`<wrapFunctionPeriodic>`

A function wrapped into a periodic output range

<wrapFunctionPeriodic> is a Math Operator that wraps the output of a <function> into a periodic range $[\text{lowerValue}, \text{upperValue})$ . Any output that falls outside that range is shifted by a whole multiple of the range’s length until it lands inside.

The result is itself a function and can be evaluated, graphed, or composed just like any other <function>. Compare with <wrapNumberPeriodic>, which wraps a single number rather than a function, and with <clampFunction>, which truncates outputs at the endpoints rather than wrapping them.

Attributes and Properties

Attributes for `<wrapFunctionPeriodic>`

Number display (5)

avoidScientificNotation

boolean. Default value: false. Whether to render numbers in full decimal form rather than scientific notation.

displayDecimals

integer. Default value: 2. Number of decimal places to display when rendering this number.

displayDigits

integer. Default value: 3. Number of significant digits to display when rendering this number.

displaySmallAsZero

number. Default value: 1e-14. Threshold below which numbers are displayed as zero.

padZeros

boolean. Default value: false. Whether to pad displayed numbers with trailing zeros to fill the requested digits/decimals.

Labels (1)

labelIsName

boolean. Default value: false. Whether to use this component's name as its rendered label.

Other (21)

applyStyleToLabel

boolean. Default value: false. Whether to apply the function's style to its label.

domain

[ intervalList ]. Restriction of the function's domain to a list of intervals.

expand

boolean. Default value: false. Whether to expand the function's formula.

extrema

[ extrema ]. Local extrema (combined minima and maxima) of an interpolated function.

labelPosition

keyword. Position of the function's label.

Value	Description
`upperRight` (default)	Place the label above and to the right of the function curve.
`upperLeft`	Place the label above and to the left of the function curve.
`lowerRight`	Place the label below and to the right of the function curve.
`lowerLeft`	Place the label below and to the left of the function curve.
`top`	Place the label directly above the function curve.
`bottom`	Place the label directly below the function curve.
`left`	Place the label directly to the left of the function curve.
`right`	Place the label directly to the right of the function curve.

layer

number. Default value: 0. Z-order layer index for stacking the function on a graph.

lowerValue

number. Default value: 0. Lower bound for the operator's range.

maxima

[ extrema ]. Local maxima of an interpolated function.

minima

[ extrema ]. Local minima of an interpolated function.

nearestPointAsCurve

boolean. Default value: false. Whether nearest-point queries should treat the function as a curve in the plane rather than a graph y = f(x).

numInputs

integer. Number of input arguments the function accepts.

numOutputs

integer. Default value: 1. Number of output values the function produces.

simplify

keyword. Level of simplification applied to the function's formula.

Value	Description
`none`	No simplification is applied.
`full` (default)	Fully simplify the function's formula.
`numbers`	Simplify numeric subexpressions only, leaving symbolic structure intact.
`numbersPreserveOrder`	Like `numbers`, but does not reorder commutative operands.
`normalizeOrder`	Reorder commutative operands into a canonical form without simplifying values.

symbolic

boolean. Default value: true. Whether the function should be evaluated symbolically rather than numerically.

through

pointList. Points the interpolated function should pass through.

throughSlopes

mathList. Slopes the interpolated function should have at each through-point.

upperValue

number. Default value: 1. Upper bound for the operator's range.

variable

_variableName. Name of the function's single input variable.

variables

[ _variableNameList ]. Names of the function's input variables.

xscale

number. Default value: 1. Scale factor used along the x-axis.

yscale

number. Default value: 1. Scale factor used along the y-axis.

Common to all components (9)

copy

reference. Create an independent copy of another component by reference. Enter a references a $name.

disabled

boolean. Default value: false. Whether this component is disabled and cannot be interacted with.

extend

reference. Extend another component by reference, inheriting its children and attributes. Enter a reference as $name.

fixed

boolean. Default value: false. Whether this component's value is fixed and cannot be modified.

fixLocation

boolean. Default value: false. Whether this component's location is fixed (preventing it from being moved while still allowing other modifications).

hide

boolean. Default value: false. Whether to hide this component from the rendered output.

isResponse

boolean. Default value: false. Whether this component is treated as a response for the purposes of assessment.

name

text. The name used to reference this component from elsewhere in the document.

styleNumber

integer. Default value: 1. The style number used to select this component's visual styling from the available style definitions.

Properties for `<wrapFunctionPeriodic name="w">`

Number display (5)

$w.avoidScientificNotation

boolean. Whether to render numbers in full decimal form rather than scientific notation.

