Category:ApCoCoA-1:Package diffalg

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.

The package diffalg provides basic functionality for computations within differential polynomial rings in n indeterminates over ${\displaystyle \mathbb{\mathbb{Q}}}$. 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 ${\displaystyle F:=u_1^2-u_2^3\in \mathbb{\mathbb{Q}}\{x_1,x_2\}}$ 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