1 | // File: alexpoly.tst |
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2 | // Tests for alexpoly lib |
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3 | LIB "tst.lib"; |
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4 | tst_init(); |
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5 | LIB "alexpoly.lib"; |
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6 | ring r=0,(x,y),ds; |
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7 | ////////////////////////////////////////////////////////////////////////// |
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8 | // Defining examples. |
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9 | ////////////////////////////////////////////////////////////////////////// |
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10 | // Examples of polynomials |
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11 | ///////////////////////////////////////////////////////////////////////// |
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12 | list f; |
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13 | f[1] =x2-y2; |
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14 | f[2] =x2+y+y2; |
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15 | f[3] =(x2+y3)*(x2+y3+xy2); |
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16 | f[4] =-x27-x25-15x24y-30x23y2+5x20y3-135x19y4+3x18y5-10x15y6-90x14y7+10x10y9-3x9y10-5x5y12+y15; |
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17 | f[5] =x5-y11; |
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18 | f[6] =xy8+y8+x4y6+4x3y6+2x5y5+6x6y4+4x8y3+x10y2+4x9y2+2x11y+x12; |
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19 | f[7] =(x6-y4); |
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20 | f[8] =(((y-x2+x3)*(y-x2-x3))); |
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21 | f[9] =((x7-2x4y2+xy4-1y5)*(x7-4x4y2+4xy4-1y5)); |
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22 | f[10]=((y2-x3)*(y2-x3-x4)); |
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23 | f[11]=((y2-x3-x4)*(y2+x3+x4)); |
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24 | f[12]=(((x2-y)^2+x5)*((2x2-y)^2+x5)); |
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25 | f[13]=((x2-y4)*(x+y4)); |
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26 | f[14]=-x9+x8-6x7y+3x6y2-2x4y3-3x3y4+y6; |
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27 | f[15]=-x21+x20-8x18y-4x15y2-8x13y3+6x10y4-4x5y6+y8; |
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28 | f[16]=-x19+x18-12x17y-6x15y2-40x14y3+15x12y4-12x11y5-20x9y6+15x6y8-6x3y10+y12; |
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29 | f[17]=x22-x21-14x20y+7x18y2-70x17y3-21x15y4-42x14y5+35x12y6-2x11y7-35x9y8+21x6y10-7x3y12+y14; |
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30 | f[18]=-x17-2x16-x15-20x13y2+5x12y2-10x10y4-10x9y4+10x6y6-5x3y8+y10; |
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31 | f[19]=(f[16]*f[17]*f[18]); |
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32 | f[20]=((x2-y3)*(x3-y5)*(x5-y7)*(x7-y11)*(x11-y13)); |
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33 | f[21]=((x3+3x2y-xy4+y10)*(x3-x2y+y8)); |
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34 | f[22]=-x11+x10-4x8y-2x5y2+y4; |
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35 | f[23]=x7-y8; |
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36 | f[24]=x15-y16; |
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37 | f[25]=f[1]*f[2]; |
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38 | f[26]=f[2]*f[3]; |
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39 | f[27]=f[4]*f[5]; |
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40 | f[28]=f[1]*f[2]*f[3]*f[4]*f[5]; |
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41 | f[29]=f[14]*f[15]; |
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42 | f[30]=f[6]*f[7]; |
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43 | f[31]=f[6]*f[8]*f[12]; |
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44 | f[32]=2x2+3xy+4xy3-x2y; |
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45 | f[33]=(x-y)*(x-2y)*(x-3y)*(x-4y); |
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46 | f[34]=(x-y)*(x-2y)*(x-3y)*(x-4y)*(x-5y); |
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47 | f[35]=(x7-y3)*(y4-2x3y2-4x5y+x6-x7)*(x2-y11); |
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48 | f[36]=-x23-2x22-x21-42x19y2+7x18y2-70x16y4-21x15y4-14x13y6+35x12y6-35x9y8+21x6y10-7x3y12+y14; |
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49 | f[37]=-x29-x28+7x24y-21x20y2+35x16y3-35x12y4+21x8y5-7x4y6+y7; |
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50 | |
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51 | poly p_1 = y2+x3; |
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52 | poly p_2 = p_1^2 + x5y; |
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53 | poly p_3 = p_2^2 + x^10 *p_1; |
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54 | poly p_4 = p_3^2 + x^20 *p_2; |
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55 | poly p_5 = p_4^2 + x^40 *p_3; |
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56 | |
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57 | f[38]=p_1; |
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58 | f[39]=p_2; |
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59 | f[40]=p_3; |
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60 | f[41]=p_4; |
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61 | f[42]=p_5; |
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62 | f[43]=p_1*p_2*p_3; |
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63 | f[44]=p_3*p_5; |
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64 | |
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65 | f[45]=(-x7+x6-4x5y-2x3y2+y4)*(-x21+x20-12x19y-30x17y2-4x15y3+3x14y4-48x12y5+6x10y6-3x7y8-4x5y9+y12); |
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66 | f[46]=f[16]*f[17]*f[18]*f[22]*f[23]*f[24]; |
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67 | f[47]=(x5-y7)*(x10-y17); |
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68 | f[48]=(x5-y7)*(x13-y23); |
