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-- -*- coding: utf-8 -*-
--- status: DRAFT.
--- author(s): kummini
--- notes:
document {
Key => target,
Headline => "target of a map",
"This command returns the target of a morphism or Gröbner basis.",
SeeAlso => {source}
}
document {
Key => (target,ChainComplexMap),
Headline => " find the target of a map of chain complexes",
Usage => "target f",
Inputs => {
"f" => ChainComplexMap
},
Outputs => {
{"the target 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 "target", " gives the target 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;",
"target f"
},
"(That was an expensive way of resolving ", TT "N", ".)",
}
document {
Key => (target,GroebnerBasis),
Headline => "find target of a Gröbner basis",
Usage => "target g",
Inputs => {
"g" => GroebnerBasis
},
Outputs => {
"the target of the matrix given by the generators of the Gröbner
basis"},
EXAMPLE {
"R = ZZ/10007[x,y,z];",
"g = gb ideal(x^2, x*y-z^2, z^5);",
"target g"
},
SeeAlso => {}
}
document {
Key => (target,Matrix),
Headline => "find the target module of matrix",
Usage => "target f",
Inputs => {
"f" => Matrix
},
Outputs => {
{"the target 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);",
"target g",
},
}
document {
Key => (target,GradedModuleMap),
Headline => "find the target of a map of graded modules",
Usage => "target f",
Inputs => {
"f"
},
}
document {
Key => (target,RingMap),
Headline => "find the target ring for a map of rings",
Usage => "target f",
Inputs => {
"f"
},
Outputs => {
"the target 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})",
"target f"
},
}
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