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Binomials :: binomialCellularDecomposition

binomialCellularDecomposition -- Binomial Cellular Decomposition

Synopsis

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

              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.

See also

Ways to use binomialCellularDecomposition :

For the programmer

The object binomialCellularDecomposition is a method function with options.