1 | LIB "tst.lib"; |
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2 | tst_init(); |
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3 | |
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4 | proc testfactors (list l, poly f) |
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5 | { |
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6 | poly g= 1; |
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7 | for (int i= 1; i <= size (l[1]); i++) |
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8 | { |
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9 | g= g*(l[1][i]^l[2][i]); |
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10 | } |
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11 | g == f; |
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12 | l; |
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13 | } |
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14 | |
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15 | |
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16 | |
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17 | // polys from L. Bernardin's thesis |
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18 | ring r= 17,(x,y),dp; |
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19 | list l; |
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20 | poly f; |
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21 | for (int n=2; n <= 700; n++) |
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22 | { |
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23 | f= x^n*y^n+x^((n div 2)+1)*y^(n div 2)*(y+1)+x^2*y+(n+1)*x*y+(n^2+3)*x-2; |
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24 | f; |
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25 | l= factorize (f); testfactors (l, f); |
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26 | } |
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27 | tst_status(); |
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28 | |
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29 | kill r; |
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30 | |
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31 | ring r= 31991,(z,w),dp; |
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32 | |
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33 | list l; |
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34 | |
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35 | poly f= 10582*w^3*z^4+21325*z^4+29620*w^4*z^3+23697*w*z^3+12439*w^6*z^2+3572*w^3*z^2+5463*z^2+16590*w*z+24885*w^3+31963; |
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36 | |
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37 | l= factorize (f); testfactors (l, f); |
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38 | |
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39 | kill r; |
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40 | |
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41 | ring r= 3, (s,t),dp; |
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42 | list l; |
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43 | |
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44 | poly f= s^85+(t)*s^84+(t^2)*s^83+(-1*t^18)*s^67+(-1*t^19)*s^66+(t^20)*s^65 |
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45 | +(t^21)*s^64+(t^22)*s^63+(-1*t^24)*s^61+(-1*t^25)*s^60+(t^29)*s^56 |
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46 | +(t^38)*s^47+(-1*t^39)*s^46+(-1*t^40)*s^45+(-1*t^42)*s^43+(-1*t^43)*s^42 |
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47 | +(-1*t^45)*s^40+(-1*t^46)*s^39+(t^47)*s^38+(t^56)*s^29+(-1*t^60)*s^25 |
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48 | +(-1*t^61)*s^24+(t^63)*s^22+(t^64)*s^21+(t^65)*s^20+(-1*t^66)*s^19 |
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49 | +(-1*t^67)*s^18+(t^83)*s^2+(t^84)*s+(t^85); |
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50 | |
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51 | l= factorize (f); testfactors (l, f); |
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52 | |
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53 | kill r; |
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54 | |
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55 | ring r= 32003, (f,g,v,y,u,x), dp; |
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56 | list l; |
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57 | poly h= f^3*u^3-4*f^2*g*v*y*u^2 + (8*f^3*v^2*y+6*f^2*g*v^2*x+4*f*g^2*v^2*y^2)*u |
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58 | -8*f^3*v^3*x-4*f*g^2*v^3*x*y + g^3*v^3*x^2; |
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59 | |
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60 | l= factorize (h); testfactors (l, h); |
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61 | |
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62 | kill r; |
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63 | ring r= 32003, (a,b,c,f), dp; |
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64 | list l; |
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65 | poly h= a^3*b^3*f^4+186*a^2*b^4*c*f^3+11532*a*b^5*c^2*f^2+14307*b^6*c^3*f; |
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66 | |
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67 | l= factorize (h); testfactors (l, h); |
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68 | |
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69 | kill r; |
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70 | ring r= 32003,(x,y,z),dp; |
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71 | list l; |
