Somos sequence¶

In mathematics, a Somos sequence is a sequence of numbers defined by a certain recurrence relation, described below.

Version: v1 · 2026-09-28 · History
Domain-specific #: 12165
Domain group: Formal Sciences
Origin domain: Mathematics
Subdomains: Number Theory, Recurrence Relations → Mathematics

Core Idea¶

Somos sequence is treated here as the recurring mathematics, logic, and statistics identity summarized by this source-grounded definition: In mathematics, a Somos sequence is a sequence of numbers defined by a certain recurrence relation, described below. In mathematics, a Somos sequence is a sequence of numbers defined by a certain recurrence relation, described below. They were discovered by mathematician Michael Somos. From the form of their defining recurrence (which involves division), one would expect the terms of the sequence to be fractions, but surprisingly, a few Somos sequences have the property that all of their.

Scope of Application¶

Integrality and the Laurent phenomenon. That is, as a function of the initial terms a0 , ..., a{k-1} , every term an is a multivariate Laurent polynomial with coefficients in \mathbb{Z}[\alpha1, \dots, \alpha{\lfloor k/2.
The general term is given by the formula. where \sigma(z) = \sigma(z; g2, g3) denotes the Weierstrass sigma function associated with the curve E written in the canonical form.
The general term is given by the formula. The (x, y) coordinates of the sequence Q + n P are given by (\wp(z0 + n \kappa), \wp'(z0 + n \kappa)) , where \wp(z) = \wp(z; g2, g3) denotes the Weierstrass.
The general term is given by the formula. The coefficients \alpha and \beta are given as elliptic functions of \kappa by.
Recurrence equations. For an integer number k larger than 1 , a Somos- k sequence {an}{n \in \mathbb{Z}} is a solution of the equation.

Clarity¶

A clear use of Somos sequence names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is In mathematics, a Somos sequence is a sequence of numbers defined by a certain recurrence relation, described below.

Manages Complexity¶

Somos sequence compresses multiple mathematics, logic, and statistics details into a stable diagnostic relation. The source shows both the central mechanism—the sequence yielded by setting \alpha1 = \alpha2 = \dots = \alpha{\lfloor k/2 \rfloor} = 1 and a0 = a1 = \dots = a{k - 1} = 1 is referred to as the Somos- k sequence.—and the practical consequence—in mathematics, a Somos sequence is a sequence of numbers defined by a certain recurrence.

Abstract Reasoning¶

Type the carrier. Identify the mathematics, logic, and statistics entities to which the claim applies.
State the relation. Use the source-grounded identity: In mathematics, a Somos sequence is a sequence of numbers defined by a certain recurrence relation, described below.
Check operation and conditions. The form of the recurrences describing the Somos sequences involves divisions, making it appear likely that the sequences defined by these recurrence will contain fractional values.
Demand recognition evidence.

Knowledge Transfer¶

Within the home domain. Knowledge about Somos sequence transfers literally when a new case preserves the same carrier type, relation, and recognition test. That is, as a function of the initial terms a0 , ..., a{k-1} , every term an is a multivariate Laurent polynomial with coefficients in \mathbb{Z}[\alpha1, \dots, \alpha{\lfloor k/2 \rfloor}] . where \sigma(z) = \sigma(z; g2, g3) denotes the Weierstrass sigma function associated with the curve E written in the canonical form. Beyond the home domain. No canonical parent is asserted for Somos sequence.

Relationships to Other Abstractions¶

Current abstraction Somos sequence Domain-specific

Parents (1) — more general patterns this builds on

Somos sequence presupposes Recurrence relation Domain-specific

A Somos sequence is generated by a defining recurrence relation.

Hierarchy path (1) — routes to 1 parentless root

Somos sequence → Recurrence relation → Recursion

Neighborhood in Abstraction Space¶

Somos sequence sits in a moderately populated region (45^th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.

Family — Unclustered & Miscellaneous (2551 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-08