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--- status: DRAFT
--- author(s): kummini
--- notes:
document {
Key => source,
Headline => "source of a map",
"Gives the source of a map of rings, chain complexes or modules",
SeeAlso => {target}
}
document {
Key => (source,RingMap),
Headline => "find the source ring for a map of rings",
Usage => "source f",
Inputs => {
"f"
},
Outputs => {
"the source ring of the map"
},
EXAMPLE {
"S = ZZ/10007[x, y, z];",
"R = ZZ/10007[t];",
"f = map(R,S,{t^3,t^4,t^5})",
"source f"
},
}
document {
Key => (source,ChainComplexMap),
Headline => " find the source of a map of chain complexes",
Usage => "source f",
Inputs => {
"f" => ChainComplexMap
},
Outputs => {
{"the source chain complex of ", TT "f"}
},
"In the example below, we have a map between two modules and extend it to
a map between projective resolutions of the two modules. Then ",
TT "source", " gives the source of the map of chain complexes.",
EXAMPLE {
"R = ZZ[x,y,z];",
"M = R^1/(x,y,z);",
"N = R^1/(x^2,y^2,x*y*z,z^2);",
"g = map(N,M,x*y);",
"f = res g;",
"source f"
},
"(That was an expensive way of resolving ", TT "M", ".)",
}
document {
Key => (source,Matrix),
Headline => "find the source module of matrix",
Usage => "source f",
Inputs => {
"f" => Matrix
},
Outputs => {
{"the source module of ", TT "f"}
},
EXAMPLE {
"R = ZZ[x,y,z];",
"M = R^1/(x,y,z);",
"N = R^1/(x^2,y^2,x*y*z,z^2);",
"g = map(N,M,x*y);",
"source g",
},
}
document {
Key => (source,GradedModuleMap),
Headline => "find the source of a map of graded modules",
Usage => "source f",
Inputs => {
"f"
},
}
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