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72 | poly f= x^25+y^23+z^18+x^4*y^10+x^8*y^5+2*x^5*y^8+x^5*y^5*z^3+x^6*y^6; |
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73 | |
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74 | l= factorize (f); testfactors (l, f); |
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75 | |
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76 | kill r; |
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77 | ring r= 32003, (x,y,z,w),dp; |
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78 | list l; |
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79 | poly f= |
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80 | -573002*x^10+240517*x^9*y+396389*x^8*y^2+535082*x^7*y^3+288429*x^6*y^4 |
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81 | +763919*x^5*y^5+3766*x^4*y^6-649376*x^3*y^7-59851*x^2*y^8-542799*x*y^9+20979*y^10 |
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82 | -461020*x^9*z-650459*x^8*y*z-944957*x^7*y^2*z+1677170*x^6*y^3*z+1666154*x^5*y^4*z |
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83 | -1232710*x^4*y^5*z+862729*x^3*y^6*z-618762*x^2*y^7*z-705768*x*y^8*z-187036*y^9*z-741032*x^8*z^2 |
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84 | +1446654*x^7*y*z^2-643320*x^6*y^2*z^2-1635676*x^5*y^3*z^2-189420*x^4*y^4*z^2+682529*x^3*y^5*z^2 |
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85 | -450284*x^2*y^6*z^2-327970*x*y^7*z^2+66106*y^8*z^2+386688*x^7*z^3+198264*x^6*y*z^3-757313*x^5*y^2*z^3+2008508*x^4*y^3*z^3-675589*x^3*y^4*z^3-2338517*x^2*y^5*z^3+413997*x*y^6*z^3+150157*y^7*z^3 |
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86 | +115299*x^6*z^4+1838075*x^5*y*z^4-821489*x^4*y^2*z^4-772496*x^3*y^3*z^4+94982*x^2*y^4*z^4 |
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87 | +552427*x*y^5*z^4+894534*y^6*z^4-173749*x^5*z^5-1322895*x^4*y*z^5+545850*x^3*y^2*z^5 |
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88 | +1506535*x^2*y^3*z^5+31641*x*y^4*z^5+858761*y^5*z^5+188464*x^4*z^6+676365*x^3*y*z^6 |
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89 | -1175321*x^2*y^2*z^6-94611*x*y^3*z^6+365391*y^4*z^6-300517*x^3*z^7-74262*x^2*y*z^7 |
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90 | +756469*x*y^2*z^7+702099*y^3*z^7+651058*x^2*z^8+261997*x*y*z^8+70610*y^2*z^8-493574*x*z^9 |
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91 | +129784*y*z^9+265065*z^10-532141*x^9*w-285474*x^8*y*w-1300132*x^7*y^2*w+908974*x^6*y^3*w |
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92 | -1966687*x^5*y^4*w-127968*x^4*y^5*w+58220*x^3*y^6*w+41679*x^2*y^7*w+479035*x*y^8*w+466832*y^9*w |
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93 | +1566035*x^8*z*w+1817709*x^7*y*z*w-688806*x^6*y^2*z*w-748313*x^5*y^3*z*w-1930577*x^4*y^4*z*w |
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94 | -957911*x^3*y^5*z*w+81915*x^2*y^6*z*w+133232*x*y^7*z*w+980198*y^8*z*w-110745*x^7*z^2*w |
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95 | -1370738*x^6*y*z^2*w-1182195*x^5*y^2*z^2*w+3215028*x^4*y^3*z^2*w-2006230*x^3*y^4*z^2*w |
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96 | +2364130*x^2*y^5*z^2*w+1457270*x*y^6*z^2*w+1484168*y^7*z^2*w+1648545*x^6*z^3*w+772215*x^5*y*z^3*w |
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97 | +554722*x^4*y^2*z^3*w+667926*x^3*y^3*z^3*w+375356*x^2*y^4*z^3*w+3601160*x*y^5*z^3*w |
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98 | +625131*y^6*z^3*w-2510503*x^5*z^4*w-2729919*x^4*y*z^4*w+1243946*x^3*y^2*z^4*w |
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99 | +2503349*x^2*y^3*z^4*w+1909123*x*y^4*z^4*w+588366*y^5*z^4*w+94641*x^4*z^5*w+1274333*x^3*y*z^5*w |
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100 | +1615834*x^2*y^2*z^5*w-1286036*x*y^3*z^5*w-491438*y^4*z^5*w-864129*x^3*z^6*w+96287*x^2*y*z^6*w |
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101 | -1641596*x*y^2*z^6*w-479951*y^3*z^6*w+865513*x^2*z^7*w+37697*x*y*z^7*w-425879*y^2*z^7*w |
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102 | -246899*x*z^8*w-1043521*y*z^8*w-615277*z^9*w-353183*x^8*w^2+1903124*x^7*y*w^2+307847*x^6*y^2*w^2 |
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103 | +153254*x^5*y^3*w^2+4494*x^4*y^4*w^2+775116*x^3*y^5*w^2+84747*x^2*y^6*w^2+1970329*x*y^7*w^2 |
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104 | +248796*y^8*w^2-200676*x^7*z*w^2-1283772*x^6*y*z*w^2+312236*x^5*y^2*z*w^2+258350*x^4*y^3*z*w^2 |
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105 | +899318*x^3*y^4*z*w^2+879951*x^2*y^5*z*w^2-197099*x*y^6*z*w^2+1027373*y^7*z*w^2 |
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106 | -939408*x^6*z^2*w^2+1231368*x^5*y*z^2*w^2+811932*x^4*y^2*z^2*w^2+136753*x^3*y^3*z^2*w^2 |
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107 | -1060314*x^2*y^4*z^2*w^2-373787*x*y^5*z^2*w^2-419717*y^6*z^2*w^2-602528*x^5*z^3*w^2 |
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108 | -279785*x^4*y*z^3*w^2+140803*x^3*y^2*z^3*w^2+1245653*x^2*y^3*z^3*w^2+611906*x*y^4*z^3*w^2 |
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109 | -1166551*y^5*z^3*w^2-878201*x^4*z^4*w^2+597628*x^3*y*z^4*w^2-220458*x^2*y^2*z^4*w^2 |
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110 | -3038116*x*y^3*z^4*w^2-2785259*y^4*z^4*w^2-425903*x^3*z^5*w^2-316206*x^2*y*z^5*w^2 |
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111 | -3764903*x*y^2*z^5*w^2-2194636*y^3*z^5*w^2-185521*x^2*z^6*w^2+419827*x*y*z^6*w^2 |
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112 | -70946*y^2*z^6*w^2+561958*x*z^7*w^2-513594*y*z^7*w^2-487215*z^8*w^2-902070*x^7*w^3 |