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69 | f[49]=(x5-y7)*(x4383-y5344); |
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70 | f[50]=(x5-y7)*(x10-y17)*(x7-y11); |
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71 | |
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72 | list f_irr=x-y,x+y,y-x2+x3,y2-x3-x4,(x2-y)^2+x5,(2x2-y)^2+x5,x-y2,x+y2,x+y4,x3-y5,x5-y7,x7-y11,x11-y13,f[2],f[4],f[5],f[6],f[14],f[15],f[16],f[17],f[18],f[22],f[23],f[24],f[36],f[37],f[38],f[39],f[40],f[41],f[42],(-x7+x6-4x5y-2x3y2+y4),(-x21+x20-12x19y-30x17y2-4x15y3+3x14y4-48x12y5+6x10y6-3x7y8-4x5y9+y12),(x10-y17),(x13-y23),x204-y1111,x4383-y5344; |
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73 | |
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74 | /////////////////////////////////////////////////////////////////////////////////////////// |
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75 | // Defining the invariants of the above examples. |
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76 | /////////////////////////////////////////////////////////////////////////////////////////// |
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77 | list FF; |
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78 | //Polynomial: f[1]=x2-y2 |
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79 | FF[1]=list(intmat(intvec(0,1,1,0),2,2),list(intvec(1),intvec(1))); |
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80 | //Polynomial: f[2]=y+x2+y2 |
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81 | FF[2]=list(intmat(intvec(0),1,1),list(intvec(1))); |
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82 | //Polynomial: f[3]=x4+x3y2+2x2y3+xy5+y6 |
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83 | FF[3]=list(intmat(intvec(0,4,4,0),2,2),list(intvec(2,3),intvec(2,3))); |
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84 | //Polynomial: f[4]=y15-5x5y12+10x10y9-3x9y10-10x15y6-90x14y7+5x20y3-135x19y4+3x18y5-x25-15x24y-30x23y2-x27 |
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85 | FF[4]=list(intmat(intvec(0),1,1),list(intvec(15,25,27))); |
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86 | //Polynomial: f[5]=x5-y11 |
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87 | FF[5]=list(intmat(intvec(0),1,1),list(intvec(5,11))); |
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88 | //Polynomial: f[6]=y8+4x3y6+xy8+6x6y4+2x5y5+x4y6+4x9y2+4x8y3+x12+2x11y+x10y2 |
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89 | FF[6]=list(intmat(intvec(0),1,1),list(intvec(8,12,14,15))); |
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90 | //Polynomial: f[7]=-y4+x6 |
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91 | FF[7]=list(intmat(intvec(0,3,3,0),2,2),list(intvec(2,3),intvec(2,3))); |
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92 | //Polynomial: f[8]=y2-2x2y+x4-x6 |
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93 | FF[8]=list(intmat(intvec(0,3,3,0),2,2),list(intvec(1),intvec(1))); |
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94 | //Polynomial: f[9]=4x2y8-5xy9+y10-12x5y6+6x4y7+13x8y4-2x7y5-6x11y2+x14 |
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95 | FF[9]=list(intmat(intvec(0,1,1,1,1,0,1,1,1,1,0,3,1,1,3,0),4,4),list(intvec(1),intvec(1),intvec(4,6,7),intvec(4,6,7))); |
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96 | //Polynomial: f[10]=y4-2x3y2+x6-x4y2+x7 |
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97 | FF[10]=list(intmat(intvec(0,5,5,0),2,2),list(intvec(2,3),intvec(2,3))); |
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98 | //Polynomial: f[11]=y4-x6-2x7-x8 |
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99 | FF[11]=list(intmat(intvec(0,3,3,0),2,2),list(intvec(2,3),intvec(2,3))); |
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100 | //Polynomial: f[12]=y4-6x2y3+13x4y2-12x6y+2x5y2+4x8-6x7y+5x9+x10 |
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101 | FF[12]=list(intmat(intvec(0,2,2,0),2,2),list(intvec(2,5),intvec(2,5))); |
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102 | //Polynomial: f[13]=x3-xy4+x2y4-y8 |
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103 | FF[13]=list(intmat(intvec(0,2,2,2,0,2,2,2,0),3,3),list(intvec(1),intvec(1),intvec(1))); |
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104 | //Polynomial: f[14]=y6-2x4y3-3x3y4+x8-6x7y+3x6y2-x9 |
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105 | FF[14]=list(intmat(intvec(0),1,1),list(intvec(6,8,9))); |
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106 | //Polynomial: f[15]=y8-4x5y6+6x10y4-8x13y3-4x15y2-8x18y+x20-x21 |
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107 | FF[15]=list(intmat(intvec(0),1,1),list(intvec(8,20,21))); |
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108 | //Polynomial: f[16]=y12-6x3y10+15x6y8-20x9y6+15x12y4-12x11y5-6x15y2-40x14y3+x18-12x17y-x19 |
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109 | FF[16]=list(intmat(intvec(0),1,1),list(intvec(12,18,19))); |
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110 | //Polynomial: f[17]=y14-7x3y12+21x6y10-35x9y8+35x12y6-2x11y7-21x15y4-42x14y5+7x18y2-70x17y3-x21-14x20y+x22 |
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111 | FF[17]=list(intmat(intvec(0),1,1),list(intvec(14,21,22))); |
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112 | //Polynomial: f[18]=y10-5x3y8+10x6y6-10x9y4+5x12y2-10x10y4-x15-20x13y2-2x16-x17 |
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113 | FF[18]=list(intmat(intvec(0),1,1),list(intvec(10,15,17))); |
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114 | //Polynomial: f[19] |
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115 | FF[19]=list(intmat(intvec(0,9,6,9,0,6,6,6,0),3,3),list(intvec(14,21,22),intvec(12,18,19),intvec(10,15,17))); |
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116 | //Polynomial: f[20] |
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117 | FF[20]=list(intmat(intvec(0,4,3,3,3,4,0,3,3,3,3,3,0,3,3,3,3,3,0,4,3,3,3,4,0),5,5),list(intvec(11,13),intvec(5,7),intvec(2,3),intvec(7,11),intvec(3,5))); |
