Sum

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

Sum(f, [a, b]) computes the sum of f from a to b; Sum(L) sums the elements of a collection L

✓ checked against that system · ! checked, with disagreements (hover a chip)WikipediaSummation↗MathWorldSum↗WikidataQ218005↗Britannicatopic/summand↗FungrimSum✓↗Fungrim entryFindStatSt000165via ParkingFunction✓↗Wolfram LanguageSum✓↗

Sum(any, tuple*) -> numberSum(f, [a, b]) computes the sum of f from a to b; Sum(L) sums the elements of a collection L

SageMathsum(any, tuple*)SymPysummation(any, tuple*)

Typed signatures

Type	Package	Applies
(any, tuple*) -> number	analyticreplaces evaluation	always
(any, tuple*) -> number	compute-engine	always
(any, tuple*) -> number	evaluationreplaces compute-engine	always

Domain: Compute engine

Examples

Basic #

Sum of squares up to 10, using the default start of 1

live ↗

In$\sum_{k}^{10}k^2$Out$385$

The Basel-type sum, $\zeta(6)=\pi^6/945$

live ↗

In$\sum_{k=1}^{∞}\frac{1}{k^6}$Out$\frac{π^6}{945}$

The members of the subset $\{1, 3\}$ of $\{1, \dots, 4\}$

live ↗

In$\mathrm{CombinatorialStat}(\operatorname{Finset}(\operatorname{Tuple}(4,\bigl\lbrack1, 3\bigr\rbrack)), \text{Sum})$Out$4$

The inversion table $0110$, whose sum is the permutation's inversion count

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{PermutationInversion}}([0, 1, 1, 0]), \text{Sum})$Out$2$

The subexcedant sequence $0011$

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{SubexcedantSeq}}([0, 0, 1, 1]), \text{Sum})$Out$2$

Scope #

live ↗

In$\sum_{k=1}^{∞}\frac{1}{k^2}$Out$\frac{π^2}{6}$

About

Examples	6
Checked against	Wolfram Language 3 agreeSageMath 3 agreeSymPy 3 agreemathlib4 1 agree
Crosswalk	WikipediaMathWorldWikidataBritannicaFungrimFungrim entry ×47FindStatWolfram LanguageSageMathSymPy

Implementation

mappedsympypackages/oracle/src/mappings.ts

The iterator (Limits or Tuple, k from a to b, or from 1 when a is Nothing) is emitted as SymPy's (k, a, b). SymPy sums reversed bounds by Karr's convention: b < a - 1 gives a negative sum.

mappedsagepackages/oracle/src/mappings.ts

mappedmathlib4packages/oracle/src/mappings.ts

The emitter reads the iterator Limits(k, a, b) or Tuple(k, a, b), from 1 when a is Nothing or left out, as the summand's lambda, a and b. Over ℤ, or ℕ where the summand needs one. An empty range is 0, as ours.