Element conservation is not reaction prediction
Distinguish a unique positive conservation vector from nonunique or impossible full-species balances without inferring real chemical reactions.
A conserved equation answers one question
Element conservation checks whether the declared left and right species have compatible counts. It does not establish whether a reaction occurs, whether it is favorable, or which mechanism and conditions apply. The input grammar also excludes charge, so ionic/redox conservation is outside this task.
- List the intended neutral species in order, without initial coefficients; keep case and hydrate separators exact.
- Check rank, nullity and the reported state before using any coefficient vector. For H2 + O2 -> H2O, the primitive ratio is 2:1:2.
- Download the full matrix and proof to check every element total. An underdetermined result requires a separate, justified choice; it does not select a reaction.
Do not turn a basis into a chosen reaction
One strictly positive basis direction yields an unambiguous primitive integer ratio. Several basis directions leave choices unresolved, even if some positive combination might exist. The tool reports underdetermined and every exact basis vector; it does not confuse “not uniquely determined” with “no possible positive balance”.
| State | Proven | Not proven |
|---|---|---|
| balanced | Exact positive element-count conservation | Real reaction occurrence or safety |
| underdetermined | More than one exact balance direction | A preferred coefficient set; impossibility of a positive combination |
| no-strictly-positive-balance | The one-dimensional vector contains zero/mixed signs | A result after deleting species or changing sides |
| no-nonzero-balance | Only the zero vector satisfies the current element-count matrix | A conclusion after changing the species formulas |
Original notation is evidence
Parentheses, brackets and hydrate separators determine element counts. H2O.2H2O has a top-level hydrate factor; whitespace inside a formula and an initial 2H2O coefficient are outside the declared grammar. Case matters: unsupported names are rejected rather than corrected to a guessed element.
Original bytes, species byte spans, exact counts and all basis vectors let a recipient reconstruct the conservation question. Copies show balanced text or status; full proof/matrix downloads preserve what the panel cannot display.
Treat guards as an explicit stop
A 16KiB declaration can still produce large exact coefficients. Integer, operation and 2MiB combined-output guards stop the whole task atomically rather than substituting floating arithmetic. Simplify the actual question within the supported grammar; do not interpret a limit refusal as a chemistry conclusion.
Independent exact matrix and formula readers verify conservation representations. Their success and local Worker cancellation are implementation evidence; production-browser interactions and final admission remain central review decisions.
References
- Neutral matrix-balancing task
Author asks for an automatic matrix nullspace calculation and explicitly counts elements without charge.
- Matrix stoichiometry question
First-person question about reducing manual balancing errors; not evidence of reaction occurrence.
Tools in this category
Expand a tool to see its steps, options and supported formats, then open its workspace.
Neutral chemical-equation balancerBalance explicitly declared neutral formulas with exact rational arithmetic, preserving the full element matrix, nullspace basis and conservation proof without guessing nonunique solutions.
Enter both sides with no initial coefficients. A unique strictly positive nullspace vector gives primitive integer coefficients; every other state remains explicit.
Steps
- Enter a neutral equation with both sides and no starting coefficients.
- Read the conservation state, rank and nullity; accept coefficients only when state is balanced.
- Copy balanced text or download the full exact proof, matrix and original equation.
Capabilities and limits
- UTF-8 equation up to16KiB,50 ordered species,109 elements H–Mt, nesting depth16 and100 digits per count. Exact intermediate integers≤4,096 bits, work≤1,000,000 operations, complete original/proof/matrix/balance/totals≤2MiB. Dimensions and coefficient growth remain coupled.
- ASCII case-sensitive symbols, positive integer counts without leading zero, nested ()/[] and top-level hydrate dot or · with an optional positive factor after that delimiter. Whitespace only around species. Exactly one ->, → or = and plus-separated species; duplicates stay ordered.
- Ds–Og, initial coefficients, charges/electrons, isotopes, states, macros, fractions and scripts are Unsupported. A hydrate dot is not decimal stoichiometry. The operation ceiling is a work guard, not a promise of a reachable successful exact1million-operation case.
- Nullity0: no-nonzero-balance. Nullity1 and all coefficients strictly positive: balanced. Nullity1 with zero/mixed signs: no-strictly-positive-balance. Nullity>1: underdetermined with the complete exact basis; no guessed positive combination or claim that no positive solution exists.
- All species counts, UTF-8 source spans, signed matrix, RREF, rational basis and primitive integer basis remain in proof.json. Balanced output adds full left/right element totals. Exact decimal/rational CSV tokens may be reinterpreted by spreadsheet software. No reaction-occurrence, mechanism, energy or safety conclusion.
- The table shows all species within the50-species cap; long cells preview2,000 UTF-16 units. Copy gives balanced text or the explicit machine-state code. Full proof and CSV downloads remain complete; failures and cancellation publish no partial files.