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118 | //Polynomial: f[21]=x6+2x5y-3x4y2-x4y4+x3y5+x3y8+3x2y9+x3y10-x2y11-xy12+y18 |
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119 | FF[21]=list(intmat(intvec(0,1,1,1,1,1,0,1,1,1,1,1,0,3,3,1,1,3,0,4,1,1,3,4,0),5,5),list(intvec(1),intvec(1),intvec(1),intvec(2,7),intvec(1))); |
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120 | //Polynomial: f[22]=y4-2x5y2-4x8y+x10-x11 |
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121 | FF[22]=list(intmat(intvec(0),1,1),list(intvec(4,10,11))); |
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122 | //Polynomial: f[23]=x7-y8 |
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123 | FF[23]=list(intmat(intvec(0),1,1),list(intvec(7,8))); |
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124 | //Polynomial: f[24]=x15-y16 |
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125 | FF[24]=list(intmat(intvec(0),1,1),list(intvec(15,16))); |
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126 | //Polynomial: f[25]=x2y-y3+x4-y4 |
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127 | FF[25]=list(intmat(intvec(0,1,1,1,0,1,1,1,0),3,3),list(intvec(1),intvec(1),intvec(1))); |
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128 | //Polynomial: f[26]=x4y+x6+x4y2+x3y3+2x2y4+x5y2+2x4y3+x3y4+2x2y5+xy6+y7+x3y5+x2y6+xy7+y8 |
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129 | FF[26]=list(intmat(intvec(0,1,1,1,0,4,1,4,0),3,3),list(intvec(1),intvec(2,3),intvec(2,3))); |
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130 | //Polynomial: f[27] |
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131 | FF[27]=list(intmat(intvec(0,1,1,0),2,2),list(intvec(15,25,27),intvec(5,11))); |
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132 | //Polynomial: f[28] |
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133 | FF[28]=list(intmat(intvec(0,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,0,2,1,1,1,1,1,2,0,1,1,1,1,1,1,1,0,4,2,1,1,1,1,4,0,2,1,1,1,1,2,2,0),7,7),list(intvec(1),intvec(1),intvec(15,25,27),intvec(1),intvec(2,3),intvec(2,3),intvec(5,11))); |
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134 | //Polynomial: f[29] |
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135 | FF[29]=list(intmat(intvec(0,2,2,0),2,2),list(intvec(6,8,9),intvec(8,20,21))); |
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136 | //Polynomial: f[30]=-y12-4x3y10-xy12-5x6y8-2x5y9-x4y10-4x8y7+x7y8+5x12y4+4x15y2+4x14y3+x18+2x17y+x16y2 |
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137 | FF[30]=list(intmat(intvec(0,3,3,3,0,4,3,4,0),3,3),list(intvec(2,3),intvec(2,3),intvec(8,12,14,15))); |
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138 | //Polynomial: f[31] |
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139 | FF[31]=list(intmat(intvec(0,2,2,2,2,2,0,2,2,2,2,2,0,3,3,2,2,3,0,3,2,2,3,3,0),5,5),list(intvec(8,12,14,15),intvec(2,5),intvec(2,5),intvec(1),intvec(1))); |
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140 | //Polynomial: f[32]=2x2+3xy-x2y+4xy3 |
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141 | FF[32]=list(intmat(intvec(0,1,1,0),2,2),list(intvec(1),intvec(1))); |
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142 | //Polynomial: f[33]=x4-10x3y+35x2y2-50xy3+24y4 |
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143 | FF[33]=list(intmat(intvec(0,1,1,1,1,0,1,1,1,1,0,1,1,1,1,0),4,4),list(intvec(1),intvec(1),intvec(1),intvec(1))); |
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144 | //Polynomial: f[34]=x5-15x4y+85x3y2-225x2y3+274xy4-120y5 |
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145 | FF[34]=list(intmat(intvec(0,1,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,1,0),5,5),list(intvec(1),intvec(1),intvec(1),intvec(1),intvec(1))); |
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146 | //Polynomial: f[35] |
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147 | FF[35]=list(intmat(intvec(0,2,1,2,0,1,1,1,0),3,3),list(intvec(4,6,7),intvec(3,7),intvec(2,11))); |
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148 | //Polynomial: f[36]=y14-7x3y12+21x6y10-35x9y8+35x12y6-21x15y4-14x13y6+7x18y2-70x16y4-x21-42x19y2-2x22-x23 |
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149 | FF[36]=list(intmat(intvec(0),1,1),list(intvec(14,21,23))); |
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150 | //Polynomial: f[37]=y7-7x4y6+21x8y5-35x12y4+35x16y3-21x20y2+7x24y-x28-x29 |
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151 | FF[37]=list(intmat(intvec(0),1,1),list(intvec(7,29))); |
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152 | //Polynomial: f[38]=y2+x3 |
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153 | FF[38]=list(intmat(intvec(0),1,1),list(intvec(2,3))); |
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154 | //Polynomial: f[39]=y4+2x3y2+x6+x5y |
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155 | FF[39]=list(intmat(intvec(0),1,1),list(intvec(4,6,7))); |
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156 | //Polynomial: f[40]=y8+4x3y6+6x6y4+2x5y5+4x9y2+4x8y3+x12+2x11y+2x10y2+x13 |
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157 | FF[40]=list(intmat(intvec(0),1,1),list(intvec(8,12,14,15))); |
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158 | //Polynomial: f[41] |
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159 | FF[41]=list(intmat(intvec(0),1,1),list(intvec(16,24,28,30,31))); |
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160 | //Polynomial: f[42] |
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161 | FF[42]=list(intmat(intvec(0),1,1),list(intvec(32,48,56,60,62,63))); |
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162 | //Polynomial: f[43] |
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163 | FF[43]=list(intmat(intvec(0,4,4,4,0,6,4,6,0),3,3),list(intvec(2,3),intvec(8,12,14,15),intvec(4,6,7))); |
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164 | //Polynomial: f[44] |
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165 | FF[44]=list(intmat(intvec(0,8,8,0),2,2),list(intvec(32,48,56,60,62,63),intvec(8,12,14,15))); |
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166 | //Polynomial: f[45] |
