# On the Relation between Pommaret and Janet Bases

@inproceedings{Gerdt2000OnTR, title={On the Relation between Pommaret and Janet Bases}, author={Vladimir P. Gerdt}, year={2000} }

In this paper the relation between Pommaret and Janet bases of polynomial ideals is studied. It is proved that if an ideal has a finite Pommaret basis then the latter is a minimal Janet basis. An improved version of the related algorithm for computation of Janet bases, initially designed by Zharkov, is described. For an ideal with a finite Pommaret basis, the algorithm computes this basis. Otherwise, the algorithm computes a Janet basis which need not be minimal. The obtained results are… CONTINUE READING

#### Topics from this paper.

#### Citations

##### Publications citing this paper.

SHOWING 1-9 OF 9 CITATIONS

## A combinatorial approach to involution and δ-regularity II: structure analysis of polynomial modules with pommaret bases

VIEW 5 EXCERPTS

CITES METHODS

HIGHLY INFLUENCED

## An Efficient Algebraic Algorithm for the Geometric Completion to Involution

VIEW 5 EXCERPTS

CITES METHODS

HIGHLY INFLUENCED

## Effective Genericity, δ-Regularity and Strong Noether Position

VIEW 1 EXCERPT

CITES METHODS

## On Exact Solvability of Anharmonic Oscillators in Large Dimensions

VIEW 2 EXCERPTS

CITES BACKGROUND & METHODS

## Parallelization of an Algorithm for Computation of Involutive Janet Bases

VIEW 1 EXCERPT

CITES BACKGROUND

## Involutive Bases in MuPAD II : Polynomial Algebras of Solvable Type Involutive Bases

VIEW 1 EXCERPT

CITES BACKGROUND

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 22 REFERENCES

## A Combinatorial Approach to Involution and δ-Regularity

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Involutive bases of polynomial ideals

VIEW 10 EXCERPTS

## Minimal involutive bases

VIEW 10 EXCERPTS

## Involutive polynomial bases:general case

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## Completion of Linear Differential Systems to Involution

VIEW 6 EXCERPTS

HIGHLY INFLUENTIAL

## Partial Differential Equations and Group Theory

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Systems of partial differential equations and Lie pseudogroups

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Differential Algebra and Algebraic Groups

VIEW 1 EXCERPT