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113 | +260239*x^6*y*w^3-1618965*x^5*y^2*w^3+1123916*x^4*y^3*w^3-1107669*x^3*y^4*w^3-1433250*x^2*y^5*w^3 |
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114 | +665446*x*y^6*w^3-1463775*y^7*w^3+778712*x^6*z*w^3-80174*x^5*y*z*w^3-93922*x^4*y^2*z*w^3 |
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115 | +1249290*x^3*y^3*z*w^3+1272307*x^2*y^4*z*w^3+513673*x*y^5*z*w^3-322676*y^6*z*w^3 |
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116 | -634533*x^5*z^2*w^3-1875741*x^4*y*z^2*w^3-2698209*x^3*y^2*z^2*w^3+937176*x^2*y^3*z^2*w^3 |
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117 | -2883756*x*y^4*z^2*w^3-1430757*y^5*z^2*w^3+485806*x^4*z^3*w^3+731831*x^3*y*z^3*w^3 |
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118 | +2196178*x^2*y^2*z^3*w^3-1491104*x*y^3*z^3*w^3-1456373*y^4*z^3*w^3-206031*x^3*z^4*w^3+314576*x^2*y*z^4*w^3-225867*x*y^2*z^4*w^3-2750466*y^3*z^4*w^3-1087247*x^2*z^5*w^3+2172840*x*y*z^5*w^3 |
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119 | -541045*y^2*z^5*w^3+624945*x*z^6*w^3+1085162*y*z^6*w^3+565094*z^7*w^3-457315*x^6*w^4 |
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120 | +342040*x^5*y*w^4-681000*x^4*y^2*w^4+297164*x^3*y^3*w^4+689*x^2*y^4*w^4+529745*x*y^5*w^4 |
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121 | -1310613*y^6*w^4-786298*x^5*z*w^4-1023635*x^4*y*z*w^4-2098764*x^3*y^2*z*w^4+1733995*x^2*y^3*z*w^4 |
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122 | +1561806*x*y^4*z*w^4+133720*y^5*z*w^4-240204*x^4*z^2*w^4+1124674*x^3*y*z^2*w^4 |
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123 | +2411690*x^2*y^2*z^2*w^4-600532*x*y^3*z^2*w^4-71275*y^4*z^2*w^4+128215*x^3*z^3*w^4 |
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124 | +567626*x^2*y*z^3*w^4+973911*x*y^2*z^3*w^4-562780*y^3*z^3*w^4-894759*x^2*z^4*w^4 |
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125 | +1265582*x*y*z^4*w^4+509433*y^2*z^4*w^4-671007*x*z^5*w^4+345729*y*z^5*w^4+80717*z^6*w^4 |
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126 | +1144765*x^5*w^5+137320*x^4*y*w^5+390809*x^3*y^2*w^5+207350*x^2*y^3*w^5+65943*x*y^4*w^5 |
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127 | -1283191*y^5*w^5-109804*x^4*z*w^5+951743*x^3*y*z*w^5-154107*x^2*y^2*z*w^5-394628*x*y^3*z*w^5 |
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128 | -3201737*y^4*z*w^5+2307230*x^3*z^2*w^5-1082386*x^2*y*z^2*w^5-240669*x*y^2*z^2*w^5 |
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129 | -1274548*y^3*z^2*w^5-1768397*x^2*z^3*w^5-2788826*x*y*z^3*w^5+1689141*y^2*z^3*w^5 |
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130 | -1051474*x*z^4*w^5+126201*y*z^4*w^5-789876*z^5*w^5-288558*x^4*w^6-697110*x^3*y*w^6 |
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131 | +659535*x^2*y^2*w^6-1659535*x*y^3*w^6+371290*y^4*w^6-1605798*x^3*z*w^6+63599*x^2*y*z*w^6 |
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132 | +273476*x*y^2*z*w^6-774681*y^3*z*w^6-113162*x^2*z^2*w^6+861980*x*y*z^2*w^6 |
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133 | +1824646*y^2*z^2*w^6-275200*x*z^3*w^6+1083821*y*z^3*w^6+803980*z^4*w^6 |
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134 | +912560*x^3*w^7-373953*x^2*y*w^7+635559*x*y^2*w^7+2023871*y^3*w^7-252773*x^2*z*w^7 |
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135 | -1013176*x*y*z*w^7-356255*y^2*z*w^7+412544*x*z^2*w^7-199680*y*z^2*w^7+190561*z^3*w^7 |
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136 | +33346*x^2*w^8-1189055*x*y*w^8+246983*y^2*w^8-220965*x*z*w^8-273745*y*z*w^8-493392*z^2*w^8 |
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137 | +411602*x*w^9+853400*y*w^9+1110886*z*w^9-580548*w^10; |
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138 | |
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139 | l= factorize (f); testfactors (l, f); |
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140 | |
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141 | kill r; |
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142 | ring r= 31991,(x,y,z,w),dp; |
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143 | list l; |
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144 | poly f= (-15*y^2*z^16+29*w^4*x^12*y^12*z^3+21*x^3*z^2+3*w^15*y^20)*(-1*z^31-w^12*z^20+y^18-y^14+x^2*y^2+x^21+w^2); |
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145 | |
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146 | l= factorize (f); testfactors (l, f); |
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147 | |
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148 | f= (w^4*z^3-x*y^2*z^2-w^4*x^5*y^6-w^2*x^3*y)*(-1*x^5-z^3+y*z+x^2*y^3)*(w^4*z^6+y^2*z^3-w^2*x^2*y^2*z^2+x^5*z-x^4*y^2-w^3*x^3*y); |
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149 | |
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150 | l= factorize (f); testfactors (l, f); |
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151 | |
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152 | kill r; |
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153 | ring r= 2,(x,y),dp; |
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154 | list l; |
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155 | poly f= x*(x+y)*(x^2+x+y^2)*(x^2+x+y+1)*(x^2+x+y^2+1)*(x^3+x+y^3)*(x^3+x+y+1)*(x^3+x+y^3+1)*(x^3+x+y^3+y+1)*(x^3+x+y^3+y^2+1); |
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156 | |
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157 | l= factorize (f); testfactors (l, f); |
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158 | |
