1 | LIB "tst.lib"; |
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2 | tst_init(); |
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3 | |
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4 | ring r1 = integer,(x,y,z),dp; |
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5 | ideal i = x4+y2+z2; |
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6 | qring q = i; |
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7 | ideal s = 2z,-4z2,-4yz,-4xz,-2x2z-2yz-2z2,-x4-y2-z2; |
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8 | module a=syz(s); |
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9 | print( NF(module(transpose(a)*transpose(s)),std(0)) ); |
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10 | |
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11 | ring r2=integer,(x, y),dp; |
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12 | ideal I=81*y^6-162*y^5-27*y^4-x^2-9*y^2+18*y+3; |
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13 | qring qr2=I; |
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14 | ideal s=6, |
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15 | -36, |
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16 | -12*x, |
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17 | -18*y^3-18*y^2-18*x-18*y-18, |
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18 | -6*x*y^3-18*x*y^2-18*x^2-18*x*y-18*x, |
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19 | -81*y^6+162*y^5+27*y^4+x^2+9*y^2-18*y-3; |
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20 | module a=syz(s); |
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21 | print( NF(module(transpose(a)*transpose(s)),std(0)) ); |
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22 | |
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23 | ring r3=integer,(x, y),dp; |
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24 | ideal I=81*y^6-162*y^5; |
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25 | qring qr3=I; |
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26 | ideal s=6; |
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27 | module a=syz(s); |
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28 | print( NF(module(transpose(a)*transpose(s)),std(0)) ); |
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29 | |
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30 | ring r4 = integer,(x, y),dp; |
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31 | ideal I=81*y^6-162*y^5-27*y^4-x^2-9*y^2+18*y+3; |
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32 | qring qr4=I; |
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33 | ideal s=6, |
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34 | -36, |
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35 | -12*x, |
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36 | -18*y^3-18*y^2-18*x-18*y-18, |
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37 | -6*x*y^3-18*x*y^2-18*x^2-18*x*y-18*x; |
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38 | module a=syz(s); |
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39 | print( NF(module(transpose(a)*transpose(s)),std(0)) ); |
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40 | |
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41 | ring r5=(integer),(x,y,z),(dp(3),C); |
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42 | |
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43 | ideal I = x*y-3, |
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44 | 3*y^6+18*y^5*z-9*y^4*z^2-27*y^2*z^4-162*y*z^5+81*z^6-y^4, |
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45 | 27*x*z^6+3*y^5+18*y^4*z-9*y^3*z^2-27*y*z^4-162*z^5-y^3, |
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46 | 9*x^2*z^6-54*x*z^5+3*y^4+18*y^3*z-9*y^2*z^2-27*z^4-y^2, |
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47 | 3*x^3*z^6-18*x^2*z^5-9*x*z^4+3*y^3+18*y^2*z-9*y*z^2-y, |
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48 | x^4*z^6-6*x^3*z^5-3*x^2*z^4+3*y^2+18*y*z-9*z^2-1; |
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49 | |
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50 | module a=syz(I); |
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51 | print( module(transpose(a)*transpose(I)) ); |
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52 | kill a; |
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53 | |
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54 | ideal s =x*y+1, |
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55 | -4, |
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56 | -2*x*y-2, |
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57 | -2*y^3-2*y^2*z-2*y*z^2-2*z^3-2*y^2, |
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58 | -2*x*z^3+2*y^2+2*y*z+2*z^2+2*y, |
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59 | -x*y+3, |
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60 | -3*y^6-18*y^5*z+9*y^4*z^2+27*y^2*z^4+162*y*z^5-81*z^6+y^4, |
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61 | -27*x*z^6-3*y^5-18*y^4*z+9*y^3*z^2+27*y*z^4+162*z^5+y^3, |
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62 | -9*x^2*z^6+54*x*z^5-3*y^4-18*y^3*z+9*y^2*z^2+27*z^4+y^2; |
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63 | |
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64 | module a=syz(s); |
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65 | print( module(transpose(a)*transpose(s)) ); |
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66 | |
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67 | tst_status(1);$ |
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68 | |
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