@@ -1,234 +1,234 @@ -REDUCE 3.6, 15-Jul-95, patched to 6 Mar 96 ... - - -% 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: modsr 16769 16769) +REDUCE 3.6, 15-Jul-95, patched to 6 Mar 96 ... + + +% 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: modsr 16769 16769)