Difference between revisions of "ApCoCoALib:RingF16"

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(update wtr. the implementation of F16.)
(adding a reference to ApCoCoA:Representation_of_finite_fields)
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ApCoCoALib  contains an implementation of the field <math>\mathbb{F}_{16}</math>
 
ApCoCoALib  contains an implementation of the field <math>\mathbb{F}_{16}</math>
 
The field is constructed via  <math>\mathbb{F}_{16} = \mathbb{F}[x]/(x^4 + x^3 + 1)</math>.  
 
The field is constructed via  <math>\mathbb{F}_{16} = \mathbb{F}[x]/(x^4 + x^3 + 1)</math>.  
The field's elements are represented as integers between 0 and 15.  The corresponding mapping is the substitution homomorphism, mapping x to 2. Therefore we have e.g. <math>x^3 + x + 1 \mapsto 2^3 + 2^1 + 2^0 = 8 + 2  + 1 = 11</math>
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The field's elements are represented as integers between 0 and 15.  The corresponding mapping is the substitution homomorphism, mapping x to 2. Therefore we have e.g. <math>x^3 + x + 1 \mapsto 2^3 + 2^1 + 2^0 = 8 + 2  + 1 = 11</math>. A more detailed description of this behavior can be found in the article [[ApCoCoA:Representation_of_finite_fields]].
  
 
This implementation is contained in the files RingF16,[CH]. A new instance can be created with the command:
 
This implementation is contained in the files RingF16,[CH]. A new instance can be created with the command:

Revision as of 10:32, 6 March 2008

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ApCoCoALib contains an implementation of the field The field is constructed via . The field's elements are represented as integers between 0 and 15. The corresponding mapping is the substitution homomorphism, mapping x to 2. Therefore we have e.g. . A more detailed description of this behavior can be found in the article ApCoCoA:Representation_of_finite_fields.

This implementation is contained in the files RingF16,[CH]. A new instance can be created with the command:

ApCoCoA::AlgebraicCore::NewRingF16();

An example, describing how to use RingF16, especially together with ring homomorphisms can be found in ApCoCoALib's example directory. It is named ex-RingF16.C