| 1 | LIB "tst.lib"; |
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| 2 | tst_init(); |
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| 3 | |
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| 4 | LIB "locnormal.lib"; |
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| 5 | // plane curves |
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| 6 | |
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| 7 | ring r24 = 0,(x,y,z),dp; |
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| 8 | int k = 2; |
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| 9 | poly f = (x^(k+1)+y^(k+1)+z^(k+1))^2-4*(x^(k+1)*y^(k+1)+y^(k+1)*z^(k+1)+z^(k+1)*x^(k+1)); |
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| 10 | f = subst(f,z,2x-y+1); |
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| 11 | ring s24 = 0,(x,y),dp; |
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| 12 | poly f = imap(r24,f); |
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| 13 | ideal i = f; |
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| 14 | |
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| 15 | locNormal(i); |
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| 16 | //modNormal(i,1); |
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| 17 | |
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| 18 | |
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| 19 | ring r24 = 0,(x,y,z),dp; |
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| 20 | int k = 3; |
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| 21 | poly f = (x^(k+1)+y^(k+1)+z^(k+1))^2-4*(x^(k+1)*y^(k+1)+y^(k+1)*z^(k+1)+z^(k+1)*x^(k+1)); |
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| 22 | f = subst(f,z,2x-y+1); |
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| 23 | ring s24 = 0,(x,y),dp; |
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| 24 | poly f = imap(r24,f); |
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| 25 | ideal i = f; |
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| 26 | locNormal(i); |
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| 27 | //modNormal(i,1,"noVerification"); |
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| 28 | |
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| 29 | |
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| 30 | ring r24 = 0,(x,y,z),dp; |
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| 31 | int k = 4; |
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| 32 | poly f = (x^(k+1)+y^(k+1)+z^(k+1))^2-4*(x^(k+1)*y^(k+1)+y^(k+1)*z^(k+1)+z^(k+1)*x^(k+1)); |
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| 33 | f = subst(f,z,2x-y+1); |
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| 34 | ring s24 = 0,(x,y),dp; |
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| 35 | poly f = imap(r24,f); |
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| 36 | ideal i = f; |
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| 37 | |
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| 38 | locNormal(i); |
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| 39 | //modNormal(i,1,"noVerification"); |
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| 40 | |
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| 41 | |
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| 42 | ring r24 = 0,(x,y,z),dp; |
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| 43 | int k = 5; |
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| 44 | poly f = (x^(k+1)+y^(k+1)+z^(k+1))^2-4*(x^(k+1)*y^(k+1)+y^(k+1)*z^(k+1)+z^(k+1)*x^(k+1)); |
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| 45 | f = subst(f,z,2x-y+1); |
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| 46 | ring s24 = 0,(x,y),dp; |
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| 47 | poly f = imap(r24,f); |
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| 48 | ideal i = f; |
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| 49 | |
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| 50 | locNormal(i); |
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| 51 | ring s24 = 0,(x,y),dp; |
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| 52 | int a=7; |
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| 53 | ideal i = ((x-1)^a-y^3)*((x+1)^a-y^3)*((x)^a-y^3)*((x-2)^a-y^3)*((x+2)^a-y^3)+y^15; |
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| 54 | |
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| 55 | locNormal(i); |
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| 56 | //modNormal(i,1); |
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| 57 | |
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| 58 | |
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| 59 | ring s24 = 0,(x,y),dp; |
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| 60 | int a=7; |
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| 61 | ideal i = ((x-1)^a-y^3)*((x+1)^a-y^3)*((x)^a-y^3)*((x-2)^a-y^3)*((x+2)^a-y^3)+y^15; |
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| 62 | |
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| 63 | locNormal(i); |
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| 64 | //modNormal(i,1); |
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| 65 | |
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| 66 | ring s24 = 0,(x,y),dp; |
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| 67 | int a=7; |
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| 68 | ideal i = ((x-1)^a-y^3)*((x+1)^a-y^3)*((x)^a-y^3)*((x-2)^a-y^3)*((x+2)^a-y^3)+y^15; |
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| 69 | |
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| 70 | locNormal(i); |
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| 71 | //modNormal(i,1,"noVerification"); |
