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

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'''Note:''' This package will first be available in the upcoming ApCoCoA-Release 1.0 (scheduled for 2008-12-22). The documentation of this package, 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>

Revision as of 10:17, 22 April 2009

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::=Q[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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