Function Repository Resource:

ExpressionToFunctionOperator

Source Notebook

An operator form of ExpressionToFunction that can be applied to expressions

Contributed by: Sjoerd Smit

ResourceFunction["ExpressionToFunctionOperator"][var₁,var₂,…][expr]

returns Function[{var₁,var₂,…},expr].

ResourceFunction["ExpressionToFunctionOperator"][…,{var_i,1,var_i,2,…},…][expr]

bundles {var_i,1,var_i,2,…} together in one function slot as a vector argument.

ResourceFunction["ExpressionToFunctionOperator"][varspec₁→index₁,varspec₂→index₂,…][expr]

binds variables specified by varspec_i to Slot[index_i].

Details and Options

ResourceFunction["ExpressionToFunctionOperator"][arg₁,arg₂,…][expr] is equivalent to ResourceFunction["ExpressionToFunction"][expr,arg₁,arg₂,…].

Examples

Basic Examples (5)

Create a function from a simple polynomial:

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Evaluate the polynomial at a given value:

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Convert a multivariate PDF to a function:

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Bind x and y to the first slot of the function as a vector:

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Bind arguments to keys in an Association:

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Bind multiple symbols to a single slot:

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$powerFun2 = x^y // ResourceFunction[ "ExpressionToFunctionOperator"][{x, y} -> "BaseExponentTuple"]$

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Combine named slots with positional slots:

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$powerFun3 = z*x^y // ResourceFunction["ExpressionToFunctionOperator"][ z -> "z", {x, y} -> 2]$

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Options (5)

Attributes (1)

Use the Attributes option to return a function that holds its arguments:

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Evaluated (4)

By default, the function body remains unevaluated:

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Use Evaluated→True to evaluate the PDF:

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When x has a value, using Evaluate directly on the first argument gives the wrong result:

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Use Evaluated → True to Block x while the body is being evaluated:

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Applications (3)

Group x and y together as a vector argument and map over a list of points:

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Add a parameter of the PDF as an argument:

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$parameterizedPDF = ResourceFunction["ExpressionToFunctionOperator"][{x, y}, \[Rho], Evaluated -> True ][PDF[BinormalDistribution[\[Rho]], {x, y}]]$

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Convert the solution of a differential equation to a function:

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Represent the function at parameter value a=10 with OperatorApplied, then map over a range of x values:

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AssociationMap[
OperatorApplied[dSolveFun][10],
Range[0, 10, 0.1]
] // ListPlot

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Properties and Relations (3)

ExpressionToFunctionOperator has the exact same functionality as the resource function ExpressionToFunction, but is used in operator form:

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$x^y // ResourceFunction["ExpressionToFunctionOperator"][{x, y}]$

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$ResourceFunction["ExpressionToFunction"][x^y, {x, y}]$

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Note, in particular, that both functions hold the expression that's being transformed into a function unless Evaluated→True is used:

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With evaluation of the expression:

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Possible Issues (3)

ExpressionToFunctionOperator is meant for expressions that do not already contain functions and may malfunction for such expressions if the replacement variables exist inside such functions:

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