Category:ApCoCoA-1:Package diffalg

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The package diffalg provides basic functionality for computations within differential polynomial rings in n Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x_1} indeterminates over the field of rationals, Q. Currently, these rings are realized by using doubly indexed indeterminates where the first index distinguishes the indeterminates 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