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undocumented {
(Tor, ZZ, Matrix, Module),
(Tor, ZZ, Matrix, Ideal),
(Tor, ZZ, Matrix, Ring),
(Tor, ZZ, Module, Matrix),
(Tor, ZZ, Ideal, Matrix),
(Tor, ZZ, Ring, Matrix),
}
document {
Key => Tor,
Headline => "Tor module",
SeeAlso => {
tensor,
"Complexes :: Tor_ZZ(Matrix,Module)",
"Complexes :: Tor_ZZ(Module,Matrix)",
Hom, Ext },
Subnodes => {
TO (Tor, ZZ, Module, Module),
}
}
document {
Key => {
(Tor, ZZ, Module, Module),
(Tor, ZZ, Module, Ideal),
(Tor, ZZ, Module, Ring),
(Tor, ZZ, Ideal, Module),
(Tor, ZZ, Ideal, Ideal),
(Tor, ZZ, Ideal, Ring),
(Tor, ZZ, Ring, Module),
(Tor, ZZ, Ring, Ideal),
(Tor, ZZ, Ring, Ring),
},
Headline => "compute a Tor module",
Usage => "Tor_i(M,N)",
Inputs => { "i", "M", "N" },
Outputs => {
{ "the ", TT "i", "-th ", TT "Tor", " module of ", TT "M", " and ", TT "N" }
},
PARA {
"If ", TT "N", " is a ring (instead of a module), then the free module of rank 1 over it is used instead. If
", TT "M", " or ", TT "N", " is an ideal of ring, then the underlying module is used instead."
}
}
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