**Minimalist Instructions**

Refer to arXiv.org:0905.2229 or here for mathematical details.

The program does two kinds of calculations: in the tautological module,
on a fixed Hilbert scheme
`X`^{[m]}_{B},
as in § 2 of the paper;
and calculations of Chern numbers of tautological bundles,
as in § 3 of the paper.

At present, the program is rather slow in degrees 5 and higher. A faster version is under construction.

Throughout, we will fix a good pencil ` X`/

**Tautological module calculations**

Data is as follows:

•
A monoblock diagonal
Γ_{(n)}[ω^{a}
L^{b}],
`n` ≥ 1,
in `X`^{[m]}_{B}
is represented
by a 1-column matrix written as
_{(n)}
[ω^{a}L^{b}]
★Γ_{(n')}
[ω^{a'}`L`^{b'}]
★...
is represented as

An analogous class on a single curve of genus `x` may be
specified as
`x` can be a symbol or a number.
If `x` is the letter `g`, it may be omitted.
The **weight** of `M` is by definition
dim_b plus the sum of the first row.
dim_b is by default equal to 1, unless specified to be 0 as above.

• A node scroll `F`
^{m,n}
_{j;n',n''...}
[ω^{b}
L^{c},...]
is represented as
`n`.
By default, the genus of this object is taken as `g`-1
but may be reset by inserting `x`,
the program itself will set the genus as `x`-1.

• A node section
Γ^{(m)}
F^{m,n}
_{j;n',n''...}
[ω^{b}L^{c},...]
is represented as
`n`.

The operation of Γ^{(m)}
on these classes is represented by `m` because it is determined as
the weight of the argument.
A power of ^{2}, δ etc. using
the operator

**Chern number calculations**

These calculations take place in
W^{m}(` X`/

_{Wm(X/B)}
`c`_{i}
(Λ_{m}(`L`))
^{k}/`m`!
=
∫_{X[m]B}
`c`_{i}
(Λ_{m}(`L`))^{k}

is evaluated by _{1}^{(m)}(c(m,•))
is evaluated by

**Examples**

^{2})

^{i}GTF^{n}_(j+1)(dim_b=x;genus=y^{2};1,i))