Difference between revisions of "CoCoASchool2007"
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== the ideals for part c.) == | == the ideals for part c.) == | ||
| − | Use Q[x[1..4]]; | + | Use Q[x[1..4]]; |
| − | 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])); | + | 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])); |
| − | + | ||
| − | Use Q[x[1..3]]; | + | Use Q[x[1..3]]; |
| − | 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])); | + | 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])); |
| − | + | ||
| − | Use Q[x[1..4]]; | + | Use Q[x[1..4]]; |
| − | 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])); | + | 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])); |
| − | + | ||
| − | Use Q[x[1..3]]; | + | Use Q[x[1..3]]; |
| − | 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]])); | + | 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]])); |
| − | + | ||
== the ideals for part f.) == | == the ideals for part f.) == | ||
Warning: Second ideal is NOT zero dimensional! | Warning: Second ideal is NOT zero dimensional! | ||
| − | Use Q[x,y]; | + | Use Q[x,y]; |
| − | ZeroDimRadical(Ideal([x^3,x^2y,x,y^2]) ); | + | ZeroDimRadical(Ideal([x^3,x^2y,x,y^2]) ); |
| − | + | ||
| − | Use Q[x,y,z]; | + | Use Q[x,y,z]; |
| − | 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])); | + | 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])); |
| − | + | ||
| − | + | Use Q[x,y,z]; | |
| − | Use Q[x,y,z]; | + | ZeroDimRadical(Ideal([x^2 + y+z -1, x+y^2 + z -1, x+y+z^2 -1])); |
| − | ZeroDimRadical(Ideal([x^2 + y+z -1, x+y^2 + z -1, x+y+z^2 -1])); | ||
Revision as of 14:26, 18 June 2007
Tutorials of the Robbiano/Kreuzer track
Tutorial 1 (82kb)
the ideals for part c.)
Use Q[x[1..4]]; 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])); Use Q[x[1..3]]; 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])); Use Q[x[1..4]]; 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])); Use Q[x[1..3]]; 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]]));
the ideals for part f.)
Warning: Second ideal is NOT zero dimensional!
Use Q[x,y]; ZeroDimRadical(Ideal([x^3,x^2y,x,y^2]) ); Use Q[x,y,z]; 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])); Use Q[x,y,z]; ZeroDimRadical(Ideal([x^2 + y+z -1, x+y^2 + z -1, x+y+z^2 -1]));
