Difference between revisions of "CoCoASchool2007"

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=Lectures of the Robbiano/Kreuzer track=
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[[:Image:Lecture_5_Hagenberg.pdf|Lecture on Approximate Computations in Commutative Algebra]]
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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)
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==the tutorials==
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[[:Image:KR_tutorial_1.pdf|Tutorial 1: A Do-It-Yourself Guide to Lex-Solving]]
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[[:Image:KR_tutorial_2.pdf|Tutorial 2: Faster! Faster! The FGLM Speed-Up]]
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[[:Image:KR_tutorial_3.pdf|Tutorial 3: Your Very Own EigenSolver]]
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[[:Image:KR_tutorial_4.pdf|Tutorial 4: The BMM-Algorithm: Not a BMW!]]
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[[:Image:KR_tutorial_5.pdf|Tutorial 5: Variations on BBA]]
  
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== the ideals for part c.) ==
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[[:Image:Reduce.coc|CoCoA function for reducing a set of polynomials]] so that they are K-linearly independent
  
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Use Q[x[1..4]];
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[[:Image:KR_tutorial_6.pdf|Tutorial 6: An Approximate Tutorial]]
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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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==input files==
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Warning: Second ideal is NOT zero dimensional!
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[[:Image:Input_1.coc|Input data for the exercises from Tutorial 1]]
  
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Use Q[x,y];
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[[:Image:Input_3.coc|Input data for the exercises from Tutorial 3]]
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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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[[:Image:Input_5.coc|Input data for the exercises from Tutorial 5]]
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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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==CoCoA 4.7.2 + ApCoCoAServer binaries==
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Use Q[x,y];
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*[http://apcocoa.org/download/cocoa/cocoa-4.7.2.exe Windows x86] (4.8MB)
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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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*[http://apcocoa.org/download/cocoa/cocoa-4.7.2-linux-x86.tar.gz Linux x86] (5.0MB) (extract to /usr/local - otherwise you need to edit the cocoa and xcocoa scripts to point to the right directory)  
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*[http://apcocoa.org/download/cocoa/cocoa-4.7.2-osx-universal.dmg OSX universal] (8.6MB)
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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()];
 

Latest revision as of 13:22, 22 June 2007

Lectures of the Robbiano/Kreuzer track

Lecture on Approximate Computations in Commutative Algebra

Tutorials of the Robbiano/Kreuzer track

the tutorials

Tutorial 1: A Do-It-Yourself Guide to Lex-Solving

Tutorial 2: Faster! Faster! The FGLM Speed-Up

Tutorial 3: Your Very Own EigenSolver

Tutorial 4: The BMM-Algorithm: Not a BMW!

Tutorial 5: Variations on BBA

CoCoA function for reducing a set of polynomials so that they are K-linearly independent

Tutorial 6: An Approximate Tutorial

input files

Input data for the exercises from Tutorial 1

Input data for the exercises from Tutorial 3

Input data for the exercises from Tutorial 5

CoCoA 4.7.2 + ApCoCoAServer binaries

  • Windows x86 (4.8MB)
  • Linux x86 (5.0MB) (extract to /usr/local - otherwise you need to edit the cocoa and xcocoa scripts to point to the right directory)
  • OSX universal (8.6MB)
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