# isSymmetricFDivisor -- checks whether a symmetric divisor intersects all the F-curves nonnegatively

## Description

We say a symmetric divisor on $\bar{M}_{0,n}$ is a symmetric F-divisor if $D . F_{I_1,I_2,I_3,I_4} \geq 0$ for every F curve.

In the example below, we see that for $n=8$, the divisor $3B_2+2B_3+4B_4$ is a symmetric F-divisor, while the divisor $B_2$ is not.

 i1 : D=symmetricDivisorM0nbar(8,3*B_2+2*B_3+4*B_4) o1 = 3*B + 2*B + 4*B 2 3 4 o1 : S_8-symmetric divisor on M-0-8-bar i2 : isSymmetricFDivisor(D) o2 = true i3 : D=symmetricDivisorM0nbar(8,B_2) o3 = B 2 o3 : S_8-symmetric divisor on M-0-8-bar i4 : isSymmetricFDivisor(D) This divisor has negative intersection with the F curve F_{3, 2, 2, 1} (and maybe others too) o4 = false

## Ways to use isSymmetricFDivisor :

• "isSymmetricFDivisor(SymmetricDivisorM0nbar)"

## For the programmer

The object isSymmetricFDivisor is .