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159 | f= x*(x+y)*(x^2+x+y^2)*(x^2+x+y+1)*(x^2+x+y^2+1); |
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160 | |
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161 | l= factorize (f); testfactors (l, f); |
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162 | |
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163 | f= (x+y^2)*(x^2+y)*(x+y^4)*(x^4+y); |
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164 | |
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165 | l= factorize (f); testfactors (l, f); |
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166 | |
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167 | f= (x+y^2)*(x^2+y); |
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168 | |
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169 | l= factorize (f); testfactors (l, f); |
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170 | |
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171 | kill r; |
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172 | |
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173 | ring r= 3,(x,y),dp; |
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174 | list l; |
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175 | poly f= (x+y^2)*(x^2+y)*(x+y^4)*(x^4+y); |
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176 | |
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177 | l= factorize (f); testfactors (l, f); |
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178 | |
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179 | f= x^3 - y^3; |
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180 | |
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181 | l= factorize (f); testfactors (l, f); |
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182 | |
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183 | kill r; |
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184 | |
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185 | ring r= 5,(x,y,z),dp; |
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186 | |
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187 | list l; |
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188 | |
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189 | poly f= (x*z+y+30)*(y*z+x+20)*(z+x*y+10); |
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190 | |
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191 | l= factorize (f); testfactors (l, f); |
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192 | |
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193 | f= (x+y^2)*(x^2+y)*(x+y^4)*(x^4+y); |
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194 | |
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195 | l= factorize (f); testfactors (l, f); |
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196 | |
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197 | f= x^10 - y^4; |
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198 | |
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199 | l= factorize (f); testfactors (l, f); |
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200 | |
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201 | kill r; |
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202 | ring r= 101, (a,b,c,d), dp; |
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203 | list l; |
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204 | poly f= (a-b)*(a^4-7*b* c-4)*(a^5-b+c-11*d^3+1); |
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205 | |
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206 | l= factorize (f); testfactors (l, f); |
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207 | |
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208 | kill r; |
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209 | ring r= 31991, (x,y,z,w,u,v,s,t), dp; |
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210 | list l; |
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211 | poly f= x^6*y^3*z^2*(3*z^3+2*w*z-8*x*y^2+14*w^2*y^2-y^2+18*x^3*y)*(w^2*z^3-12*w^2*x*y*z^3+3*x*y^2+29*x-w^2); |
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212 | |
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213 | l= factorize (f); testfactors (l, f); |
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214 | |
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215 | f= (22*y^5-18*x^4*y^5-26*x^3*y^4-38*x^2*y^4+29*x^2*y^3-41*x^4*y^2+37*x^4)*(33*x^5*y^6+11*y^2+35*x^3*y-22*x^4); |
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216 | |
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217 | l= factorize (f); testfactors (l, f); |
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218 | |
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219 | f= (3*z^3+2*w*z-9*y^3-y^2+45*x^3)*(w^2*z^3+47*x*y-w^2); |
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220 | |
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221 | l= factorize (f); testfactors (l, f); |
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222 | |
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223 | f= (z+y+x-3)*(z+y+x-3)*(z+y+x-3); |
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224 | |
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225 | l= factorize (f); testfactors (l, f); |
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226 | |
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227 | f= (z+y+x-3)*(z+y+x-3)*(z+y+x-3)*(z+y+x-2)*(z+y+x-2); |
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228 | |
