`<differences>`

Differences between successive child math or number values; one shorter than the inputAdded in 0.7.27

<differences> is a Math Operator component that renders the differences between successive arguments: for inputs $a_1, a_2, \ldots, a_n$ it gives $a_2 - a_1,\; a_3 - a_2,\; \ldots,\; a_n - a_{n-1}$ .

The result is one shorter than the input, and is empty when the input has fewer than two values. <differences> undoes <cumulativeSum>, apart from the first value, which the running total has already absorbed.

Attributes and Properties

Attributes for `<differences>`

Highlighted (3)

asList

boolean. Default value: true. Whether to render the items separated by commas (true) or with no separator (false).

forceNumeric

boolean. Default value: false. Whether to force the operator to evaluate numerically rather than symbolically.

forceSymbolic

boolean. Default value: false. Whether to force the operator to evaluate symbolically rather than numerically.

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.

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 `<differences name="d">`

Highlighted (2)

$d.forceNumeric

boolean. Whether to force the operator to evaluate numerically rather than symbolically.

$d.forceSymbolic

boolean. Whether to force the operator to evaluate symbolically rather than numerically.

Number display (5)

$d.avoidScientificNotationIn development

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

$d.displayDecimalsIn development

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

$d.displayDigitsIn development

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

$d.displaySmallAsZeroIn development

number. Threshold below which numbers are displayed as zero.

$d.padZerosIn development

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

Common to all components (8)

$d.disabledIn development

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

$d.doenetML

text. The DoenetML source code that produced this component.

$d.fixedIn development

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

$d.fixLocationIn development

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

$d.hiddenIn development

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

$d.hide

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

$d.isResponse

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

$d.styleNumber

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

Examples

Example: successive differences

Four inputs give three differences.

Example: first differences of a sequence

The first differences of the squares are the odd numbers, and their differences are constant — the signature of a quadratic.

Example: inverting a cumulative sum

Taking differences recovers the original values, except for the first one, which the cumulative sum folded into its starting entry.

<differences>