Difference between revisions of "Category:ApCoCoA-1:Package diffalg"

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'''Note:''' This package will not be available until the upcoming ApCoCoA-Release 1.0. The documentation of the package diffalg as well is still under construction.
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The package diffalg provides basic functionality for computations within differential polynomial rings in n indeterminates over the field of rationals, Q. Currently, these rings are realized by using doubly indexed indeterminates where the first index distinguishes the indeterminates <math>x_1,\dots,x_n</math> and the second index denotes the order of the corresponding derivative.
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The package diffalg provides basic functionality for computations within differential polynomial rings in n indeterminates over <math>\mathbb{Q}</math>. Currently, these rings are realized by using doubly indexed indeterminates where the first index distinguishes the indeterminates <math>x_1,\dots,x_n</math> and the second index denotes the order of the corresponding derivative.
 
  
 
==Example==
 
==Example==
  
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The differential polynomial <math>F:=u_1^{2}-u_2^{3}\in\mathbb{Q}\{x_1,x_2\}</math> with <math>u_1=x_1^{(4)}</math> and <math>u_2=x_2^{(4)}</math> where we consider only orders up to 20 is defined as follows:
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The differential polynomial F:=u_1^2-u_2^3 in Q{x_1,x_2} with u_1=x_1^(4) and u_2=x_2^(4) where we consider only orders up to 20 is defined as follows:
  
 
   <code>
 
   <code>
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   Use S::=Q[x[1..2,0..20]];
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   Use S::=QQ[x[1..2,0..20]];
 
   F:=x[1,4]^2-x[2,4]^3;
 
   F:=x[1,4]^2-x[2,4]^3;
 
   </code>
 
   </code>
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* H. Bluhm: ''Gröbnerbasen in gewöhnlichen differentiellen Polynomringen'', Doctoral Thesis, Dortmund, 2008
 
* H. Bluhm: ''Gröbnerbasen in gewöhnlichen differentiellen Polynomringen'', Doctoral Thesis, Dortmund, 2008
  
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[[Category:ApCoCoA_Manual]]
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[[Category:ApCoCoA-1 Manual]]

Latest revision as of 15:17, 2 October 2020

The package diffalg provides basic functionality for computations within differential polynomial rings in n indeterminates over the field of rationals, Q. Currently, these rings are realized by using doubly indexed indeterminates where the first index distinguishes the indeterminates and the second index denotes the order of the corresponding derivative.

Example

The differential polynomial F:=u_1^2-u_2^3 in Q{x_1,x_2} with u_1=x_1^(4) and u_2=x_2^(4) where we consider only orders up to 20 is defined as follows: 

 
 Use S::=QQ[x[1..2,0..20]];
 F:=x[1,4]^2-x[2,4]^3;

References

  • H. Bluhm: Gröbnerbasen in gewöhnlichen differentiellen Polynomringen, Doctoral Thesis, Dortmund, 2008
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