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229 | l= factorize (f); testfactors (l, f); |
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230 | |
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231 | f= (z^2+x^3*y^4+u^2)*((y^2+x)*z^2 + 3*u^2*x^3*y^4*z+19*y^2)*(u^2*y^4*z^2+x^2*z+5); |
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232 | |
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233 | l= factorize (f); testfactors (l, f); |
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234 | |
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235 | f= (z^2-x^3*y+3)*(z^2+x^3*y^4)*(y^4*z^2+x^2*z+5); |
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236 | |
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237 | l= factorize (f); testfactors (l, f); |
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238 | |
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239 | f= (y*z^3+x*y*z+y^2+x^3)*(x*(z^4+1)+z+x^3*y^2); |
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240 | |
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241 | l= factorize (f); testfactors (l, f); |
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242 | |
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243 | f= (x^3*(z+y)+z-11)*(x^2*(z^2+y^2)+y+90); |
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244 | |
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245 | l= factorize (f); testfactors (l, f); |
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246 | |
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247 | f= x^10 - y^4; |
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248 | |
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249 | l= factorize (f); testfactors (l, f); |
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250 | |
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251 | f= (x*z^2+2*x*z*w+x*w^2+z^2+w+2*z*w)*(x*z^2+2*x*z*w+x*w^2+z); |
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252 | |
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253 | l= factorize (f); testfactors (l, f); |
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254 | |
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255 | f= (x^2-x*z+z*y+2)*(x^2+3*x-y^2-15); |
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256 | |
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257 | l= factorize (f); testfactors (l, f); |
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258 | |
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259 | f= (z^3+x*y*z+y^2+x^3)*(x*(z^4+1)+z+x^3*y^2); |
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260 | |
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261 | l= factorize (f); testfactors (l, f); |
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262 | |
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263 | f= (x^2*y+x*y+1)*(x^2*y+2*x*y+3)*(2*x^2*y+3*x*y+5)*(3*x^2*y+4*x*y+7); |
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264 | |
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265 | l= factorize (f); testfactors (l, f); |
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266 | |
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267 | f= w^2*x^7*y^6*12*z^5+31962*z^2*y^5*x^7+87*z^5*y^3*x^7+31967*z^2*y^7*x^8+31759*z^2*y^5*x^8+31988*z^2*y^7*x^7+54*z^2*y^6*x^10+522*z^2*y^4*x^10+9*z^5*y^5*x^7+z^2*y^5*x^6*w^2+3*z^8*y^3*x^6*w^2+2*z^6*y^3*x^6*w^3+31989*z^3*y^3*x^6*w^3+31977*z^2*y^5*x^6*w^4+31988*z^5*y^3*x^6*w^2+414*z^2*y^5*x^7*w^2+42*z^2*y^7*x^7*w^2+14*z^5*y^5*x^6*w^4+31990*z^5*y^5*x^6*w^2+31973*z^2*y^4*x^9*w^2+58*z^3*y^3*x^7*w+31955*z^8*y^4*x^7*w^2+6*z^3*y^5*x^7*w+31967*z^6*y^4*x^7*w^3+96*z^5*y^6*x^8*w^2+31983*z^5*y^5*x^7*w^2+31823*z^5*y^6*x^7*w^4+31775*z^5*y^5*x^10*w^2+18*z^5*y^4*x^9*w^2; |
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268 | |
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269 | l= factorize (f); testfactors (l, f); |
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270 | |
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271 | f= (z+x*y+10)*(x*z+y+30)*(y*z+x+20); |
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272 | |
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273 | l= factorize (f); testfactors (l, f); |
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274 | |
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275 | f= (x^3*y+x^3*z+z-11)*(x^2*z^2+x^2*y^2+y+90); |
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276 | |
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277 | l= factorize (f); testfactors (l, f); |
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278 | |
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279 | f= (x-w)*(y-w)*(x-y)*(z-w)*(x-z)*(y-z); |
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280 | |
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281 | l= factorize (f); testfactors (l, f); |
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282 | |
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283 | f= (10*y+x^3+9)*(6*x*y^2+x+y+x^3+15); |
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284 | |
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285 | l= factorize (f); testfactors (l, f); |
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286 | |
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287 | f= (3*z^3+2*w*z-10*y^2+45*x^3)*(w^2*z^3+47*x*y-w^2); |
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288 | |
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289 | l= factorize (f); testfactors (l, f); |
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290 | |
