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Fungrim entry: 5862bb

Symbol: Solutions solutionsxSQ(x)\mathop{\operatorname{solutions}\,}\limits_{x \in S} Q(x) Solution set
Solutions(Q(x), ForElement(x, S)), rendered solutionsxSQ(x)\mathop{\operatorname{solutions}\,}\limits_{x \in S} Q(x), represents the set of values xSx \in S satisfying Q(x)Q(x).
Solutions(Q(x), ForElement(x, S), P(x)), rendered solutionsxS,P(x)Q(x)\mathop{\operatorname{solutions}\,}\limits_{x \in S,\,P(x)} Q(x), represents the set of values xSx \in S satisfying P(x)P(x) and Q(x)Q(x).
Solutions(Q(x), For(x), P(x)), rendered solutionsP(x)Q(x)\mathop{\operatorname{solutions}\,}\limits_{P(x)} Q(x), represents the set of values xx satisfying P(x)P(x) and Q(x)Q(x).
Solutions(Q(x, y), For(Tuple(x, y)), P(x, y)), rendered solutionsP(x,y)Q ⁣(x,y)\mathop{\operatorname{solutions}\,}\limits_{P\left(x, y\right)} Q\!\left(x, y\right), represents the set of tuples (x,y)\left(x, y\right) satisfying P ⁣(x,y)P\!\left(x, y\right) and Q ⁣(x,y)Q\!\left(x, y\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
SolutionssolutionsxSQ(x)\mathop{\operatorname{solutions}\,}\limits_{x \in S} Q(x) Solution set
Source code for this entry:
Entry(ID("5862bb"),
    SymbolDefinition(Solutions, Solutions(Q(x), ForElement(x, S)), "Solution set"),
    Description(SourceForm(Solutions(Q(x), ForElement(x, S))), ", rendered", Solutions(Q(x), ForElement(x, S)), ", represents the set of values", Element(x, S), "satisfying", Q(x), "."),
    Description(SourceForm(Solutions(Q(x), ForElement(x, S), P(x))), ", rendered", Solutions(Q(x), ForElement(x, S), P(x)), ", represents the set of values", Element(x, S), "satisfying", P(x), "and", Q(x), "."),
    Description(SourceForm(Solutions(Q(x), For(x), P(x))), ", rendered", Solutions(Q(x), For(x), P(x)), ", represents the set of values", x, "satisfying", P(x), "and", Q(x), "."),
    Description(SourceForm(Solutions(Q(x, y), For(Tuple(x, y)), P(x, y))), ", rendered", Solutions(Q(x, y), For(Tuple(x, y)), P(x, y)), ", represents the set of tuples", Tuple(x, y), "satisfying", P(x, y), "and", Q(x, y), ", 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.

2020-08-27 09:56:25.682319 UTC