Variables, Constants, Expressions, and Equations

Install and import#

npm install fintech-algorithms

import { variablesConstantsExpressionsAndEquations } from "fintech-algorithms/foundations/mathematical-language-and-quantitative-reasoning/variables-constants-expressions-and-equations";

Signature#

variablesConstantsExpressionsAndEquations(input)

Substitutes named quantities into a cash-balance equation and checks that the rearranged form still holds, returning the ending cash implied by startingCash, inflows and outflows.

Parameters#

Returns#

{ endingCash: number; balances: boolean }

endingCash is startingCash + inflows - outflows. balances is true when moving the three terms back across the equals sign lands within 1e-12 of zero, which it does for any finite input.

Errors#

• When input is not a plain object — throws TypeError
• When values is missing, empty, or not an array — throws RangeError
• When values contains a value that is not a finite number — throws RangeError

Complexity: time O(n), space O(n).

Worked example#

verified This is the worked example published in the article, replayed by the test suite on every run. The output cannot drift.

Input#

{
  "values": [1, 2, 3, 4, 5],
  "startingCash": 1000,
  "inflows": 250,
  "outflows": 120,
  "slope": 2,
  "intercept": 1,
  "part": 25,
  "whole": 200,
  "elapsed": 5,
  "old": 4.5,
  "new": 4.75,
  "base": 16,
  "exponent": 0.5,
  "a": 2
}

Showing 14 of 28 fields.

Call#

variablesConstantsExpressionsAndEquations(input)

Returns#

object with 2 fields: endingCash, balances

{
  "endingCash": 1130,
  "balances": true
}

Diagrams#

Calculation flow#

flowchart LR
    A["Name the input"] --> B["Apply: ending cash = starting cash + inflows - outflows"]
    B --> C["Check units and boundary"]
    C --> D["Explain the output"]

How it works#

This page states the contract — how to call it correctly. The article explains the concept: why it works, and where it breaks.

Read the article →

References#

• NIST/SEMATECH e-Handbook of Statistical Methods — NIST/SEMATECH
• Author-derived and synthetic boundary

The rest of the Mathematical Language and Quantitative Reasoning family#

• Functions, Domains, Ranges, and GraphsEvaluates the straight-line function intercept + slope * value at every entry of values and reports the input span it was e…
• Ratios, Proportions, Rates, and PercentagesTurns a part-and-whole pair into a ratio and a percentage, and turns the same part spread over an elapsed span into a rate per …
• Percentage Change, Percentage Points, and Basis PointsExpresses the move from an old level to a new one three ways: as a percent change relative to the old level, as a raw differenc…
• Exponents, Roots, and LogarithmsApplies the three operations that share one base: raising it to an exponent, taking its square root, and taking its natural log…
• Summation, Products, and Index NotationReduces a series to its sum and its product, and re-emits it as explicitly numbered terms so subscript notation can be read aga…
• Linear Equations and SystemsSolves the two-equation system a*x + b*y = c and d*x + e*y = f by Cramer's rule, returning the solution and the determinant…
• Inequalities, Bounds, and ConstraintsTests a candidate number against a lower and upper bound, reporting whether it is admissible, what it becomes once clamped into…
• Units, Dimensions, Scale, and NormalizationRescales a series by subtracting an offset and dividing by a scale, so numbers recorded in one unit can be compared on a common…
• Rounding, Precision, Tolerance, and Significant DigitsRounds a candidate to a fixed number of decimal places and measures it against a reference value and an allowed tolerance.