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291 | f= (x^2-10748*y*x+y^2)*(y^2+x^2)*(x^2+10748*y*x+y^2); |
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292 | |
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293 | l= factorize (f); testfactors (l, f); |
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294 | |
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295 | f= (y*z-x*z+x^2+2)*(z^3-y^2+x^2+3*x-15); |
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296 | |
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297 | l= factorize (f); testfactors (l, f); |
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298 | |
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299 | f= (x+y+z)*(z-y+x)*(x-z-y); |
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300 | |
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301 | l= factorize (f); testfactors (l, f); |
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302 | |
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303 | f= (y*z+x*y^2+9)*(y*z+x*z+x^2*y); |
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304 | |
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305 | l= factorize (f); testfactors (l, f); |
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306 | |
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307 | f= (3*z^2+2*y^2+x^2)*(4*z^2-3*y^2+2*x^2); |
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308 | |
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309 | l= factorize (f); testfactors (l, f); |
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310 | |
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311 | f= x^4 + y^3 + z^5; |
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312 | |
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313 | l= factorize (f); testfactors (l, f); |
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314 | |
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315 | f= -9944*(x^2-5265*x+14343)*(x^2+5943*x-3555)*(x-8995)*(x-15035); |
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316 | |
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317 | l= factorize (f); testfactors (l, f); |
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318 | |
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319 | f= x^8 + x +1 ; |
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320 | |
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321 | l= factorize (f); testfactors (l, f); |
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322 | |
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323 | f= x^14-1; |
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324 | |
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325 | l= factorize (f); testfactors (l, f); |
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326 | |
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327 | kill r; |
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328 | |
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329 | ring r = (2,a),(x,y),dp; |
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330 | minpoly = a^2 + a + 1; |
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331 | poly f=(a + 1)*x^145*y^84 + (a + 1)*x^205*y^17 + x^32*y^112 + x^92*y^45; |
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332 | poly g = x7y11+xy17+(a)*x7y10+(a)*xy16+(a)*x8y8+(a+1)*x8y7+(a)*y12+(a+1)*x8y3+(a+1)*x2y9+(a+1)*y11+x9+xy4; |
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333 | list l; |
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334 | for (int i= 1; i < 33002; i= i+33) |
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335 | { |
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336 | system ("--random", i); |
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337 | l= factorize (f); |
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338 | if (size (l[1]) != 5) |
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339 | { |
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340 | l; |
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341 | break; |
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342 | } |
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343 | system ("--random", i); |
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344 | l= factorize (g); |
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345 | testfactors (l,g); |
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346 | } |
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347 | |
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348 | ring r = 2,(x,y),dp; |
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349 | poly f=x^6 + y^5 + x^5 + y^4; |
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350 | poly g=x^6 + y^6 + x^5 + x^3 + x + 1; |
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351 | poly h=x^6 + x*y^5 + y^5 + y^4 + x*y^2 + y^3 + 1; |
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352 | list l1, l2, l3; |
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353 | for (int i= 1; i < 33002; i= i+33) |
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354 | { |
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355 | system ("--random", i); |
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356 | l1= factorize (f); |
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357 | l2= factorize (g); |
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358 | l3= factorize (h); |
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359 | l1; |
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360 | l2; |
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361 | l3; |
