Description
Return leadingZeros=min(length,delay), retained=length-leadingZeros, and discarded=leadingZeros for nonnegative integer length and delay.
A sequence rule specifies an index origin, state order, and relation among terms. Advancing one step, mapping an index, and checking a local residual answer different questions. Supplied coefficients or periods define a model; they do not establish that observations follow it.
Return leadingZeros=min(length,delay), retained=length-leadingZeros, and discarded=leadingZeros for nonnegative integer length and delay.
When to use this tool
Use Sequence Delay Zero Padding Count when you need this particular index map, recurrence step, count, or local algebraic term under supplied sequence conventions.
How to use the tool and how it works
- Enter length, delay. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read leadingZeros, retained, discarded. Use the output convention below.
Return leadingZeros=min(length,delay), retained=length-leadingZeros, and discarded=leadingZeros for nonnegative integer length and delay.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| length | Length | Required. Safe integer; minimum 0. |
| delay | Delay | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| leadingZeros | Leading Zeros | Required. Safe integer. |
| retained | Retained | Required. Safe integer. |
| discarded | Discarded | Required. Safe integer. |
{
"input": {
"length": 10,
"delay": 3
},
"output": {
"leadingZeros": 3,
"retained": 7,
"discarded": 3
}
}Limitations and assumptions
- This models a fixed-length delayed sequence with leading zero padding and tail truncation. No values are shifted, and discarded counts positions rather than observed zero-valued entries.
- The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
- 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. Signed zero is exported as zero.
Alternative or Complementary methods
Choose exact integer arithmetic when the index or coefficient range requires it. A complete sequence analysis needs actual terms and a consistent index and state-order convention beyond one local step.
References
Similar or alternative tools
- Recurrence Delay State Shift Index
Return nextIndex=index+1 for a bounded state index except the final position, which returns minus one and dropped true.
- Interleaved Sequence Odd Even Length
Return evenPositions=ceil(length/2) and oddPositions=floor(length/2) for nonnegative integer length.