| 1 | // $Id: paramet.tst,v 1.1 1998-08-07 11:58:32 obachman Exp $ |
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| 2 | |
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| 3 | // |
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| 4 | // paramet.tst -- short test fopr paramet.lib |
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| 5 | // |
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| 6 | LIB "tst.lib"; |
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| 7 | tst_init(); |
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| 8 | tst_ignore("$Id: paramet.tst,v 1.1 1998-08-07 11:58:32 obachman Exp $"); |
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| 9 | LIB "paramet.lib"; |
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| 10 | |
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| 11 | /// Examples for parametrize |
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| 12 | |
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| 13 | /// Example 1 |
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| 14 | |
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| 15 | |
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| 16 | ring r=0,(x,y),dp; |
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| 17 | ideal i=x^2-y^3; |
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| 18 | parametrize(i); |
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| 19 | |
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| 20 | /// Example 2 |
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| 21 | |
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| 22 | ring r=0,(x,y,z),dp; |
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| 23 | ideal i=x2-y2z2-y3; |
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| 24 | parametrize(i); |
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| 25 | |
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| 26 | /// Example 3 |
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| 27 | |
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| 28 | ring r=0,(x,y,z),dp; |
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| 29 | ideal i=z2-x2y; |
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| 30 | parametrize(i); |
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| 31 | |
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| 32 | /// Example 4 |
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| 33 | |
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| 34 | ring r=0,(x,y,z),dp; |
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| 35 | ideal i=z2-x2y; |
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| 36 | parametrize(i); |
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| 37 | |
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| 38 | /// Example 5 |
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| 39 | |
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| 40 | ring r=0,(x,y,z),dp; |
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| 41 | ideal i=x2-y3; |
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| 42 | parametrize(i); |
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| 43 | |
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| 44 | /// Example 6 |
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| 45 | |
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| 46 | ring r=0,(x,y,z),dp; |
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| 47 | ideal i=y2-xz,z2-x2y,x3-yz; |
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| 48 | parametrize(i); |
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| 49 | |
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| 50 | /// Example 7 - ideal is not prime |
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| 51 | |
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| 52 | ring r=0,(x,y),dp; |
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| 53 | ideal i=xy; |
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| 54 | parametrize(i); |
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| 55 | |
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| 56 | /// Example 8 - you get a parametrization of the reduced ideal |
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| 57 | |
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| 58 | ring r=0,(x,y),dp; |
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| 59 | ideal i=x2; |
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| 60 | parametrize(i); |
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| 61 | |
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| 62 | /// Example 9 - wrong ordering |
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| 63 | |
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| 64 | //ring r=0,(x,y),ls; |
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| 65 | //ideal i=x2-y3; |
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| 66 | //parametrize(i); |
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| 67 | |
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| 68 | |
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| 69 | |
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| 70 | |
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| 71 | |
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| 72 | ///////////////////////////////////////////////////////////////////// |
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| 73 | |
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| 74 | /// Examples for parametrizepd |
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| 75 | |
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| 76 | /// Example 1 |
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| 77 | ring r=0,(x,y,z),dp; |
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| 78 | ideal i=y2z5-x2y2z2+y2z4-z6-z5+x4-x2z2,-y3z3+yz4+x2yz; |
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| 79 | parametrizepd(i); |
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| 80 | |
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| 81 | /// Example 2 |
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| 82 | |
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| 83 | ring r=0,(x,y,z),dp; |
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| 84 | ideal i=z^2-x^2*y,y^2-x*z; |
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| 85 | parametrizepd(i); |
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| 86 | |
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| 87 | /// Example 3 |
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| 88 | |
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| 89 | ring r=0,(x,y,z),dp; |
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| 90 | ideal i=y^5*z^2-x^2*y^6-x*y^3*z^3+x^3*y^4*z-x^4*y^2*z^2+x^6*y^3+x^5*z^3-x^7*y*z,y^6*z^2-x^2*y^7-2*x^4*y^3*z^2+2*x^6*y^4+x^8*z^2-x^(10)*y; |
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| 91 | parametrizepd(i); |
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| 92 | |
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| 93 | /// Example 4 |
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| 94 | |
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| 95 | ring r=0,(x,y,z),dp; |
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| 96 | ideal i=y^6*z^2-x^2*y^7-x*y^4*z^3+x^3*y^5*z-x^3*y^2*z^2+x^5*y^3+x^4*z^3-x^6*y*z,y^8*z^2-x^2*y^9-2*x^3*y^4*z^2+2*x^5*y^5+x^6*z^2-x^8*y; |
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| 97 | parametrizepd(i); |
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| 98 | |
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| 99 | /// Example 5 - gives a parametrization which is not suitable for plotting reasons |
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| 100 | |
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| 101 | ring r=0,(x,y,z,u),dp; |
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| 102 | ideal i=x-zu,y2-zu2; |
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| 103 | parametrizepd(i); |
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| 104 | |
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| 105 | /// Example 6 - one component has no parametrization |
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| 106 | |
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| 107 | ring r=0,(x,y,z),dp; |
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| 108 | ideal i=-x2y3+x3yz+y2z2-xz3,y2z-xz2; |
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| 109 | parametrizepd(i); |
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| 110 | |
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| 111 | /// Example 7 - wrong ordering! |
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| 112 | |
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| 113 | //ring r=0,(x,y,z),ls; |
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| 114 | //ideal i=x2-y2z2-y3; |
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| 115 | //parametrizepd(i); |
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| 116 | |
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| 117 | |
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| 118 | |
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| 119 | /////////////////////////////////////////////////////////////////// |
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| 120 | |
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| 121 | /// Examples for parametrizesing |
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| 122 | |
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| 123 | /// Example 1 |
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| 124 | |
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| 125 | ring r=0,(x,y),ls; |
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| 126 | poly f=x^2-y^3; |
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| 127 | parametrizesing(f); |
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| 128 | |
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| 129 | /// Example 2 |
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| 130 | |
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| 131 | ring r=0,(x,y),ls; |
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| 132 | poly f=x^3+y^3-3*x*y; |
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| 133 | parametrizesing(f); |
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| 134 | |
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| 135 | /// Example 3 |
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| 136 | |
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| 137 | ring r=0,(x,y),ls; |
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| 138 | poly f=y*x^2-y^8; |
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| 139 | parametrizesing(f); |
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| 140 | |
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| 141 | /// Example 4 |
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| 142 | |
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| 143 | ring r=0,(x,y),ls; |
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| 144 | poly f=-x6-x5+2x3y2+x2y2-y4; |
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| 145 | parametrizesing(f); |
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| 146 | |
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| 147 | /// Example 5 |
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| 148 | |
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| 149 | ring r=0,(x,y),ls; |
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| 150 | poly f=x6y4-x8y+x5y4-2x3y6-x7y+2x5y3-x2y6+y8+x4y3-x2y5; |
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| 151 | parametrizesing(f); |
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| 152 | |
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| 153 | /// Example 6 - wrong number of variables |
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| 154 | |
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| 155 | ring r=0,(x,y,z),dp; |
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| 156 | poly f=x2-y2z2-y3; |
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| 157 | parametrizesing(f); |
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| 158 | |
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| 159 | /// Example 7 - wrong ring ordering |
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| 160 | |
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| 161 | ring r=0,(x,y),lp; |
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| 162 | poly f=x2-y3; |
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| 163 | parametrizesing(f); |
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| 164 | tst_status(1);$ |
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| 165 | |
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| 166 | |
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| 167 | |
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