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362 | if (size (l1[1]) != 2) |
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363 | { |
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364 | l1; |
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365 | break; |
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366 | } |
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367 | if (size (l2[1]) != 3) |
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368 | { |
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369 | l2; |
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370 | break; |
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371 | } |
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372 | if (size (l3[1]) != 3) |
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373 | { |
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374 | l3; |
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375 | break; |
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376 | } |
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377 | } |
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378 | |
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379 | // tr. 440 |
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380 | kill r; |
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381 | ring r=7,(x,y),dp; |
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382 | poly f = y^5*x^4 - y^2*x^7 - y^3 + x^3; |
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383 | list l=factorize(f); |
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384 | size (l[1]) < 6; |
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385 | testfactors (l,f); |
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386 | |
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387 | |
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388 | kill r; |
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389 | ring r=2,(x,y),dp; |
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390 | poly f= (x^6*y+x^4*y^2+x^5+x^2*y^2+x^2*y+y^2+x)*(x^6*y^2+y^7+x^3*y^3+x^4+y); |
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391 | list l= factorize (f); |
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392 | testfactors (l, f); |
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393 | |
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394 | f= (x^3*y^2+y^3+x^2+1)*(x^2*y^6+x^4*y^2+y^4+y^3+x*y+x+1); |
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395 | l= factorize (f); |
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396 | testfactors (l, f); |
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397 | |
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398 | |
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399 | f= (x^3*y^4+y^3+x+1)*(x*y^7+y^6+x^2*y^2+x^3+x*y+y); |
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400 | l= factorize (f); |
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401 | testfactors (l, f); |
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402 | |
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403 | |
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404 | f= (x^4*y^3+x^2*y^4+x^5+x*y^2+1)*(x^2*y^6+x*y^5+x*y^4+x^2*y^2+x^2*y+y); |
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405 | l= factorize (f); |
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406 | testfactors (l, f); |
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407 | |
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408 | |
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409 | f= (x^5+x*y^2+y)*(x^4*y^2+x^3+x*y+1); |
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410 | l= factorize (f); |
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411 | testfactors (l, f); |
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412 | |
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413 | |
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414 | f= (x^2*y^3+y^3+x^2+x)*(x^7+x^5*y+x^2*y^3+y^3+1); |
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415 | l= factorize (f); |
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416 | testfactors (l, f); |
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417 | |
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418 | |
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419 | f= (x^3*y+x*y+1)*(x^5*y+x*y^4+x^2*y^2+y^2+y+1); |
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420 | l= factorize (f); |
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421 | testfactors (l, f); |
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422 | |
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423 | |
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424 | f= (x^4*y^2+x^3*y+x*y+1)*(x*y^5+y^5+x^2*y+x*y+x+1); |
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425 | l= factorize (f); |
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426 | testfactors (l, f); |
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427 | |
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428 | |
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429 | |
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430 | f= (y^6+x^5+y^3+x)*(x^2*y^3+y^4+y); |
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431 | l= factorize (f); |
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432 | testfactors (l, f); |
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433 | |
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434 | |
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435 | f= (x*y^3+x*y^2+1)*(x^3*y^3+x^4*y+1); |
