Category:ApCoCoA-1:Package diffalg

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.

The package diffalg provides basic functionality for computations within differential polynomial rings in n indeterminates over ${\displaystyle \mathbb {Q} }$. Currently, these rings are realized by using doubly indexed indeterminates where the first index distinguishes the indeterminates ${\displaystyle x_{1},\dots ,x_{n}}$ and the second index denotes the order of the corresponding derivative.

Example

The differential polynomial ${\displaystyle F:=u_{1}^{2}-u_{2}^{3}\in \mathbb {Q} \{x_{1},x_{2}\}}$ with ${\displaystyle u_{1}=x_{1}^{(4)}}$ and ${\displaystyle u_{2}=x_{2}^{(4)}}$ 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