user_guide:tutorials:transformations

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tutorial:transformations [2010/10/14 10:29] – created joswiguser_guide:tutorials:transformations [2019/01/28 17:40] – ↷ Links adapted because of a move operation oroehrig
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 ===== Polytopes and Linear Maps ===== ===== Polytopes and Linear Maps =====
  
-polymake works with homogeneous coordinates, which is why //projective// linear transformations are natural to apply to polytopes. Affine transformations are a special case.  By the way, a //transformation// is always bijective, by definition.+polymake works with [[user_guide:tutorials:coordinates|homogeneous coordinates]], which is why //projective// linear transformations are natural to apply to polytopes. Affine transformations are a special case.  By the way, a //transformation// is always bijective, by definition.
  
 ==== Transformations ==== ==== Transformations ====
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 <code> <code>
 polytope > $A=new Matrix<Rational>([[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,0]]); polytope > $A=new Matrix<Rational>([[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,0]]);
 +</code>
  
-polytope > transform($c,$A); +Using transform would not work in this case: 
 +<code> 
 +# polytope > transform($c,$A);
 polymake:  ERROR: matrix not invertible polymake:  ERROR: matrix not invertible
 </code> </code>
 +The above error says that transform is not the proper function to deal with this situation as the linear map given by A is not invertible.  
  
-The above error says that transform is not the proper function to deal with this situation as the linear map given by A is not invertible.  To produce the image the following command works:+To produce the image the following command works:
  
 <code> <code>
  • user_guide/tutorials/transformations.txt
  • Last modified: 2019/02/04 22:55
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