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167 | FF[45]=list(intmat(intvec(0,3,3,0),2,2),list(intvec(4,6,7),intvec(12,20,21))); |
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168 | //Polynomial: f[46] |
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169 | FF[46]=list(intmat(intvec(0,1,1,2,2,2,1,0,8,1,1,1,1,8,0,1,1,1,2,1,1,0,9,6,2,1,1,9,0,6,2,1,1,6,6,0),6,6),list(intvec(4,10,11),intvec(7,8),intvec(15,16),intvec(12,18,19),intvec(14,21,22),intvec(10,15,17))); |
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170 | //Polynomial: f[47]=(x5-y7)(x10-y17) |
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171 | FF[47]=list(intmat(intvec(0,3,3,0),2,2),list(intvec(5,7),intvec(10,17))); |
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172 | //Polynomial: f[48]=(x5-y7)(x13-y23) |
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173 | FF[48]=list(intmat(intvec(0,3,3,0),2,2),list(intvec(5,7),intvec(13,23))); |
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174 | //Polynomial: f[49]=(x5-y7)(x4383-y5344) |
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175 | FF[49]=list(intmat(intvec(0,4,4,0),2,2),list(intvec(5,7),intvec(4383,5344))); |
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176 | //Polynomial: f[50]=(x5-y7)(x10-y17)(x7-y11) |
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177 | FF[50]=list(intmat(intvec(0,3,3,3,0,4,3,4,0),3,3),list(intvec(5,7),intvec(10,17),intvec(7,11))); |
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178 | //Polynomial: f[51]=f[4]*(x2+y3)*f[5]; |
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179 | FF[51]=list(intmat(intvec(0,1,1,1,0,2,1,2,0),3,3),list(intvec(15,25,27),intvec(2,3),intvec(5,11))); |
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180 | |
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181 | ////////////////////////////////////////////////////////////////////////////////////// |
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182 | /// Examples, created from f_irr |
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183 | ////////////////////////////////////////////////////////////////////////////////////// |
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184 | // Consider the product of all the polynomials in f_irr. |
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185 | // Polynomial: (x-y) (x+y) (y-x2+x3) (y2-x3-x4) (y2-2x2y+x4+x5) (y2-4x2y+4x4+x5) (x-y2) (x+y2) (x+y4) (x3-y5) (x5-y7) (x7-y11) (x11-y13) (y+x2+y2) (y15-5x5y12+10x10y9-3x9y10-10x15y6-90x14y7+5x20y3-135x19y4+3x18y5-x25-15x24y-30x23y2-x27) (x5-y11) (y8+4x3y6+xy8+6x6y4+2x5y5+x4y6+4x9y2+4x8y3+x12+2x11y+x10y2) (y6-2x4y3-3x3y4+x8-6x7y+3x6y2-x9) (y8-4x5y6+6x10y4-8x13y3-4x15y2-8x18y+x20-x21) (y12-6x3y10+15x6y8-20x9y6+15x12y4-12x11y5-6x15y2-40x14y3+x18-12x17y-x19) (y14-7x3y12+21x6y10-35x9y8+35x12y6-2x11y7-21x15y4-42x14y5+7x18y2-70x17y3-x21-14x20y+x22) (y10-5x3y8+10x6y6-10x9y4+5x12y2-10x10y4-x15-20x13y2-2x16-x17) (y4-2x5y2-4x8y+x10-x11) (x7-y8) (x15-y16) (y14-7x3y12+21x6y10-35x9y8+35x12y6-21x15y4-14x13y6+7x18y2-70x16y4-x21-42x19y2-2x22-x23) (y7-7x4y6+21x8y5-35x12y4+35x16y3-21x20y2+7x24y-x28-x29) (y2+x3) (y4+2x3y2+x6+x5y) (y8+4x3y6+6x6y4+2x5y5+4x9y2+4x8y3+x12+2x11y+2x10y2+x13) (y16+8x3y14+28x6y12+4x5y13+56x9y10+24x8y11+70x12y8+60x11y9+8x10y10+56x15y6+80x14y7+34x13y8+28x18y4+60x17y5+56x16y6+8x15y7+8x21y2+24x20y3+44x19y4+20x18y5+x24+4x23y+16x22y2+16x21y3+5x20y4+2x25+4x24y+6x23y2+2x26+x25y) (y32+16x3y30+120x6y28+8x5y29+560x9y26+112x8y27+1820x12y24+728x11y25+32x10y26+4368x15y22+2912x14y23+388x13y24+8008x18y20+8008x17y21+2160x16y22+80x15y23+11440x21y18+16016x20y19+7304x19y20+824x18y21+12870x24y16+24024x23y17+16720x22y18+3840x21y19+138x20y20+11440x27y14+27456x26y15+27324x25y16+10680x24y17+1180x23y18+8008x30y12+24024x29y13+32736x28y14+19680x27y15+4480x26y16+170x25y17+4368x33y10+16016x32y11+29040x31y12+25200x30y13+9920x29y14+1168x28y15+1820x36y8+8008x35y9+19008x34y10+22848x33y11+14140x32y12+3472x31y13+152x30y14+560x39y6+2912x38y7+9020x37y8+14640x36y9+13496x35y10+5824x34y11+804x33y12+120x42y4+728x41y5+2992x40y6+6480x39y7+8680x38y8+6020x37y9+1776x36y10+96x35y11+16x45y2+112x44y3+648x43y4+1880x42y5+3680x41y6+3920x40y7+2112x39y8+364x38y9+x48+8x47y+80x46y2+320x45y3+970x44y4+1568x43y5+1448x42y6+544x41y7+42x40y8+4x49+24x48y+140x47y2+352x46y3+564x45y4+400x44y5+104x43y6+8x50+34x49y+112x48y2+144x47y3+94x46y4+12x45y5+8x51+20x50y+36x49y2+16x48y3+5x52+6x51y+3x50y2+x53) (y4-2x3y2+x6-4x5y-x7) (y12-4x5y9-3x7y8+6x10y6-48x12y5-4x15y3+3x14y4-30x17y2+x20-12x19y-x21) (x10-y17) (x13-y23) (x204-y1111) (x4383-y5344) |
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186 | FF[52]=list(intmat(intvec(0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,2,3,2,1,1,1,1,1,1,1,2,2,1,2,2,2,2,2,2,2,1,1,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,2,0,2,2,1,1,1,1,1,1,1,2,3,1,3,3,2,4,4,4,2,1,1,4,2,3,3,3,3,3,4,3,1,1,1,1,1,1,3,2,0,2,1,1,1,1,1,1,1,2,2,1,2,2,2,2,2,2,2,1,1,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,2,2,2,0,1,1,1,1,1,1,1,2,2,1,2,2,2,2,2,2,2,1,1,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,0,2,2,2,2,2,2,1,1,2,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,2,0,2,2,2,2,2,1,1,2,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,2,2,0,2,2,2,2,1,1,3,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,2,2,4,2,1,1,1,1,1,1,2,2,2,0,3,4,3,1,1,2,1,1,1,1,1,1,1,3,3,1,1,1,1,1,1,1,1,1,4,4,2,3,1,1,1,1,1,1,2,2,2,3,0,3,4,1,1,2,1,1,1,1,1,1,1,4,4,1,1,1,1,1,1,1,1,1,3,3,2,4,1,1,1,1,1,1,2,2,2,4,3,0,3,1,1,2,1,1,1,1,1,1,1,3,3,1,1,1,1,1,1,1,1,1,4,4,2,3,1,1,1,1,1,1,2,2,2,3,4,3,0,1,1,2,1,1,1,1,1,1,1,7,7,1,1,1,1,1,1,1,1,1,3,3,2,6,1,1,2,2,2,2,1,1,1,1,1,1,1,0,2,1,2,2,2,2,2,2,2,1,1,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,2,3,2,2,1,1,1,1,1,1,1,2,0,1,3,3,2,3,3,3,2,1,1,3,2,3,3,3,3,3,3,7,1,1,1,1,1,1,1,1,1,1,2,2,3,2,2,2,2,1,1,0,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,2,2,3,2,1,1,2,3,2,2,1,1,1,1,1,1,1,2,3,1,0,3,2,3,3,3,2,1,1,3,2,4,6,7,7,7,3,3,1,1,1,1,1,1,2,3,2,2,1,1,1,1,1,1,1,2,3,1,3,0,2,3,3,3,2,1,1,3,2,3,3,3,3,3,3,3,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1,2,2,1,2,2,0,2,2,2,6,1,1,2,3,2,2,2,2,2,2,2,1,1,1,1,1,1,2,4,2,2,1,1,1,1,1,1,1,2,3,1,3,3,2,0,9,6,2,1,1,7,2,3,3,3,3,3,5,3,1,1,1,1,1