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Sun Jan  3 23:47:43 MET 1999
REDUCE 3.7, 15-Jan-99 ...

1: 1: 
2: 2: 2: 2: 2: 2: 2: 2: 2: 
3: 3: % 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;

4: 4: 4: 4: 4: 4: 4: 4: 4: 

Time for test: 220 ms
5: 5: 
Quitting
Sun Jan  3 23:47:50 MET 1999