Description
Check divisibility of a group order by a proposed orbit size.
Combinatorial checks often evaluate necessary conditions or one algebraic component. Parity can be combined from supplied signs, a divisibility test can constrain an orbit size, and prefix sums can enforce a strict positivity condition. Passing one condition does not construct or prove the existence of the full combinatorial object.
Check divisibility of a group order by a proposed orbit size.
When to use this tool
Use Orbit Size Divisibility Remainder when you already have groupOrder, proposedOrbitSize and need to check divisibility of a group order by a proposed orbit size.
How to use the tool and how it works
- Enter groupOrder, proposedOrbitSize. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read remainder, dividesGroupOrder. Inspect dividesGroupOrder before interpreting the associated values.
Require both positive safe integers; return groupOrder%size and remainder===0.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| groupOrder | Group Order | Required. Safe integer; minimum 1. |
| proposedOrbitSize | Proposed Orbit Size | Required. Safe integer; minimum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| remainder | Remainder | Required. Safe integer. |
| dividesGroupOrder | Necessary divisibility condition only; not proof that an orbit of that size exists. | Required. Boolean. |
{
"input": {
"groupOrder": 12,
"proposedOrbitSize": 4
},
"output": {
"remainder": 0,
"dividesGroupOrder": true
}
}Limitations and assumptions
- Divisibility is a necessary arithmetic check in an applicable finite group action, not proof that the proposed orbit or action exists.
- 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
Use a complete construction, enumeration or proof for the mathematical question. Keep integer ranges, empty-input conventions and strict inequalities explicit when incorporating these local checks into a larger algorithm.
References
Similar or alternative tools
- Binomial Coefficient Symmetry Index
Calculate symmetric and smaller binomial-coefficient indices.
- Ballot Prefix Surplus
Calculate exact cumulative supplied ballot surpluses and a strict-prefix flag.