,1,2,4,2,2,1,1,1,1,1,1,1,2,3,1,3,3,2,9,0,6,2,1,1,7,2,3,3,3,3,3,5,3,1,1,1,1,1,1,2,4,2,2,1,1,1,1,1,1,1,2,3,1,3,3,2,6,6,0,2,1,1,6,2,3,3,3,3,3,5,3,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1,2,2,1,2,2,6,2,2,2,0,1,1,2,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,2,2,2,3,4,3,7,1,1,2,1,1,1,1,1,1,1,0,8,1,1,1,1,1,1,1,1,1,3,3,2,6,1,1,1,1,1,1,2,2,2,3,4,3,7,1,1,2,1,1,1,1,1,1,1,8,0,1,1,1,1,1,1,1,1,1,3,3,2,6,1,1,2,4,2,2,1,1,1,1,1,1,1,2,3,1,3,3,2,7,7,6,2,1,1,0,2,3,3,3,3,3,5,3,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1,2,2,1,2,2,3,2,2,2,3,1,1,2,0,2,2,2,2,2,2,2,1,1,1,1,1,1,2,3,2,2,1,1,1,1,1,1,1,2,3,1,4,3,2,3,3,3,2,1,1,3,2,0,4,4,4,4,3,3,1,1,1,1,1,1,2,3,2,2,1,1,1,1,1,1,1,2,3,1,6,3,2,3,3,3,2,1,1,3,2,4,0,6,6,6,3,3,1,1,1,1,1,1,2,3,2,2,1,1,1,1,1,1,1,2,3,1,7,3,2,3,3,3,2,1,1,3,2,4,6,0,8,8,3,3,1,1,1,1,1,1,2,3,2,2,1,1,1,1,1,1,1,2,3,1,7,3,2,3,3,3,2,1,1,3,2,4,6,8,0,10,3,3,1,1,1,1,1,1,2,3,2,2,1,1,1,1,1,1,1,2,3,1,7,3,2,3,3,3,2,1,1,3,2,4,6,8,10,0,3,3,1,1,1,1,1,1,2,4,2,2,1,1,1,1,1,1,1,2,3,1,3,3,2,5,5,5,2,1,1,5,2,3,3,3,3,3,0,3,1,1,1,1,1,1,2,3,2,2,1,1,1,1,1,1,1,2,7,1,3,3,2,3,3,3,2,1,1,3,2,3,3,3,3,3,3,0,1,1,1,1,1,1,1,1,1,1,2,2,2,4,3,4,3,1,1,2,1,1,1,1,1,1,1,3,3,1,1,1,1,1,1,1,1,1,0,5,2,3,1,1,1,1,1,1,2,2,2,4,3,4,3,1,1,2,1,1,1,1,1,1,1,3,3,1,1,1,1,1,1,1,1,1,5,0,2,3,1,1,1,1,1,1,2,2,4,2,2,2,2,1,1,3,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,2,2,0,2,1,1,1,1,1,1,2,2,2,3,4,3,6,1,1,2,1,1,1,1,1,1,1,6,6,1,1,1,1,1,1,1,1,1,3,3,2,0),38,38),list(intvec(1),intvec(1),intvec(1),intvec(2,3),intvec(2,5),intvec(2,5),intvec(1),intvec(1),intvec(1),intvec(3,5),intvec(5,7),intvec(7,11),intvec(11,13),intvec(1),intvec(15,25,27),intvec(5,11),intvec(8,12,14,15),intvec(6,8,9),intvec(8,20,21),intvec(12,18,19),intvec(14,21,22),intvec(10,15,17),intvec(4,10,11),intvec(7,8),intvec(15,16),intvec(14,21,23),intvec(7,29),intvec(2,3),intvec(4,6,7),intvec(8,12,14,15),intvec(16,24,28,30,31),intvec(32,48,56,60,62,63),intvec(4,6,7),intvec(12,20,21),intvec(10,17),intvec(13,23),intvec(204,1111),intvec(4383,5344))); |
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187 | |
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188 | // Polynomial : as in FF[52] without the last four polynomials: (x-y) (x+y) (y-x2+x3) (y2-x3-x4) (y2-2x2y+x4+x5) (y2-4x2y+4x4+x5) (x-y2) (x+y2) (x+y4) (x3-y5) (x5-y7) (x7-y11) (x11-y13) (y+x2+y2) (y15-5x5y12+10x10y9-3x9y10-10x15y6-90x14y7+5x20y3-135x19y4+3x18y5-x25-15x24y-30x23y2-x27) (x5-y11) (y8+4x3y6+xy8+6x6y4+2x5y5+x4y6+4x9y2+4x8y3+x12+2x11y+x10y2) (y6-2x4y3-3x3y4+x8-6x7y+3x6y2-x9) (y8-4x5y6+6x10y4-8x13y3-4x15y2-8x18y+x20-x21) (y12-6x3y10+15x6y8-20x9y6+15x12y4-12x11y5-6x15y2-40x14y3+x18-12x17y-x19) (y14-7x3y12+21x6y10-35x9y8+35x12y6-2x11y7-21x15y4-42x14y5+7x18y2-70x17y3-x21-14x20y+x22) (y10-5x3y8+10x6y6-10x9y4+5x12y2-10x10y4-x15-20x13y2-2x16-x17) (y4-2x5y2-4x8y+x10-x11) (x7-y8) (x15-y16) (y14-7x3y12+21x6y10-35x9y8+35x12y6-21x15y4-14x13y6+7x18y2-70x16y4-x21-42x19y2-2x22-x23) (y7-7x4y6+21x8y5-35x12y4+35x16y3-21x20y2+7x24y-x28-x29) (y2+x3) (y4+2x3y2+x6+x5y) (y8+4x3y6+6x6y4+2x5y5+4x9y2+4x8y3+x12+2x11y+2x10y2+x13) (y16+8x3y14+28x6y12+4x5y13+56x9y10+24x8y11+70x12y8+60x11y9+8x10y10+56x15y6+80x14y7+34x13y8+28x18y4+60x17y5+56x16y6+8x15y7+8x21y2+24x20y3+44x19y4+20x18y5+x24+4x23y+16x22y2+16x21y3+5x20y4+2x25+4x24y+6x23y2+2x26+x25y) (y32+16x3y30+120x6y28+8x5y29+560x9y26+112x8y27+1820x12y24+728x11y25+32x10y26+4368x15y22+2912x14y23+388x13y24+8008x18y20+8008x17y21+2160x16y22+80x15y23+11440x21y18+16016x20y19+7304x19y20+824x18y21+12870x24y16+24024x23y17+16720x22y18+3840x21y19+138x20y20+11440x27y14+27456x26y15+27324x25y16+10680x24y17+1180x23y18+8008x30y12+24024x29y13+32736x28y14+19680x27y15+4480x26y16+170x25y17+4368x33y10+16016x32y11+29040x31y12+25200x30y13+9920x29y14+1168x28y15+1820x36y8+8008x35y9+19008x34y10+22848x33y11+14140x32y12+3472x31y13+152x30y14+560x39y6+2912x38y7+9020x37y8+14640x36y9+13496x35y10+5824x34y11+804x33y12+120x42y4+728x41y5+2992x40y6+6480x39y7+8680x38y8+6020x37y9+1776x36y10+96x35y11+16x45y2+112x44y3+648x43y4+1880x42y5+3680x41y6+3920x40y7+2112x39y8+364x38y9+x48+8x47y+80x46y2+320x45y3+970x44y4+1568x43y5+1448x42y6+544x41y7+42x40y8+4x49+24x48y+140x47y2+352x46y3+564x45y4+400x44y5+104x43y6+8x50+34x49y+112x48y2+144x47y3+94x46y4+12x45y5+8x51+20x50y+36x49y2+16x48y3+5x52+6x51y+3x50y2+x53) (y4-2x3y2+x6-4x5y-x7) (y12-4x5y9-3x7y8+6x10y6-48x12y5-4x15y3+3x14y4-30x17y2+x20-12x19y-x21) |
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189 | FF[53]=list(intmat(intvec(0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,2,3,2,1,1,1,1,1,1,1,2,2,1,2,2,2,2,2,2,2,1,1,2,2,2,2,2,2,2,2,2,1,1,2,0,2,2,1,1,1,1,1,1,1,2,3,1,3,3,2,4,4,4,2,1,1,4,2,3,3,3,3,3,4,3,1,1,3,2,0,2,1,1,1,1,1,1,1,2,2,1,2,2,2,2,2,2,2,1,1,2,2,2,2,2,2,2,2,2,1,1,2,2,2,0,1,1,1,1,1,1,1,2,2,1,2,2,2,2,2,2,2,1,1,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,0,2,2,2,2,2,2,1,1,2,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,0,2,2,2,2,2,1,1,2,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,0,2,2,2,2,1,1,3,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,0,3,4,3,1,1,2,1,1,1,1,1,1,1,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,0,3,4,1,1,2,1,1,1,1,1,1,1,4,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,4,3,0,3,1,1,2,1,1,1,1,1,1,1,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,4,3,0,1,1,2,1,1,1,1,1,1,1,7,7,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,1,1,1,1,1,1,1,0,2,1,2,2,2,2,2,2,2,1,1,2,2,2,2,2,2,2,2,2,1,1,2,3,2,2,1,1,1,1,1,1,1,2,0,1,3,3,2,3,3,3,2,1,1,3,2,3,3,3,3,3,3,7,1,1,1,1,1,1,2,2,3,2,2,2,2,1,1,0,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,1,1,1,1,2,3,2,2,1,1,1,1,1,1,1,2,3,1,0,3,2,3,3,3,2,1,1,3,2,4,6,7,7,7,3,3,1,1,2,3,2,2,1,1,1,1,1,1,1,2,3,1,3,0,2,3,3,3,2,1,1,3,2,3,3,3,3,3,3,3,1,1,2,2,2,2,1,1,1,1,1,1,1,2,2,1,2,2,0,2,2,2,6,1,1,2,3,2,2,2,2,2,2,2,1,1,2,4,2,2,1,1,1,1,1,1,1,2,3,1,3,3,2,0,9,6,2,1,1,7,2,3,3,3,3,3,5,3,1,1,2,4,2,2,1,1,1,1,1,1,1,2,3,1,3,3,2,9,0,6,2,1,1,7,2,3,3,3,3,3,5,3,1,1,2,4,2,2,1,1,1,1,1,1,1,2,3,1,3,3,2,6,6,0,2,1,1,6,2,3,3,3,3,3,5,3,1,1,2,2,2,2,1,1,1,1,1,1,1,2,2,1,2,2,6,2,2,2,0,1,1,2,3,2,2,2,2,2,2,2,1,1,1,1,1,1,2,2,2,3,4,3,7,1,1,2,1,1,1,1,1,1,1,0,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,3,4,3,7,1,1,2,1,1,1,1,1,1,1,8,0,1,1,1,1,1,1,1,1,1,1,1,2,4,2,2,1,1,1,1,1,1,1,2,3,1,3,3,2,7,7,6,2,1,1,0,2,3,3,3,3,3,5,3,1,1,2,2,2,2,1,1,1,1,1,1,1,2,2,1,2,2,3,2,2,2,3,1,1,2,0,2,2,2,2,2,2,2,1,1,2,3,2,2,1,1,1,1,1,1,1,2,3,1,4,3,2,3,3,3,2,1,1,3,2,0,4,4,4,4,3,3,1,1,2,3,2,2,1,1,1,1,1,1,1,2,3,1,6,3,2,3,3,3,2,1,1,3,2,4,0,6,6,6,3,3,1,1,2,3,2,2,1,1,1,1,1,1,1,2,3,1,7,3,2,3,3,3,2,1,1,3,2,4,6,0,8,8,3,3,1,1,2,3,2,2,1,1,1,1,1,1,1,2,3,1,7,3,2,3,3,3,2,1,1,3,2,4,6,8,0,10,3,3,1,1,2,3,2,2,1,1,1,1,1,1,1,2,3,1,7,3,2,3,3,3,2,1,1,3,2,4,6,8,10,0,3,3,1,1,2,4,2,2,1,1,1,1,1,1,1,2,3,1,3,3,2,5,5,5,2,1,1,5,2,3,3,3,3,3,0,3,1,1,2,3,2,2,1,1,1,1,1,1,1,2,7,1,3,3,2,3,3,3,2,1,1,3,2,3,3,3,3,3,3,0 ),34,34),list(intvec(1),intvec(1),intvec(1),intvec(2,3),intvec(2,5),intvec(2,5),intvec(1),intvec(1),intvec(1),intvec(3,5),intvec(5,7),intvec(7,11),intvec(11,13),intvec(1),intvec(15,25,27),intvec(5,11),intvec(8,12,14,15),intvec(6,8,9),intvec(8,20,21),intvec(12,18,19),intvec(14,21,22),intvec(10,15,17),intvec(4,10,11),intvec(7,8),intvec(15,16),intvec(14,21,23),intvec(7,29),intvec(2,3),intvec(4,6,7),intvec(8,12,14,15),intvec(16,24,28,30,31),intvec(32,48,56,60,62,63),intvec(4,6,7),intvec(12,20,21))); |
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190 | |
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191 | //Polynomial: f[54]=f_irr[26]*f_irr[27]*f_irr[28]*f_irr[29]; |
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192 | FF[54]=list(intmat(intvec(0,2,3,3,2,0,2,2,3,2,0,4,3,2,4,0),4,4),list(intvec(14,21,23),intvec(7,29),intvec(2,3),intvec(4,6,7))); |
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193 | |
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194 | ///////////////////////////////////////////////////////////////////////////////////// |
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195 | /// Examples of characteristic exponents |
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196 | ///////////////////////////////////////////////////////////////////////////////////// |
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197 | list vv; |
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198 | vv[1]=intvec(18,27,75,125); |
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199 | vv[2]=intvec(27,36,60,100); |
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200 | vv[3]=intvec(2,3); |
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201 | vv[4]=intvec(3,7); |
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202 | vv[5]=intvec(4,6,7); |
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203 | vv[6]=intvec(5,8); |
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204 | vv[7]=intvec(6,15,19); |
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205 | vv[8]=intvec(7,16); |
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206 | vv[9]=intvec(8,12,30,34); |
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207 | vv[10]=intvec(9,21,23); |
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208 | vv[11]=intvec(10,35,41); |
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209 | vv[12]=intvec(30,115,1001); |
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210 | vv[13]=intvec(100,150,375,420,672); |
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211 | vv[14]=intvec(8,20,30,31); |
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212 | |
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213 | ///////////////////////////////////////////////////////////////////////////////////// |
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214 | /// Examples of multiplicity sequences |
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215 | ///////////////////////////////////////////////////////////////////////////////////// |
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216 | list w; |
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217 | w[1]=intvec(2,1,1); |
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218 | w[2]=intvec(3,3,1,1,1); |
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219 | w[3]=intvec(4,2,2,1,1); |
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220 | w[4]=intvec(5,3,2,1,1); |
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221 | w[5]=intvec(6,6,3,3,3,1,1,1); |
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222 | w[6]=intvec(7,7,2,2,2,1,1); |
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223 | w[7]=intvec(8,4,4,4,4,4,4,2,2,2,2); |
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224 | w[8]=intvec(9,9,3,3,3,2,1,1); |
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225 | w[9]=intvec(10,10,10,5,5,5,1,1,1,1,1); |
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226 | w[10]=intvec(30,30,30,25,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,1,1,1,1,1); |
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227 | w[11]=intvec(100,50,50,50,50,50,50,25,25,25,20,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,2,2,1,1); |
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228 | w[12]=intvec(8,8,4,4,4,4,2,2,1,1); |
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229 | w[13]=intvec(18,9,9,9,9,9,9,9,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,2,1,1); |
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230 | w[14]=intvec(27,9,9,9,9,9,6,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,1,1,1); |
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231 | w[15]=intvec(36,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,6,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1); |
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232 | w[16]=intvec(21,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,2,1,1); |
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233 | |
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234 | // ------------ test of resolutiongraph: ------------------- |
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235 | resolutiongraph(f[1]); |
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236 | resolutiongraph(f[2]); |
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237 | list Hne=develop(f[6]); |
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238 | resolutiongraph(Hne); |
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239 | resolutiongraph(f[36]); |
