binomialCellularDecomposition -- Binomial Cellular Decomposition

Synopsis

Usage:
binomialCellularDecomposition I
Inputs:
- I, a binomial ideal
Optional inputs:
- returnCellVars => ..., -- Binomial Cellular Decomposition
- verbose => ..., -- Binomial Cellular Decomposition
Outputs:
- l, a list of cellular ideals whose intersection is I or a list of pairs of these ideals and their cellular variables if the option returnCellVars => true is used

Description

A binomial ideal I is called cellular if modulo I every variable in the polynomial ring is either a non-zerodivisor or nilpotent. This routine returns a minimal cellular decomposition of a binomial ideal.

i1 : R = QQ[x,y,z]

o1 = R

o1 : PolynomialRing

i2 : I = ideal (x*y-z, x*z-y^2)

                        2
o2 = ideal (x*y - z, - y  + x*z)

o2 : Ideal of R

i3 : bcd = binomialCellularDecomposition I
cellular components found: 1
cellular components found: 2

              2                  2
o3 = {ideal (y  - x*z, x*y - z, x  - y), ideal (z, y)}

o3 : List

i4 : intersect bcd == I

o4 = true

i5 : binomialCellularDecomposition (I, returnCellVars=>true, verbose=>false)

               2                  2
o5 = {{ideal (y  - x*z, x*y - z, x  - y), {x, y, z}}, {ideal (z, y), {x}}}

o5 : List

A synonym for this function is 'BCD'.If the option verbose is set (default), then output about the number of components found so far will be generated.

Ways to use `binomialCellularDecomposition` :

binomialCellularDecomposition(Ideal)

binomialCellularDecomposition -- Binomial Cellular Decomposition

Synopsis

Description

See also

Ways to use binomialCellularDecomposition :

Ways to use `binomialCellularDecomposition` :