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Finite Difference Row Entry Tool

Return one entry of the first forward-difference row from adjacent sequence values.

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Description

Choose a valid adjacent position and subtract values[index] from values[index + 1].

A sequence depends on its starting index, initial values, and recurrence or difference rule. A component evaluated at one index does not establish the behavior of an arbitrary sequence outside those supplied conventions.

Choose a valid adjacent position and subtract values[index] from values[index + 1].

When to use this tool

Use Finite Difference Row Entry when you need a bounded sequence-index or adjacent-difference calculation.

How to use the tool and how it works

  1. Enter values, index. Use the units and conventions below.
  2. Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
  3. Read difference. Use the output convention below.

Choose a valid adjacent position and subtract values[index] from values[index + 1].1

Input fieldMeaning and unitsAccepted input
valuesValuesRequired. Array of finite number; maximum items 256.
indexPosition under the zero-based or one-based convention stated above.Required. Safe integer; minimum 0.
Output fieldInterpretationReturned shape
differenceDifferenceRequired. Finite number.
json
{
  "input": {
    "values": [
      2,
      5,
      11,
      20
    ],
    "index": 1
  },
  "output": {
    "difference": 6
  }
}

Limitations and assumptions

  • This is one forward finite difference in value units, without division by coordinate spacing or a derivative estimate.
  • Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
  • Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.

Alternative or Complementary methods

Write down the full sequence definition and verify its indexing when comparing with another source.

References

  1. Calculation and input contract: sequence/finite-difference-row-entry — tool.io

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