# Difference between revisions of "Category:ApCoCoA-1: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. | |

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− | The package diffalg provides basic functionality for computations within differential polynomial rings in n indeterminates over | ||

==Example== | ==Example== | ||

− | The differential polynomial | + | 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: |

<code> | <code> | ||

− | Use S::= | + | Use S::=QQ[x[1..2,0..20]]; |

F:=x[1,4]^2-x[2,4]^3; | F:=x[1,4]^2-x[2,4]^3; | ||

</code> | </code> | ||

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* H. Bluhm: ''Gröbnerbasen in gewöhnlichen differentiellen Polynomringen'', Doctoral Thesis, Dortmund, 2008 | * H. Bluhm: ''Gröbnerbasen in gewöhnlichen differentiellen Polynomringen'', Doctoral Thesis, Dortmund, 2008 | ||

− | [[Category: | + | [[Category:ApCoCoA-1 Manual]] |

## Latest revision as of 15:17, 2 October 2020

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 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

## Pages in category "ApCoCoA-1:Package diffalg"

The following 17 pages are in this category, out of 17 total.

### D

- ApCoCoA-1:DA.Class
- ApCoCoA-1:DA.DiffAutoReduce
- ApCoCoA-1:DA.Differentiate
- ApCoCoA-1:DA.DiffGB
- ApCoCoA-1:DA.DiffOrd
- ApCoCoA-1:DA.DiffReduce
- ApCoCoA-1:DA.DiffSupp
- ApCoCoA-1:DA.DiffTO
- ApCoCoA-1:DA.Initial
- ApCoCoA-1:DA.InitialOfDer
- ApCoCoA-1:DA.LD
- ApCoCoA-1:DA.LPot
- ApCoCoA-1:DA.NthDerivation
- ApCoCoA-1:DA.PseudoAutoReduce
- ApCoCoA-1:DA.PseudoReduce
- ApCoCoA-1:DA.Sep
- ApCoCoA-1:DA.Weight