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240 | resolutiongraph(FF[37]); |
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241 | intvec v=6,9,16; |
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242 | resolutiongraph(v); |
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243 | intmat M1[2][2]=0,3,3,0; |
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244 | intvec v1=2,3; |
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245 | intvec v2=4,6,7; |
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246 | list vectors=v1,v2; |
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247 | list L1=M1,vectors; |
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248 | resolutiongraph(L1); |
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249 | intmat M2[3][3]=0,2,4,2,0,2,4,2,0; |
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250 | intvec u1=6,8,9; |
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251 | intvec u2=6,14,15; |
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252 | intvec u3=8,10,11; |
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253 | resolutiongraph(list(M2,list(u1,u2,u3))); |
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254 | // ------------ test of totalmultiplicities and proximitymatrix: ------------------- |
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255 | totalmultiplicities(f[7]); |
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256 | totalmultiplicities(hnexpansion(f[8])); |
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257 | totalmultiplicities(f[9]); |
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258 | totalmultiplicities(f[14]*f[15]); |
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259 | totalmultiplicities(f[16]*f[17]*f[18]); |
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260 | intmat m1[2][2]=0,10,10,0; |
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261 | intvec v3=9,10; |
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262 | intvec v4=10,11; |
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263 | list L2=m1,list(v3,v4); |
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264 | totalmultiplicities(L2); |
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265 | intmat M3[3][3]=0,4,5,4,0,4,5,4,0; |
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266 | intvec z1=21,28,36; |
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267 | intvec z2=25,30,33; |
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268 | intvec z3=24,32,35; |
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269 | totalmultiplicities(list(M2,list(z1,z2,z3))); |
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270 | list TM; |
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271 | for (int i=1;i<=52;i++) |
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272 | { |
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273 | TM[i]=totalmultiplicities(FF[i]); |
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274 | TM[i]; |
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275 | proximitymatrix(TM[i][1]); |
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276 | } |
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277 | // ------------ test of alexanderpolynomial: ------------------- |
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278 | list ALEX=alexanderpolynomial(f[22]*f[23]); |
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279 | def ALEXring=ALEX[1]; |
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280 | setring ALEXring; |
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281 | alexpoly; |
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282 | zeta_monodromy; |
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283 | alexnumerator; |
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284 | alexdenominator; |
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285 | setring r; |
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286 | kill ALEXring; |
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287 | ALEX=alexanderpolynomial(f[22]*f[23]*f[24]); |
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288 | def ALEXring=ALEX[1]; |
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289 | setring ALEXring; |
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290 | alexpoly; |
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291 | zeta_monodromy; |
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292 | alexnumerator; |
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293 | alexdenominator; |
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294 | setring r; |
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295 | kill ALEXring; |
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296 | intvec vvv=18,27,30,31; |
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297 | ALEX=alexanderpolynomial(vvv); |
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298 | def ALEXring=ALEX[1]; |
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299 | setring ALEXring; |
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300 | alexpoly; |
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301 | zeta_monodromy; |
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302 | alexnumerator; |
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303 | alexdenominator; |
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304 | setring r; |
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305 | kill ALEXring; |
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306 | ALEX=alexanderpolynomial(hnexpansion(f[4]*f[5])); |
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307 | def ALEXring=ALEX[1]; |
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308 | setring ALEXring; |
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309 | alexpoly; |
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310 | zeta_monodromy; |
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311 | alexnumerator; |
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312 | alexdenominator; |
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313 | setring r; |
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314 | kill ALEXring; |
