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# Tor -- computes Tor of two Cp-Mackey fuctors

- Usage:
    `Tor_i(M,N)`
- Inputs:
  - i, an integer,
  - M, a C_p Mackey Functor,
  - N, a C_p Mackey Functor,
- Outputs:
  - a C_p Mackey Functor, the $i$th Tor Cp-Mackey Functor of $M$ and $N$

## Description

Given two Cp-Mackey functors $M$ and $N$, we can compute their $i$th Tor.

    i1 : RU = makeComplexRepresentationMackeyFunctor(3);

    i2 : prune Tor_3(RU,RU)

    o2 =                                         Res : 0
         cokernel | 3 0 0 0 0 0 0 0 0 0 0 0 |  -----------> 0  -┐ Conj : 0
                                              <-----------     <┘
                                                 Tr : 0

    o2 : CpMackeyFunctor

## Ways to use Tor:

- `Tor_ZZ(CpMackeyFunctor,CpMackeyFunctor)`
- `Tor_ZZ(Ideal,Ideal)` -- see Tor_ZZ(Module,Module) -- compute a Tor module
- `Tor_ZZ(Ideal,Module)` -- see Tor_ZZ(Module,Module) -- compute a Tor module
- `Tor_ZZ(Ideal,Ring)` -- see Tor_ZZ(Module,Module) -- compute a Tor module
- `Tor_ZZ(Module,Ideal)` -- see Tor_ZZ(Module,Module) -- compute a Tor module
- Tor_ZZ(Module,Module) -- compute a Tor module
- `Tor_ZZ(Module,Ring)` -- see Tor_ZZ(Module,Module) -- compute a Tor module
- `Tor_ZZ(Ring,Ideal)` -- see Tor_ZZ(Module,Module) -- compute a Tor module
- `Tor_ZZ(Ring,Module)` -- see Tor_ZZ(Module,Module) -- compute a Tor module
- `Tor_ZZ(Ring,Ring)` -- see Tor_ZZ(Module,Module) -- compute a Tor module

## For the programmer

The object Tor is a scripted functor.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/CpMackeyFunctors/Documentation/HomAlgDoc.m2:46:0.