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RegularChains[ChainTools]

  

EquiprojectableDecomposition

  

equiprojectable decomposition of a variety

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

EquiprojectableDecomposition(lrc, R)

Parameters

lrc

-

list of regular chains of R

R

-

polynomial ring

Description

• 

The command EquiprojectableDecomposition(lrc, R) returns the equiprojectable decomposition of the variety given by lrc.

• 

The variety encoded by lrc is the union of the regular zero sets of the regular chains of lrc.

• 

It is assumed that every regular chain in lrc is zero-dimensional and strongly normalized.

• 

This command is part of the RegularChains[ChainTools] package, so it can be used in the form EquiprojectableDecomposition(..) only after executing the command with(RegularChains[ChainTools]).  However, it can always be accessed through the long form of the command by using RegularChains[ChainTools][EquiprojectableDecomposition](..).

Examples

withRegularChains:

withChainTools:

RPolynomialRingz,y,x

R:=polynomial_ring

(1)

sysx2+y+z1,x+y2+z1,x+y+z21

sys:=x2+y+z1,y2+x+z1,z2+x+y1

(2)

lrcTriangularizesys,R,normalized=yes

lrc:=regular_chain,regular_chain,regular_chain,regular_chain

(3)

mapEquations,lrc,R

zx,yx,x2+2x1,z,y,x1,z,y1,x,z1,y,x

(4)

edEquiprojectableDecompositionlrc,R

ed:=regular_chain,regular_chain

(5)

mapEquations,ed,R

z+y1,y2y,x,2z+x21,2y+x21,x3+x23x+1

(6)

References

  

Dahan, X.; Moreno Maza, M.; Schost, E.; Wu, W. and Xie, Y. "Equiprojectable decompositions of zero-dimensional varieties" In proc. of International Conference on Polynomial System Solving, University of Paris 6, France, 2004.

See Also

Equations

MatrixCombine

PolynomialRing

RegularChains

Triangularize

 


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