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315 | // ------------ test of semigroup: ------------------ |
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316 | semigroup(intvec(18,27,75,125)); |
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317 | semigroup(f[24]); |
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318 | for (i=1;i<=52;i++) |
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319 | { |
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320 | semigroup(FF[i]); |
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321 | } |
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322 | // ------------ test of charexp2multseq: ------------------ |
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323 | for (i=1;i<=14;i++) |
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324 | { |
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325 | charexp2multseq(vv[i]); |
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326 | } |
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327 | // ------------ test of charexp2generators: ------------------------ |
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328 | for (i=1;i<=14;i++) |
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329 | { |
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330 | charexp2generators(vv[i]); |
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331 | } |
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332 | // ------------ test of charexp2inter: ------------------------ |
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333 | charexp2inter(intmat(intvec(0,1,1,0),2,2),list(vv[3],vv[4])); |
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334 | charexp2inter(intmat(intvec(0,4,4,0),2,2),list(vv[2],vv[4])); |
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335 | charexp2inter(intmat(intvec(0,1,3,1,0,2,3,2,0),2,2),list(vv[13],vv[4],vv[9])); |
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336 | // ------------ test of charexp2conductor: ------------------------ |
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337 | for (i=1;i<=14;i++) |
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338 | { |
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339 | charexp2conductor(vv[i]); |
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340 | } |
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341 | // ------------ test of multseq2charexp: ------------------------ |
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342 | for (i=1;i<=16;i++) |
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343 | { |
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344 | multseq2charexp(w[i]); |
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345 | } |
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346 | // ------------ test of charexp2poly: ------------------- |
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347 | intvec a1=30,45,50,53; |
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348 | vector b1=[1,1,1]; |
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349 | charexp2poly(a1,b1); |
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350 | intvec a2=24,40,60,180,181; |
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351 | vector b2=[1,1,1,1]; |
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352 | charexp2poly(a2,b2); |
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353 | intvec a3=80,120,300,301; |
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354 | vector b3=[1,1,1]; |
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355 | charexp2poly(a3,b3); |
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356 | // ------------ test of tau_es2 -------------------------- |
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357 | for (i=2;i<=20;i++) |
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358 | { |
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359 | tau_es2(x^2-y^i); |
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360 | } |
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361 | for (i=2;i<=10;i++) |
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362 | { |
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363 | tau_es2(hnexpansion(y*(x^2-y^i))); |
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364 | } |
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365 | for (i=1;i<=size(FF)-1;i++) |
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366 | { |
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367 | tau_es2(FF[i]); |
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368 | } |
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369 | tau_es2(a1); |
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370 | // --------------- additions: ----------------------------- |
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371 | example resolutiongraph; |
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372 | example totalmultiplicities; |
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373 | example alexanderpolynomial; |
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374 | example semigroup; |
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375 | example proximitymatrix; |
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376 | example charexp2multseq; |
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377 | example multseq2charexp; |
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378 | example charexp2generators; |
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379 | example charexp2inter; |
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380 | example charexp2conductor; |
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381 | example charexp2poly; |
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382 | example tau_es2; |
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383 | // -------------------------------------------------------- |
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384 | tst_status(1);$ |
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385 | |
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