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# psi -- cotangent line class

- Usage:
    `psi_i`
- Inputs:
  - i, an integer
- Outputs:
  - a ring element

## Description

This is an element in the ring created by hodgeRing. It is the $i$-th cotangent line class. Definitions and properties can be found in [AC].

Here is a simple example which calculates $\int_{{\bar M}_{1,1}} \psi_1$.

    i1 : R = hodgeRing (1, 1);

    i2 : psi_1

    o2 = psi
            1

    o2 : R

    i3 : integral(1, 1, psi_1)
    warning: clearing value of symbol tempCh to allow access to subscripted variables based on it
           : debug with expression   debug 1257   or with command line option   --debug 1257

          1
    o3 = --
         24

    o3 : R

## References

[AC] Arbarello, E. and Cornalba, M. Combinatorial and algebro-geometric cohomology classes on the moduli spaces of curves. J. Algebraic Geom. 5. (1996), no. 4, 705--749.

## See also

- HodgeIntegrals -- Hodge integrals on the moduli space of curves
- hodgeRing -- create a ring containing algebraic classes on moduli spaces of curves
- integral -- evaluate Hodge integrals

## For the programmer

The object psi is an indexed variable table.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/HodgeIntegrals.m2:794:0.