Range

Generated from the engine's own definition: compute-engine's symbol, which we neither extend nor document by hand.

A sequence of numbers from a start to an end value with an optional step.

✓ checked against that system · ! checked, with disagreements (hover a chip)FungrimRange↗Wolfram LanguageRange✓↗

Range(number, number?, step: number?) -> indexed_collection<number>as compute-engine declares it

Typed signatures

Type	Package	Applies
(number, number?, step: number?) -> list<number>	compute-engine	always

Domain: Compute engine

Examples

Basic #

Ranges are inclusive at both ends

live ↗

In$1..4$Out$\bigl\lbrack1, 2, 3, 4\bigr\rbrack$

Scope #

A step of 2 skips every other integer

live ↗

In$1..3..10$Out$\bigl\lbrack1, 3, 5, 7, 9\bigr\rbrack$

A negative step counts down

live ↗

In$10..9..1$Out$\bigl\lbrack10, 9, 8, 7, 6, 5, 4, 3, 2, 1\bigr\rbrack$

A high-precision step gives machine floats, stopping before 10

live ↗

In$0..(0+3.141\,592\,653\,589\,793\,238\,46)..10$Out$\bigl\lbrack0, 3.141\,592\,653\,589\,793, 6.283\,185\,307\,179\,586, 9.424\,777\,960\,769\,38\bigr\rbrack$

The same range with a slightly shorter step literal gives the same floats

live ↗

In$0..(0+3.141\,592\,653\,589\,793\,238\,46)..10$Out$\bigl\lbrack0, 3.141\,592\,653\,589\,793, 6.283\,185\,307\,179\,586, 9.424\,777\,960\,769\,38\bigr\rbrack$

A rational step materializes exact thirds, not floating-point approximations

live ↗

In$0..(0+\frac{1}{3})..3$Out$\bigl\lbrack0, \frac{1}{3}, \frac{2}{3}, 1, \frac{4}{3}, \frac{5}{3}, 2, \frac{7}{3}, \frac{8}{3}, 3\bigr\rbrack$

Known value · Range(a, b, s): each element is a + k*s, exact over ℚ

Same for a rational step that lands on integers partway through

live ↗

In$1..(1+\frac{1}{2})..5$Out$\bigl\lbrack1, \frac{3}{2}, 2, \frac{5}{2}, 3, \frac{7}{2}, 4, \frac{9}{2}, 5\bigr\rbrack$

Known value · Range(a, b, s): each element is a + k*s, exact over ℚ

live ↗

In$2^{225}..(5+2^{225})$Out$\bigl\lbrack53\,919\,893\,334\,301\,279\,589\,334\,030\,174\,039\,261\,347\,274\,288\,845\,081\,144\,962\,207\,220\,498\,432, 53\,919\,893\,334\,301\,279\,589\,334\,030\,174\,039\,261\,347\,274\,288\,845\,081\,144\,962\,207\,220\,498\,433, 53\,919\,893\,334\,301\,279\,589\,334\,030\,174\,039\,261\,347\,274\,288\,845\,081\,144\,962\,207\,220\,498\,434, 53\,919\,893\,334\,301\,279\,589\,334\,030\,174\,039\,261\,347\,274\,288\,845\,081\,144\,962\,207\,220\,498\,435, 53\,919\,893\,334\,301\,279\,589\,334\,030\,174\,039\,261\,347\,274\,288\,845\,081\,144\,962\,207\,220\,498\,436, 53\,919\,893\,334\,301\,279\,589\,334\,030\,174\,039\,261\,347\,274\,288\,845\,081\,144\,962\,207\,220\,498\,437\bigr\rbrack$

Applications #

live ↗

In$q^{1..5}$Out$\bigl\lbrack q, q^2, q^3, q^4, q^5\bigr\rbrack$

Properties #

Starts at $-4$ and steps by 3, stopping at 8

live ↗

In$(-4)..(-1)..9$Out$\bigl\lbrack-4, -1, 2, 5, 8\bigr\rbrack$

At reaches the same exact element, not the double it would round to

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In$(0..(0+\frac{1}{3})..3)[3]$Out$\frac{2}{3}$

Known value · Range(a, b, s): each element is a + k*s, exact over ℚ

The element count is exact too, not a floor of a rounded quotient

live ↗

In$\mathrm{Length}(0..(0+\frac{1}{3})..3)$Out$10$

Known value · Range(a, b, s): the grid runs from a to the last multiple of s at or before b

Possible issues #

The end 10 is not hit exactly, so the last element is 9

live ↗

In$0..3..10$Out$\bigl\lbrack0, 3, 6, 9\bigr\rbrack$

About

Examples	13
Checked against	Wolfram Language 13 agreemathlib4 6 agree6 error
Crosswalk	FungrimWolfram Language

Implementation

mappedmathlib4packages/oracle/src/mappings.ts

inclusive, counting down when the start is past the end; integer endpoints only (a rational endpoint fails to elaborate rather than rounding), read as rationals like the lane's lists

mappedmathlib4packages/oracle/src/mappings.ts

stops before an end the step misses; empty when the step is 0 or points away from the end; integer endpoints and step only (a rational or decimal one fails to elaborate rather than rounding)

mappedmathlib4packages/oracle/src/mappings.ts

Range(n) is Range(1, n), so it counts down from 1 when n is below 1; an integer n only