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-- -*- coding: utf-8 -*-
--- status: TODO
--- author(s):
--- notes:
document {
Key => isSubset,
Headline => "whether one object is a subset of another"
}
document {
Key => { (isSubset, Set, Set), (isSubset, Set, VisibleList), (isSubset, VisibleList, Set), (isSubset, VisibleList, VisibleList)},
Usage => "isSubset(x,y)",
Inputs => {
"x" => {ofClass {Set, List}},
"y" => {ofClass {Set, List}},
},
Outputs => {
Boolean => {"whether every element of ", TT "x", " is in ", TT "y"},
},
EXAMPLE {
"isSubset(set{a},set{a,b,c})",
"isSubset({a},set{a,b,c})",
"isSubset({a,a},{a,b,c})"
},
SeeAlso => {Set}
}
document {
Key => {(isSubset,Module,Module),(isSubset,Ideal,Module),(isSubset,Module,Ideal)},
Usage => "isSubset(M,N)",
Inputs => { "M", "N" },
Outputs => { Boolean => {"whether ", TT "M", " is contained in ", TT "N"} },
EXAMPLE lines ///
R = QQ[x,y]
M = image matrix {{x,0},{0,y}}
N = image matrix {{x^2,0},{-y,y}}
isSubset(N,M)
isSubset(M,N)
///
}
document {
Key => {(isSubset,Ideal,Ideal)},
Usage => "isSubset(I,J)",
Inputs => { "I", "J" },
Outputs => { Boolean => {"whether ", TT "I", " is contained in ", TT "J"} },
EXAMPLE {
"R = QQ[a..d];",
"I = ideal(a^2-b*c-1,a*c-1,b^3-1);",
"isSubset(I^2,I)",
"isSubset(I,I^2)"
},
"In polynomial rings, this is accomplished by computing a Gröbner basis of ", TT "J", " and testing
whether every element of ", TT "I", " reduces to 0 modulo ", TT "I", "."
}
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