Linear-factor Partial Fractions Workbench

How to use Linear-factor Partial Fractions Workbench

Construct the declared denominator, long-divide any improper fraction and solve a coefficient identity for every repeated-factor term without parsing symbolic code.

1. Use the example as the schema; replace its labels and entered model assumptions.
2. Construct the declared denominator, long-divide any improper fraction and solve a coefficient identity for every repeated-factor term without parsing symbolic code.
3. Calculate, inspect the complete witnesses and limitations, then copy or download the JSON report.

Good to know

• Numerator has 1–21 ascending-power decimal-string coefficients; nonzero scale and distinct decimal-string roots have magnitude at most 1 billion. Each multiplicity is an integer 1–6, total denominator degree at most 12.
• Only supplied rational linear factors; no automatic root finding, irreducible quadratic/complex factors, symbolic variable parsing or integration. Original denominator poles remain excluded, including canceled factors. Exact intermediate bit budgets may refuse extreme coefficient growth.
• Local calculation with no upload, input persistence or outside lookup. Model JSON is limited to 30,000 characters and 10,000 values. Decimal quantities are strings with up to six places; count fields use plain JSON integers. Exact fractions are capped at 8,192 bits. The complete JSON output is limited to 1,000,000 characters; approximate numbers preserve their stored values. Unsupported states fail explicitly.