Category:ApCoCoA-1:Package diffalg

The package diffalg provides basic functionality for computations within differential polynomial rings in ${\displaystyle n^{2}2}$ indeterminates over the field of rationals, 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 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