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436 | l= factorize (f); |
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437 | testfactors (l, f); |
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438 | |
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439 | |
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440 | f= (x^4*y^2+x^3*y^2+x*y+1)*(x^6+y^5); |
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441 | l= factorize (f); |
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442 | testfactors (l, f); |
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443 | |
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444 | |
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445 | f= (x^5*y+x^2*y^3+x*y^3+x^2+y+1)*(x*y^5+x^2); |
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446 | l= factorize (f); |
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447 | testfactors (l, f); |
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448 | |
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449 | |
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450 | f= (x^2*y^3+x*y^2+x+1)*(x^5+x*y^2+x*y+1); |
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451 | l= factorize (f); |
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452 | testfactors (l, f); |
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453 | |
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454 | |
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455 | f= (x^6+x*y^2+x^2+y)*(y^5+x^3*y+y+1); |
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456 | l= factorize (f); |
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457 | testfactors (l, f); |
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458 | |
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459 | |
---|
460 | f= (y^6+x*y^4+y^4+y^3+1)*(y^6+x^5+x^2*y^2+x^2*y+x*y+1); |
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461 | l= factorize (f); |
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462 | testfactors (l, f); |
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463 | |
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464 | |
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465 | f= (x^5+y^3+x)*(x*y^5+x^3*y+x^2+y); |
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466 | l= factorize (f); |
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467 | testfactors (l, f); |
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468 | |
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469 | |
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470 | f=x^2*y^5+x^4*y^2+x^2*y^4+x^4*y+x^3*y^2+x*y^4+x^2*y^2+y^3+x^2+x*y+x+1; |
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471 | l= factorize (f); |
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472 | testfactors (l,f); |
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473 | |
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474 | kill r; |
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475 | ring r=2,(x,y,z,s,t,u,v),dp; |
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476 | poly f= y*z*s^2*t^2+x^4*y*u+y^3*z*s*u+x*y*z^2*s*u+x^2*z^2*u^2+x*y^4*v+x^2*t*u^2*v+x*y*z*s*t+z^2*s^2*t+z^2*s*t^2+x*y^3*v+y*s*t^2*v+x*z^2*s+y^2*t*u+x*y*z+y*z*v; |
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477 | poly g= x^2*z^2*s^2+x^2*y*s^3+y^2*z*s*t^2+x*s^3*t^2+y^3*z*s*u+y*t^4*u+x^2*z^2*u^2+y^2*z*t*u^2+x*s*t^2*u^2+y*t^2*u^3+y^2*z^3*v+x^2*s*u^2*v+x*z*s*u^2*v+y^2*z*s^2+y*z^3*t+x^2*z*t^2+z^2*s*t*v+z^2*t^2*v+z^3*u*v+s^2*t*u*v+s*v^4+y^3*u+x*z^2*u+x*z*s*v+u*v^3+x^2*t+z*t+u; |
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478 | poly h= x^2*y*s+z*s^2*t+z^3*u+x^2*s*u+y*s^2*u+x*y*u*v+x*s*u*v+x*z*t+z^2*t+x*y*u+x*t*u+y*s; |
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479 | poly k=f*g*h; |
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480 | def l= factorize (k); |
---|
481 | testfactors (l, k); |
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482 | |
---|
483 | kill r; |
---|
484 | // from P. Zimmermann via libsingular-devel |
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485 | ring r = 2,(y,t),dp; |
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486 | poly f = y*t^8 + y^5*t^2 + y*t^6 + t^7 + y^6 + y^5*t + y^2*t^4 + y^2*t^2 + |
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487 | y^2*t + t^3 + y^2 + t^2; |
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488 | def l=factorize (f); |
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489 | testfactors (l, f); |
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490 | |
---|
491 | // tr. 482 |
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492 | ring R6s = (32003,s),(x,y),dp; |
---|
493 | minpoly = (s6-11914s5+3952s4-5439s3-15290s2-15431s+15606); |
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494 | poly G3 = x3+y3+(-s-1)*x2+(s-2)*xy+(-s-1)*y2+(s+1)*x+(s+1)*y+(-s); |
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495 | def l=factorize(G3); |
---|
496 | testfactors (l, G3); |
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497 | |
---|
498 | kill r; |
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499 | ring r=(32003,s),(x,y,z),dp; |
---|
500 | minpoly=(s6-11914s5+3952s4-5439s3-15290s2-15431s+15606); |
---|
501 | poly f=x32003+y32003+(-15819s5+10130s4-13478s3-9892s2+7280s+7612)+z32003; |
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502 | factorize (f); |
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503 | |
---|
504 | tst_status(1);$ |
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