Artifact 21206afb5d37f049b92c7f93874aade184d4e35e0b2869f9bd5c755cf859be69:
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r38/log/modsr.rlg
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2011-09-02 18:13:33
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Tue Apr 15 00:32:30 2008 run on win32 % Test series for the package MODSR: SOLVE and ROOTS for % modular polynomials and modular polynomial systems. % Moduli need not be primes. on modular; setmod 8; 1 m_solve(2x=3); {} % {} m_solve(2x=4); {{x=2},{x=6}} % {{x=2},{x=6}} m_solve(x^2-1); {{x=1},{x=3},{x=5},{x=7}} % {{x=1},{x=3},{x=5},{x=7}} m_solve({x^2-y^3=3}); {{x=0,y=5}, {x=2,y=1}, {x=4,y=5}, {x=6,y=1}} % {{x=0,y=5}, {x=2,y=1}, {x=4,y=5}, {x=6,y=1}} m_solve({x^2-y^3=3,x=2}); {{y=1,x=2}} % {{y=1,x=2}} m_solve({x=2,x^2-y^3=3}); {{x=2,y=1}} % {{x=2,y=1}} m_solve({x1,x2 + 6,2*x1**3 + 4*x2**4 + x3 + 6}); {{x1=0,x2=2,x3=2}} % {{x1=0,x2=2,x3=2}} setmod 800; 8 m_solve(x^2-1); {{x=1}, {x=49}, {x=351}, {x=399}, {x=401}, {x=449}, {x=751}, {x=799}} % {{x=1}, {x=49}, {x=351}, {x=399}, {x=401}, {x=449}, {x=751}, {x=799}} m_solve({x1 + 51, 282*x1^4 + x2 + 468, x3 + 1054, 256*x1^2 + 257*x2^4 + 197*x3 + x4 + 653, 255*x1^4 + 40*x2^2 + x5 + 868, 230*x1^4 + 670*x3 + 575*x4^4 + 373*x5^3 + x6 + 1328, 182*x4^4 + 727*x5^2 + 609*x6**4 + x7 + 1032, 623*x1^3 + 614*x2^4 + 463*x3**2 + 365*x4 + 300*x7 + x8 + 1681}); {{x1=749,x2=50,x3=546,x4=729,x5=77,x6=438,x7=419,x8=399}} % {{x1=749,x2=50,x3=546,x4=729,x5=77,x6=438,x7=419,x8=399}} m_solve{x+y=4,x^2+y^2=8}; {{x=2,y=2}, {x=22,y=782}, {x=42,y=762}, {x=62,y=742}, {x=82,y=722}, {x=102,y=702}, {x=122,y=682}, {x=142,y=662}, {x=162,y=642}, {x=182,y=622}, {x=202,y=602}, {x=222,y=582}, {x=242,y=562}, {x=262,y=542}, {x=282,y=522}, {x=302,y=502}, {x=322,y=482}, {x=342,y=462}, {x=362,y=442}, {x=382,y=422}, {x=402,y=402}, {x=422,y=382}, {x=442,y=362}, {x=462,y=342}, {x=482,y=322}, {x=502,y=302}, {x=522,y=282}, {x=542,y=262}, {x=562,y=242}, {x=582,y=222}, {x=602,y=202}, {x=622,y=182}, {x=642,y=162}, {x=662,y=142}, {x=682,y=122}, {x=702,y=102}, {x=722,y=82}, {x=742,y=62}, {x=762,y=42}, {x=782,y=22}} off modular; % m_roots has the modulus as its second argument. m_roots(x^2-1,8); {1,3,5,7} % {1,3,5,7} m_roots(x^3-1,7); {1,2,4} % {1,2,4} m_roots(x^3-x,7); {0,1,6} % {0,1,6} m_roots((x-1)*(x-2)*(x-3),7); {1,2,3} % {1,2,3} m_roots((x-1)*(x-2)*(x^3-1)*(x-5),7); {1,2,4,5} % {1,2,4,5} m_roots((x-1)*(x-2)*(x^3-1)*(x-5),1009); {1,2,5,374,634} % {1,2,5,374,634} m_roots((x-1)*(x-2)*(x^3-1)*(x-5),1000); {1,2,5,26,51,101,127,130,151,201,226,251,255,301,351,377,401,426,451,501,505,551 ,601,626,627,651,701,751,755,801,826,851,877,901,951} length ws; 35 % 35 end; Time for test: 50 ms, plus GC time: 8 ms