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| 72 | |
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| 73 | ring r=0,(x,y),dp; |
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| 74 | ideal i=9127158539954x10+3212722859346x8y2+228715574724x6y4-34263110700x4y6 |
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| 75 | -5431439286x2y8-201803238y10-134266087241x8-15052058268x6y2+12024807786x4y4 |
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| 76 | +506101284x2y6-202172841y8+761328152x6-128361096x4y2+47970216x2y4-6697080y6 |
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| 77 | -2042158x4+660492x2y2-84366y4+2494x2-474y2-1; |
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| 78 | |
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| 79 | locNormal(i); |
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| 80 | //modNormal(i,1); |
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| 81 | |
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| 82 | |
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| 83 | // surfaces in A3 |
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| 84 | |
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| 85 | |
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| 86 | ring r7 = 0,(x,y,t),dp; |
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| 87 | int a=11; |
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| 88 | ideal i = x*y*(x-y)*(x+y)*(y-1)*t+(x^a-y^2)*(x^10-(y-1)^2); |
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| 89 | locNormal(i); |
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| 90 | //modNormal(i,1,"noVerification"); |
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| 91 | |
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| 92 | ring r7 = 0,(x,y,t),dp; |
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| 93 | int a=12; |
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| 94 | ideal i = x*y*(x-y)*(x+y)*(y-1)*t+(x^a-y^2)*(x^10-(y-1)^2); |
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| 95 | locNormal(i); |
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| 96 | //modNormal(i,1,"noVerification"); |
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| 97 | |
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| 98 | |
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| 99 | ring r7 = 0,(x,y,t),dp; |
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| 100 | int a=13; |
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| 101 | ideal i = x*y*(x-y)*(x+y)*(y-1)*t+(x^a-y^2)*(x^10-(y-1)^2); |
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| 102 | |
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| 103 | locNormal(i); |
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| 104 | |
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| 105 | ring r22 = 0,(x,y,z),dp; |
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| 106 | ideal i = z2-(y2-1234x3)^2*(15791x2-y3)*(1231y2-x2*(x+158))*(1357y5-3x11); |
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| 107 | |
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| 108 | locNormal(i); |
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| 109 | //modNormal(i,1,"noVerification"); |
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| 110 | |
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| 111 | |
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| 112 | ring r23 = 0,(x,y,z),dp; |
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| 113 | ideal i = z5-((13x-17y)*(5x2-7y3)*(3x3-2y2)*(19y2-23x2*(x+29)))^2; |
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| 114 | |
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| 115 | locNormal(i); |
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| 116 | // curve in A3 |
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| 117 | |
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| 118 | ring r23 = 0,(x,y,z),dp; |
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| 119 | ideal i = z3-(19y2-23x2*(x+29))^2,x3-(11y2-13z2*(z+1)); |
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| 120 | |
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| 121 | locNormal(i); |
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| 122 | //modNormal(i,1,"noVerification"); |
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| 123 | |
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| 124 | |
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| 125 | ring r23 = 0,(x,y,z),dp; |
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| 126 | ideal i = z3-(19y2-23x2*(x+29))^2,x3-(11y2-13z2*(z+1))^2; |
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| 127 | |
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| 128 | locNormal(i); |
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| 129 | //modNormal(i,1,"noVerification"); |
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| 130 | |
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| 131 | // surface in A4 |
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| 132 | |
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| 133 | ring r23 = 0,(x,y,z,w),dp; |
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| 134 | ideal i = z2-(y3-123456w2)*(15791x2-y3)^2, w*z-(1231y2-x*(111x+158)); |
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| 135 | |
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| 136 | |
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| 137 | locNormal(i); |
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| 138 | //modNormal(i,1,"noVerification"); |
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| 139 | |
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| 140 | tst_status(1);$ |
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