`<equilibriumLine>`

An equilibrium line of a dynamical system, rendered solid if stable or dashed if unstable

<equilibriumLine> extends <line> to mark a line of equilibria of a dynamical system. Use it to indicate a continuum of equilibrium states (for example a nullcline that consists entirely of equilibrium points) while making the stability visually apparent. The component accepts the full set of <line> attributes.

Attributes and Properties

Attributes for `<equilibriumLine>`

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 (13)

applyStyleToLabel

boolean. Default value: false. Whether to apply this component's selected style to its label.

draggable

boolean. Default value: true. Whether the line can be dragged on a graph.

equation

math. Implicit equation defining the line.

labelPosition

keyword. Where the label sits along this line/curve.

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

layer

integer. Default value: 0. Z-order layer index used to stack graphical components (higher values render on top).

lineWidth

number. Stroke width for lines, in pixels.

parallelTo

_directionComponent. Direction the line should be parallel to (e.g. another line or vector).

perpendicularTo

_directionComponent. Direction the line should be perpendicular to (e.g. another line or vector).

slope

number. Slope of the line.

stable

boolean. Default value: true. Whether the equilibrium is stable (rendered solid) or unstable (rendered dashed).

switchable

boolean. Default value: false. Whether the user can toggle the stability of this equilibrium by clicking it.

through

pointList. Points the line passes through.

variables

[ _variableNameList ]. Names of the variables used in the line equation.

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 `<equilibriumLine name="e">`

Number display (5)

$e.avoidScientificNotation

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

$e.displayDecimals

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

$e.displayDigits

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

$e.displaySmallAsZero

number. Threshold below which numbers are displayed as zero.

$e.padZeros

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

Labels (2)

$e.label

label. The label rendered with this component.

$e.labelIsName

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

Other (27)

$e.applyStyleToLabel

boolean. Whether to apply this component's selected style to its label.

$e.backgroundColor

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

$e.coeff0

math. The constant term in the implicit line equation coeff0 + coeffvar1·x + coeffvar2·y = 0.

$e.coeffvar1

math. The coefficient of the first variable in the implicit line equation coeff0 + coeffvar1·x + coeffvar2·y = 0.

$e.coeffvar2

math. The coefficient of the second variable in the implicit line equation coeff0 + coeffvar1·x + coeffvar2·y = 0.

$e.disabled

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

$e.draggable

boolean. Whether the line can be dragged on a graph.

$e.equation

math. The line's equation as a math expression.

$e.fixed

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

$e.fixLocation

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

$e.hidden

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

$e.labelPosition

text. Where the label sits along this line/curve.

$e.latex

latex. The line's equation rendered as LaTeX.

$e.layer

integer. Z-order layer index used to stack graphical components (higher values render on top).

$e.numDimensions

number. Number of dimensions the line lives in.

$e.points

[ math ]. Two points the line passes through.

$e.slope

math. The slope of the line (2D only).

$e.stable

boolean. Whether the equilibrium is stable (rendered solid) or unstable (rendered dashed).

$e.styleDescription

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

$e.styleDescriptionWithNoun

text. Style description including the word "line".

$e.switchable

boolean. Whether the user can toggle the stability of this equilibrium by clicking it.

$e.text

text. The line's equation rendered as plain text.

$e.textColor

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

$e.textStyleDescription

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

$e.variables

[ _variableName ]. Variable names used in the line's equation.

$e.xintercept

math. The x-intercept of the line.

$e.yintercept

math. The y-intercept of the line.

Common to all components (4)

$e.doenetML

text. The DoenetML source code that produced this component.

$e.hide

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

$e.isResponse

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

$e.styleNumber

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

Examples

Example: Stable and unstable equilibrium lines

Two lines of equilibria: the vertical line is drawn solid (stable) and the horizontal line is drawn dashed (unstable). The stable attribute defaults to true; setting it to false switches the rendering to a dashed line.

Attribute Examples

Attribute Example: switchable

When switchable is set, clicking the line toggles its stable state and the solid/dashed rendering. Useful for exercises where the learner must classify a nullcline.

Attribute Example: stable bound to a boolean input

The stable attribute accepts any boolean expression, so the line’s stability can be driven from any source of state in the document.

equilibriumCurve equilibriumPoint

<equilibriumLine>