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# manualExt -- computes the Ext module of two modules as the core Ext function sometimes does not work properly in the negatively graded case

- Usage:
    `M = manualExt(t, N, P)`
- Inputs:
  - t, an integer, the homological degree
  - N, a module, a module
  - P, a module, a module
- Outputs:
  - M, a module,

## Description

Given two modules $N$ and $P$ over a ring $R$ and an integer $t$, this function computes and returns ${Ext}_R^t(N,P)$.

    i1 : R = S = QQ[X,T,Degrees=>{1,-1}];

    i2 : N = S^1/ideal(X*T-1);

    i3 : P = S^1;

    i4 : manualExt(1, N, P)

    o4 = cokernel | XT-1 |

                                1
    o4 : S-module, quotient of S

    i5 : Ext^1(N,P)

    o5 = cokernel | XT-1 |

                                1
    o5 : S-module, quotient of S

## See also

- Ext -- compute an Ext module

## Ways to use manualExt:

- `manualExt(ZZ,Module,Module)`

## For the programmer

The object manualExt is a method function with options.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/NonPrincipalTestIdeals.m2:1177:0.