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Fungrim entry: be4926

Symbol: ArgMaxUnique arg max*xSf(x)\mathop{\operatorname{arg\,max*}}\limits_{x \in S} f(x) Unique location of maximum value
ArgMaxUnique(f(x), ForElement(x, S)), rendered arg max*xSf(x)\mathop{\operatorname{arg\,max*}}\limits_{x \in S} f(x), represents the unique value xSx \in S such that f(x)=maxsSf(s)f(x) = \mathop{\max}\limits_{s \in S} f(s). This operation is only defined if such a unique value exists.
ArgMaxUnique(f(x), ForElement(x, S), P(x)), rendered arg max*xS,P(x)f(x)\mathop{\operatorname{arg\,max*}}\limits_{x \in S,\,P(x)} f(x), represents the unique value xSx \in S satisfying P(x)P(x) and such that f(x)=maxsSf(s)f(x) = \mathop{\max}\limits_{s \in S} f(s). This operation is only defined if such a unique value exists.
ArgMaxUnique(f(x, y), For(Tuple(x, y)), P(x, y)) represents the unique tuple (x,y)\left(x, y\right) satisfying P ⁣(x,y)P\!\left(x, y\right) such that f ⁣(x,y)=maxP(s,t)f ⁣(s,t)f\!\left(x, y\right) = \mathop{\max}\limits_{P\left(s, t\right)} f\!\left(s, t\right), and similarly for any number n2n \ge 2 of variables.
The special expression For(x) or ForElement(x, S) declares x as a locally bound variable within the scope of the arguments to this operator. If For(x) is used instead of ForElement(x, S), the corresponding predicate P(x)P(x) 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. Similarly, For(Tuple(x, y)), For(Tuple(x, y, z)), etc. defines multiple locally bound variables which must be accompanied by a multivariate predicate P ⁣(x,y)P\!\left(x, y\right), P ⁣(x,y,z)P\!\left(x, y, z\right), etc.
Definitions:
Fungrim symbol Notation Short description
ArgMaxUniquearg max*xSf(x)\mathop{\operatorname{arg\,max*}}\limits_{x \in S} f(x) Unique location of maximum value
MaximummaxxSf(x)\mathop{\max}\limits_{x \in S} f(x) Maximum value of a set or function
Source code for this entry:
Entry(ID("be4926"),
    SymbolDefinition(ArgMaxUnique, ArgMaxUnique(f(x), ForElement(x, S)), "Unique location of maximum value"),
    Description(SourceForm(ArgMaxUnique(f(x), ForElement(x, S))), ", rendered", ArgMaxUnique(f(x), ForElement(x, S)), ", ", "represents the unique value", Element(x, S), "such that", Equal(f(x), Maximum(f(s), ForElement(s, S))), ". This operation is only defined if such a unique value exists."),
    Description(SourceForm(ArgMaxUnique(f(x), ForElement(x, S), P(x))), ", rendered", ArgMaxUnique(f(x), ForElement(x, S), P(x)), ", ", "represents the unique value", Element(x, S), "satisfying", P(x), "and", "such that", Equal(f(x), Maximum(f(s), ForElement(s, S))), ". This operation is only defined if such a unique value exists."),
    Description(SourceForm(ArgMaxUnique(f(x, y), For(Tuple(x, y)), P(x, y))), "represents the unique tuple", Tuple(x, y), "satisfying", P(x, y), "such that", Equal(f(x, y), Maximum(f(s, t), For(Tuple(s, t)), P(s, t))), ", and similarly for any number", GreaterEqual(n, 2), "of variables."),
    Description("The special expression", SourceForm(For(x)), "or", SourceForm(ForElement(x, S)), "declares", SourceForm(x), "as a locally bound variable within the scope of the arguments to this operator. ", "If", SourceForm(For(x)), "is used instead of", SourceForm(ForElement(x, S)), ", 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. Similarly,", SourceForm(For(Tuple(x, y))), ", ", SourceForm(For(Tuple(x, y, z))), ", etc.", "defines multiple locally bound variables which must be accompanied by a multivariate predicate", P(x, y), ", ", P(x, y, z), ", etc."))

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

2020-01-31 18:09:28.494564 UTC