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# expectedDimension -- compute the expected dimension of a linear system on a rational surface

- Usage:
    `expectedDimension(d,L)`
- Inputs:
  - d, an integer, degree of the desired forms
  - L, a list, {r_1,...,r_s} of multiplicities
- Outputs:
  - an integer, the expected dimension of L(d;r_1p_1,...,r_sp_s)

## Description

computes the expected dimension max(0,binomial(d+2,2)-sum binomial(r_i+1,2)) of a linear system with assigned base points on P2

    i1 : d=8

    o1 = 8

    i2 : L=toList(3:3)|toList(2:4)|{1}

    o2 = {3, 3, 3, 4, 4, 1}

    o2 : List

    i3 : expectedDimension(d,L)

    o3 = 6

    i4 : kk=ZZ/nextPrime(10^3)

    o4 = kk

    o4 : QuotientRing

    i5 : t=symbol t

    o5 = t

    o5 : Symbol

    i6 : P2=kk[t_0..t_2]

    o6 = P2

    o6 : PolynomialRing

    i7 : betti(H=linearSystemOnRationalSurface(P2,d,L))

                0 1
    o7 = total: 1 6
             0: 1 .
             1: . .
             2: . .
             3: . .
             4: . .
             5: . .
             6: . .
             7: . 6

    o7 : BettiTally

## Ways to use expectedDimension:

- `expectedDimension(ZZ,List)`

## For the programmer

The object expectedDimension is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/AdjunctionForSurfaces.m2:456:0.