+126*x**15+189*x**14+27*x**13- 540*x**12-1215*x**11+1377*x**10+15444*x**9+46899*x**8+ 90153*x**7+133893*x**6+125388*x**5+29160*x**4- 32076*x**3+26244*x**2-8748*x+2916$ test(18,1); Problem number 18 (The random seed is 92933) Time = 1768 OK % Test 19 - another example chosen to lead to false splits mod p; a(1) := x**16+4*x**12-16*x**11+80*x**9+2*x**8+160*x**7+ 128*x**6-160*x**5+28*x**4-48*x**3+128*x**2-16*x+1$ a(2) := x**16+4*x**12+16*x**11-80*x**9+2*x**8-160*x**7+ 128*x**6+160*x**5+28*x**4+48*x**3+128*x**2+16*x+1$ test(19,2); Problem number 19 (The random seed is 379724) Time = 2210 OK % End of all tests; end; 5: 5: Time: 30855 ms plus GC time: 1190 ms 6: 6: Quitting Sat May 30 16:10:27 PDT 1992