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Fungrim entry: f4fbb8

Symbol: ArgMinUnique arg min*P(x)f ⁣(x)\mathop{\operatorname{arg\,min*}}\limits_{P\left(x\right)} f\!\left(x\right) Unique location of minimum value
ArgMinUnique(f(x), x, P(x)) represents the unique point rr satisfying P ⁣(r)P\!\left(r\right) such that f ⁣(r)=minP(x)f ⁣(x)f\!\left(r\right) = \mathop{\min}\limits_{P\left(x\right)} f\!\left(x\right). This operation is only defined if such a unique point exists.
The argument x to this operator defines a locally bound variable. The corresponding predicate P ⁣(x)P\!\left(x\right) must define the domain of xx unambiguously; that is, it must include a statement such as xSx \in S where SS is a known set. More generally, x can be a collection of variables (x,y,)\left(x, y, \ldots\right) all of which become locally bound, with a corresponding predicate P ⁣(x,y,)P\!\left(x, y, \ldots\right).
Definitions:
Fungrim symbol Notation Short description
ArgMinUniquearg min*P(x)f ⁣(x)\mathop{\operatorname{arg\,min*}}\limits_{P\left(x\right)} f\!\left(x\right) Unique location of minimum value
MinimumminP(x)f ⁣(x)\mathop{\min}\limits_{P\left(x\right)} f\!\left(x\right) Minimum value of a set or function
Source code for this entry:
Entry(ID("f4fbb8"),
    SymbolDefinition(ArgMinUnique, ArgMinUnique(f(x), x, P(x)), "Unique location of minimum value"),
    Description(SourceForm(ArgMinUnique(f(x), x, P(x))), "represents the unique point", r, "satisfying", P(r), "such that", Equal(f(r), Minimum(f(x), x, P(x))), ". This operation is only defined if such a unique point exists."),
    Description("The argument", SourceForm(x), "to this operator defines a locally bound variable.", "The corresponding predicate", P(x), "must define the domain of", x, "unambiguously; that is, it must include a statement such as", Element(x, S), "where", S, "is a known set.", "More generally,", SourceForm(x), "can be a collection of variables", Tuple(x, y, Ellipsis), "all of which become locally bound, with a corresponding predicate", P(x, y, Ellipsis), "."))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-06-18 07:49:59.356594 UTC