symbolic powers of edge ideals.

[Madineh Jafari]

Hi every one.

For edge ideal I={X*Y, Y*Z, X*Z, X*U, Y*U, Z*U}

I want to calculate symbolic power.

I saw the package related to 'symbolic power" in macaulay 2, but i dont know how to use the package.but when i use them, it dosent work.

Let me know please if you have some suggestion that can help for that purpose. Thank you very much! we have following commands in macaulay2:

i1 : B = QQ[x,y,z];

i2 : I = ideal(x*(y^3-z^3),y*(z^3-y^3),z*(x^3-y^3)); o2 : Ideal of B

i3 : J = symbolicPower(I,3) 3 6 9 3 3 4 6 4 3 7 3 7 6 3 2 9 2 6 5 o3 = ideal (x y z - y z - 2x y z + 2y z + x z - y z , x y z - y z - x z ------------------------------------------------------------------------ 3 3 5 6 5 3 8 3 8 9 3 9 3 6 6 6 6 3 9 - 2x y z + 3y z + 2x z - 2y z , x z - y z - 3x z + 3y z + 3x z - ------------------------------------------------------------------------ 3 9 12 9 3 6 6 3 9 11 8 3 5 6 2 9 3y z , y - 3y z + 3y z - y z , x*y - 3x*y z + 3x*y z - x*y z , ------------------------------------------------------------------------ 2 10 2 7 3 2 4 6 2 9 3 9 9 3 3 3 6 6 6 x y - 3x y z + 3x y z - x y*z , x y - 3y z - 3x y z + 6y z + ------------------------------------------------------------------------ 3 9 3 9 2x z - 3y z ) o3 : Ideal of B

: R=QQ[X,Y,Z,U]
o1 = R o1 : PolynomialRing

i2 : I=ideal(X*Y,Y*Z,X*Z,X*U,Y*U,Z*U)
o2 = ideal(XY,YZ,XZ,XU,YU,ZU) o2 : Ideal of R

i3 : loadPackage"SymbolicPowers"
o3 = SymbolicPowers o3 : Package

i4 : J=symbolicpower(I,2)
stdio:4:15:(3): error: no method for adjacent objects:

• symbolicpower (of class Symbol)
• (ideal (X Y,Y Z,X Z,X U,Y U,Z U),2) (of class Sequence)

[David Eisenbud]

you misspelled symbolicPower (note the capital P)

--

David Eisenbud

Professor of Mathematics

University of California Berkeley

https://eisenbud.github.io/

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[Madineh Jafari]

Thank you very much

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