Prime-field Linear System Workbench
Solve a rectangular modular system and preserve inconsistent, unique and affine-family outcomes with exact solution witnesses.
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How to use Prime-field Linear System Workbench
Reduce coefficients modulo a verified small prime and perform Gauss–Jordan elimination using field inverses. Free columns supply an explicit nullspace basis; a particular solution is checked against every original equation.
- Enter model json (schema and units below).
- Choose the stated convention and check the units and supported model.
- Calculate, inspect the result, then copy or download it.
Good to know
- Prime modulus 2–1,009; matrix 1–20 rows/columns with integer coefficients and RHS from −1,000,000,000 through 1,000,000,000. Composite moduli are refused. This is a finite-field teaching calculation, not a cryptographic key generator or arbitrary ring solver.
- Local calculation only; no input persistence or external lookup. Text/JSON is limited to 30000 characters and output to 1000000 characters. Numeric model inputs and precision/work limits are stated on this page. Approximate JSON numbers retain full stored values; exact arithmetic outputs retain decimal or fraction strings. Unsupported states fail explicitly.
Common questions
Why are composite moduli refused?
Nonzero residues can fail to have inverses over a composite modulus. The field elimination and solution-count model used here would no longer apply.
Is the input uploaded or saved?
No. The tool calculates inside this browser tab and provides a local download; it does not persist your input.
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