`<equilibriumPoint>`

An equilibrium point of a dynamical system, rendered as a filled point if stable or open if unstable

<equilibriumPoint> extends <point> to mark an equilibrium of a dynamical system. This conventional notation lets a single diagram convey both the location and the stability of an equilibrium. The component otherwise accepts the full set of <point> attributes (coordinates, label, style, etc.).

Attributes and Properties

Attributes for `<equilibriumPoint>`

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 (17)

addControls

keyword. Whether to render interactive control handles.

Value	Description
`none`	Show no control handles.
`both` (default)	Show control handles for moving the point in both x and y.
`xOnly`	Show a control handle that constrains motion to the x direction.
`yOnly`	Show a control handle that constrains motion to the y direction.

applyStyleToLabel

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

controlOrder

integer. Default value: 0. Slot order for graph controls (1-indexed; 0 means no explicit slot request).

coords

coords. The point's coordinates as a single math expression.

draggable

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

hideOffGraphIndicator

boolean. Whether to suppress the indicator drawn at the edge when the point is off-screen.

labelPosition

keyword. Position of the point's label.

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

layer

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

markerSize

number. Marker size in pixels.

markerStyle

keyword. Marker shape.

Value	Description
`circle`	Circular marker.
`square`	Square marker.
`triangle`	Triangular marker pointing up (alias for "triangleUp").
`triangleUp`	Triangular marker pointing up.
`triangleDown`	Triangular marker pointing down.
`triangleLeft`	Triangular marker pointing left.
`triangleRight`	Triangular marker pointing right.
`diamond`	Diamond-shaped marker.

showCoordsWhenDragging

boolean. Default value: true. Whether to show coordinate labels while dragging.

stable

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

switchable

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

x

math. The first coordinate (x) of the point.

xs

[ mathList ]. The point's coordinates as a list.

y

math. The second coordinate (y) of the point.

z

math. The third coordinate (z) of the point.

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 `<equilibriumPoint 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 (30)

$e.addControls

text. Whether to render interactive control handles.

$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.constraintUsed

boolean. Whether this constraint was applied to the component.

$e.controlOrder

integer. Slot order for graph controls (1-indexed; 0 means no explicit slot request).

$e.coords

coords. The point's coordinates as a math expression.

$e.disabled

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

$e.draggable

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

$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.hideOffGraphIndicator

boolean. Whether to suppress the off-graph indicator when out of view.

$e.labelPosition

text. Position of the point's label.

$e.latex

latex. The point rendered as a LaTeX string.

$e.layer

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

$e.numDimensions

number. Number of dimensions of the point.

$e.numDimensionsForConstraints

number. Number of dimensions exposed to constraint computations (alias for numDimensions).

$e.scales

number. The graph axis scales (x and y) used when applying this constraint.

$e.showCoordsWhenDragging

boolean. Whether to show coordinate labels while dragging.

$e.stable

boolean. Whether the equilibrium is stable (rendered filled) or unstable (rendered open).

$e.styleDescription

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

$e.styleDescriptionWithNoun

text. Style description including the word "point".

$e.switchable

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

$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.value

coords. The point's coordinates as a single math expression.

$e.x

math. The first coordinate (x) of the point.

$e.xs

[ math ]. The point's coordinates as a list.

$e.y

math. The second coordinate (y) of the point.

$e.z

math. The third coordinate (z) of the point.

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 equilibria

Three equilibria on the $x$ -axis: the filled points are stable and the open point is unstable. The stable attribute defaults to true; setting it to false flips the rendering to an open point.

Attribute Examples

Attribute Example: switchable

When switchable is set, clicking the point toggles its stable state (and therefore its filled/open rendering). Use this for interactive exercises where the learner must classify each equilibrium.

Attribute Example: stable bound to a boolean input

The stable attribute accepts any boolean expression, so the rendering can be driven from a <booleanInput> or any other state.

Property Examples

Property Example: stable

The stable property reflects the current stability of the equilibrium. Combined with switchable it can be read back to grade the learner’s classification.

equilibriumLine evaluate

<equilibriumPoint>