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| =Tutorials of the Robbiano/Kreuzer track= | | =Tutorials of the Robbiano/Kreuzer track= |
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| [http://apcocoa.org/~mabshoff/CoCoAVII/KR_tutorial_1.pdf Tutorial 1] (82kb) | | ==the tutorials== |
| | [[Image:KR_tutorial_1.pdf]] |
| | [[Image:KR_tutorial_2.pdf]] |
| | [[Image:KR_tutorial_3.pdf]] |
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| == the ideals for part c.) == | | ==input files== |
| | | [[Image:Input_1.coc]] |
| Use Q[x[1..4]];
| | [[Image:Input_3.coc]] |
| IsZeroDim(Ideal([x[1]x[3], x[1]x[4]-x[2]x[3], x[2]x[4]-x[3]^3, x[2]^2x[3]-x[1]x[3]^2]));
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| Use Q[x[1..3]];
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| IsZeroDim(Ideal([x[1]^3 - x[2]x[3]^2, x[1]^2x[2]x[3] - x[2]^2, x[1]^2 + x[2]^2 + x[3]^2]));
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| Use Q[x[1..4]];
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| IsZeroDim(Ideal([x[1]x[2]-x[3]^2,x[2]^2-x[3]x[4],x[1]x[3] - x[4]^3,x[2]x[4] - x[3]^2]));
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| Use Q[x[1..3]];
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| IsZeroDim(Ideal([x[1]^2 - x[1]x[2],x[2]^2-x[2]x[3],x[3]^2-x[3]x[1],x[1]x[2] + x[2]x[3] + x[1]x[3]]));
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| == the ideals for part f.) ==
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| Warning: Second ideal is NOT zero dimensional!
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| Use Q[x,y];
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| ZeroDimRadical(Ideal([x^3,x^2y,x,y^2]) );
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| Use Q[x,y,z];
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| ZeroDimRadical(Ideal([x^2 +2xy + y^2, xz+ yz, xy^2+y^3 + xy + y^2,y^4+2y^3 + y^2, y^2z + yz]));
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| Use Q[x,y,z];
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| ZeroDimRadical(Ideal([x^2 + y+z -1, x+y^2 + z -1, x+y+z^2 -1]));
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| == the ideals for part h.) ==
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| Use Q[x,y];
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| [IsNormalPos(Ideal([x^2+y^2-1,4xy-2x-2y+1]),I) | I In 1..NumIndets()];
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| Use Q[x,y];
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| [IsNormalPos(Ideal([x^2-y,x^2-3x+2]),I) | I In 1..NumIndets()];
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| Use Q[x,y,z];
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| [IsNormalPos(Ideal([yz + z, y^2+y,x+y+z,z^2-z]),I) | I In 1..NumIndets()];
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| == the ideals for part i.) ==
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| Use Q[x,y];
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| [NormalPosTrafo(Ideal([x^2 + y^2 +3, x^2 - y^2 +1]),I) | I In 1..NumIndets()];
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| Use Q[x,y];
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| [NormalPosTrafo(Ideal([xy,x^2+x,y^3+2y^2 + y]),I) | I In 1..NumIndets()];
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| Use Q[x,y,z];
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| [NormalPosTrafo(Ideal([x^3 - x, y^2 -y, z^2 - z]),I) | I In 1..NumIndets()];
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