FromContinuedFraction

The value of a continued fraction given its list of terms $[a_0, a_1, \ldots]$.

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

FromContinuedFraction(terms)For a flat list of integers/symbols with at least one symbol, builds the nested unsimplified form $a + 1/(b + 1/c)$ term by term rather than compute-engine's combined single ratio.

SageMathcontinued_fraction(terms).value()SymPycontinued_fraction_reduce(terms)

Typed signatures

Type	Package	Applies
(collection<any>) -> number	analyticreplaces compute-engine	always
(collection<any>) -> number	compute-engine	always
(collection<any>) -> number	modularreplaces analytic	always

Domain: Compute engine

Details

• Takes the list of terms $[a_0; a_1, \ldots]$, or $[a_0, [\text{period}]]$ for a periodic tail, as Wolfram's does; ContinuedFraction is its inverse.
• The empty list stays unevaluated, where Wolfram answers Infinity.

Examples

Basic #

$[3;7,15,1]$ is the convergent $355/113$

live ↗

In$\mathrm{FromContinuedFraction}(\bigl\lbrack3, 7, 15, 1\bigr\rbrack)$Out$\frac{355}{113}$

Scope #

Built term by term, unsimplified

live ↗

In$\mathrm{FromContinuedFraction}(\bigl\lbrack a, b, c\bigr\rbrack)$Out$a+\frac{1}{b+\frac{1}{c}}$

$[1;\overline{1}]$ is the golden ratio

live ↗

In$\mathrm{FromContinuedFraction}(\bigl\lbrack1, \bigl\lbrack1\bigr\rbrack\bigr\rbrack)$Out$\frac{1+\sqrt{5}}{2}$

A one-term list is that integer

live ↗

In$\mathrm{FromContinuedFraction}(\bigl\lbrack5\bigr\rbrack)$Out$5$

The first term may be negative: $-3+1/(2+1/5)$

live ↗

In$\mathrm{FromContinuedFraction}(\bigl\lbrack-3, 2, 5\bigr\rbrack)$Out$-\frac{28}{11}$

Properties #

Inverts ContinuedFraction: a rational round-trips through its expansion

live ↗

In$\mathrm{FromContinuedFraction}(\mathrm{ContinuedFraction}(\frac{47}{17}))$Out$\frac{47}{17}$

Possible issues #

The empty list has no value here

live ↗

In$\mathrm{FromContinuedFraction}(\bigl\lbrack\bigr\rbrack)$Out$\mathrm{FromContinuedFraction}(\bigl\lbrack\bigr\rbrack)$

About

Examples	7
Checked against	Wolfram Language 6 agree1 differSageMath 4 agree3 errorSymPy 6 agree1 unevaluated
Crosswalk	Wolfram LanguageSageMathSymPy

Implementation

mappedsympypackages/oracle/src/mappings.ts

A periodic tail [a0, [period]] is SymPy's own nested-list form. The empty list is 0 there, where ours stays unevaluated and Wolfram answers Infinity.

mappedsagepackages/oracle/src/mappings.ts

See also: ContinuedFraction