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

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New page: 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...
 
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==Example==
==Example==


The differential polynomial <math>F:=u_1^{2}-2u_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:
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:


   <code>
   <code>

Revision as of 10:12, 8 December 2008

The package diffalg provides basic functionality for computations within differential polynomial rings in n indeterminates over . Currently, these rings are realized by using doubly indexed indeterminates where the first index distinguishes the indeterminates x1,,xn and the second index denotes the order of the corresponding derivative.

Example

The differential polynomial F:=u12u23{x1,x2} with u1=x1(4) and u2=x2(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