Description
Generate bounded symbolic binomial term prompts and exact integer coefficient keys using delegated combination counts and BigInt powers.
A generated practice exercise contains a prompt and an answer key under a specific rule set. A planted answer establishes one possible solution; only an explicit enumeration or uniqueness check establishes whether alternatives exist.
Generate bounded symbolic binomial term prompts and exact integer coefficient keys using delegated combination counts and BigInt powers.
When to use this tool
Use this generator to create reproducible binomial expansion coefficient quiz cases from the supplied model or bank. Inspect the returned evidence before using cases in a test or exercise.
How to use the tool and how it works
- Supply minimumDegree, maximumDegree, a, b in the field shapes below. Set seed when you need an explicit replay.
- Run the tool and correct any input error. For generated controls, distinguish a successful fixture containing an invalid case from failure to generate the fixture.
- Read expression, degree, termIndex, xPower, yPower, coefficient. Use the conventions below. Keep answer-bearing fields separate when presenting an exercise.
Draw a degree and zero-based term index for (a*x+b*y)^degree. Delegate the binomial combination count, multiply signed integer powers with BigInt, and return the exact coefficient as decimal text with x/y exponents.1
Delegated operations used for this result: combination count. Their calculation or parsing conventions apply to the corresponding result fields.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| minimumDegree | Minimum Degree | Required. Safe integer; minimum 0; maximum 20. |
| maximumDegree | Maximum Degree | Required. Safe integer; minimum 0; maximum 20. |
| a | A | Required. Safe integer; minimum -8; maximum 8. |
| b | B | Required. Safe integer; minimum -8; maximum 8. |
| seed | Optional numeric seed; takes precedence over context randomness. Without either, use the fixed tool.io default seed. | Optional. Safe integer. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| expression | Expression | Required. Text. |
| degree | Degree | Required. Safe integer. |
| termIndex | Term Index | Required. Safe integer. |
| xPower | X Power | Required. Safe integer. |
| yPower | Y Power | Required. Safe integer. |
| coefficient | Coefficient | Required. Text. |
| randomness | Replay source and normalized 32-bit seed, or null seed for an advancing context source. | Required. Object; no unknown keys. |
| randomness.seed | Optional safe-integer replay seed; normalization and precedence are explained below. | Required. Safe integer. or Null. |
| randomness.source | Source | Required. Text; one of "context", "seed". |
An explicit safe-integer seed takes precedence over injected context randomness and is normalized to an unsigned 32-bit integer. With no seed and no context source, replay uses the fixed tool.io default seed. A context source must return finite values from zero inclusive to one exclusive; its advancing state must be retained separately. randomness records the source and normalized seed, or null for context. These generators are not cryptographic random sources.
{
"input": {
"minimumDegree": 3,
"maximumDegree": 5,
"a": 2,
"b": -1,
"seed": 42
},
"output": {
"expression": "(2*x+(-1)*y)^4",
"degree": 4,
"termIndex": 2,
"xPower": 2,
"yPower": 2,
"coefficient": "24",
"randomness": {
"seed": 42,
"source": "seed"
}
}
}Limitations and assumptions
- The result is one coefficient rather than a complete expansion. Negative coefficients and zero powers follow exact integer arithmetic; generated bounds keep the delegated combination count valid.
- A replay requires the same complete input and implementation. The stated sampling convention applies within its eligible space. A finite draw does not exhaust all possible outputs; repeats remain possible unless a distinct-selection rule is explicit.
- The field tables state structural bounds; cross-field constraints and bounded search or output budgets also apply. Unknown keys are rejected where the object contract disallows them. Input errors are distinct from null fields and deliberate invalid controls in a successful output.
Alternative or Complementary methods
For a supplied example, inspect the returned construction or delegated check directly. To evaluate a consumer, also test cases chosen for its own boundaries; a generated finite corpus does not establish exhaustive coverage.
References
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