Category:Package diffalg

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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.

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