$w.displayDecimals

integer. Number of decimal places to display when rendering this number.

$w.displayDigits

integer. Number of significant digits to display when rendering this number.

$w.displaySmallAsZero

number. Threshold below which numbers are displayed as zero.

$w.padZeros

boolean. Whether to pad displayed numbers with trailing zeros to fill the requested digits/decimals.

Labels (2)

$w.label

label. The label rendered with this component.

$w.labelIsName

boolean. Whether to use this component's name as its rendered label.

Other (44)

$w.applyStyleToLabel

boolean. Whether to apply the function's style to its label.

$w.backgroundColor

text. Human-readable name for this component's background color, derived from the active style and theme.

$w.disabled

boolean. Whether this component is disabled and cannot be interacted with.

$w.domain

[ interval ]. Domain interval(s) of the function.

$w.expand

text. Whether to expand the formula.

$w.expandSpecified

boolean. Whether to expand the function's formula.

$w.extrema

[ number ]. Local extrema (minima + maxima) of the function.

$w.extremumLocations

[ number ]. The x-coordinates of the function's local extrema.

$w.extremumValues

[ number ]. The values of the function's local extrema.

$w.fixed

boolean. Whether this component's value is fixed and cannot be modified.

$w.fixLocation

boolean. Whether this component's location is fixed (preventing it from being moved while still allowing other modifications).

$w.formula

math. The symbolic formula of the function produced by this operator.

$w.globalInfimum

[ number ]. The global infimum of the function.

$w.globalMaximum

[ number ]. The global maximum of the function (if attained).

$w.globalMinimum

[ number ]. The global minimum of the function (if attained).

$w.globalSupremum

[ number ]. The global supremum of the function.

$w.hidden

boolean. Whether this component is hidden from the rendered output.

$w.labelPosition

text. Position of the function's label.

$w.latex

latex. The function rendered as a LaTeX string.

$w.layer

number. Z-order layer index for stacking the function on a graph.

$w.lowerValue

number. Lower bound for the operator's range.

$w.maxima

[ number ]. Local maxima of the function.

$w.maximumLocations

[ number ]. The x-coordinates of the function's local maxima.

$w.maximumValues

[ number ]. The values of the function's local maxima.

$w.minima

[ number ]. Local minima of the function.

$w.minimumLocations

[ number ]. The x-coordinates of the function's local minima.

$w.minimumValues

[ number ]. The values of the function's local minima.

$w.numExtrema

number. Number of local extrema (minima + maxima) of the function.

$w.numInputs

integer. Number of input variables of the function.

$w.numMaxima

number. Number of local maxima of the function.

$w.numMinima

number. Number of local minima of the function.

$w.numOutputs

integer. Number of output values of the function.

$w.simplify

text. Level of simplification applied when displaying the formula.

$w.styleDescription

text. A textual description of the function's style.

$w.styleDescriptionWithNoun

text. Style description including the word "function".

$w.symbolic

boolean. Whether the function is treated symbolically.

$w.text

text. The function rendered as a plain text string.

$w.textColor

text. Human-readable name for this component's text color, derived from the active style and theme.

$w.textStyleDescription

text. Human-readable description of this component's text styling (color and any background color).

$w.upperValue

number. Upper bound for the operator's range.

$w.variable

_variableName. The function's first input variable name.

$w.variables

[ _variableName ]. The names of the function's input variables.

$w.xscale

number. Scale factor used along the x-axis.

$w.yscale

number. Scale factor used along the y-axis.

Common to all components (4)

$w.doenetML

text. The DoenetML source code that produced this component.

$w.hide

boolean. Whether to hide this component from the rendered output.

$w.isResponse

boolean. Whether this component is treated as a response for the purposes of assessment.

$w.styleNumber

integer. The style number used to select this component's visual styling from the available style definitions.

Examples

Example: Wrap a linear function to $[0, 1)$

The underlying function f(x) = x/4 is plotted alongside its periodic wrap. Each time the line would leave $[0, 1)$ , the wrap brings it back to the other side, producing the sawtooth pattern.

Example: Evaluate a periodically-wrapped function

For an input that already lies in $[0, 1)$ the wrap is a no-op; for an input outside the range the function returns the equivalent value inside the range.

Attribute Examples

Attribute Example: lowerValue, upperValue

lowerValue and upperValue set the periodic range. The wrapped function takes values in $[-2, 2)$ — outputs above $2$ are reduced by $4$ until they fall inside, and outputs below $-2$ are increased by $4$ until they do.

when wrapNumberPeriodic

<wrapFunctionPeriodic>