# Send Pywayne Maths to your agent
Hand the extracted package to your coding agent with a concrete install brief instead of figuring it out manually.
## Fast path
- Download the package from Yavira.
- Extract it into a folder your agent can access.
- Paste one of the prompts below and point your agent at the extracted folder.
## Suggested prompts
### New install

```text
I downloaded a skill package from Yavira. Read SKILL.md from the extracted folder and install it by following the included instructions. Tell me what you changed and call out any manual steps you could not complete.
```
### Upgrade existing

```text
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## Machine-readable fields
```json
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        "Review SKILL.md after the package is downloaded.",
        "Confirm the extracted package contains the expected setup assets."
      ],
      "postInstallChecks": [
        "Confirm the extracted package includes the expected docs or setup files.",
        "Validate the skill or prompts are available in your target agent workspace.",
        "Capture any manual follow-up steps the agent could not complete."
      ]
    }
  },
  "links": {
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    "downloadUrl": "https://openagent3.xyz/downloads/maths",
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```
## Documentation

### Pywayne Maths

Mathematical utility functions for number theory, digit analysis, and optimized integer operations.

### Quick Start

from pywayne.maths import get_all_factors, digitCount, karatsuba_multiplication

# Get all factors of a number
factors = get_all_factors(28)
print(factors)  # [1, 2, 4, 7, 14, 28]

# Count digit occurrences
count = digitCount(100, 1)
print(count)  # 21 (digit 1 appears 21 times in 1-100)

# Large integer multiplication
product = karatsuba_multiplication(1234, 5678)
print(product)  # 7006652

### get_all_factors

Return all factors of a positive integer.

get_all_factors(n: int) -> list

Parameters:

n - Positive integer to factorize

Returns:

List of all factors of n

Use Cases:

Number theory problems
Finding divisors
Simplifying fractions
Greatest common divisor (GCD) calculation

Example:

from pywayne.maths import get_all_factors

factors = get_all_factors(36)
print(factors)  # [1, 2, 3, 4, 6, 9, 12, 18, 36]

# Check if number is prime
n = 17
factors = get_all_factors(n)
if len(factors) == 2:  # Only 1 and itself
    print(f"{n} is prime")
else:
    print(f"{n} is not prime")

### digitCount

Count occurrences of digit k from 1 to n.

digitCount(n, k) -> int

Parameters:

n - Positive integer, upper bound of counting range
k - Digit to count (0-9)

Returns:

Count of digit k in range [1, n]

Special Case:

When k = 0, counts all numbers with trailing zeros after n

Use Cases:

Digit frequency analysis
Number theory problems
Data analysis tasks

Example:

from pywayne.maths import digitCount

# Count digit 1 from 1 to 100
count = digitCount(100, 1)
print(count)  # 21

# Count each digit 0-9 in range 1-1000
for k in range(10):
    count = digitCount(1000, k)
    print(f"Digit {k}: {count} times")

### karatsuba_multiplication

Multiply two integers using Karatsuba's divide-and-conquer algorithm.

karatsuba_multiplication(x: int, y: int) -> int

Parameters:

x - Integer multiplier
y - Integer multiplicand

Returns:

Product of x and y

Algorithm:

Karatsuba algorithm uses recursive divide-and-conquer to multiply large integers
Time complexity: O(n^log₂3) ≈ O(n^1.585)
More efficient than naive multiplication O(n²) for very large numbers

Use Cases:

Large integer multiplication
Algorithm optimization
Competitive programming
Cryptography applications

Example:

from pywayne.maths import karatsuba_multiplication

# Compare with standard multiplication
a, b = 123456789, 987654321
result = karatsuba_multiplication(a, b)
print(result)  # 121932631112635269

# Verify
assert result == a * b

### Prime Number Detection

from pywayne.maths import get_all_factors

def is_prime(n):
    factors = get_all_factors(n)
    return len(factors) == 2 and factors == [1, n]

print(is_prime(17))   # True
print(is_prime(18))   # False

### Greatest Common Divisor (GCD)

from pywayne.maths import get_all_factors

def gcd(a, b):
    factors_a = set(get_all_factors(a))
    factors_b = set(get_all_factors(b))
    common = factors_a & factors_b
    return max(common)

print(gcd(24, 36))  # 12

### Digit Frequency Analysis

from pywayne.maths import digitCount

def digit_frequency(n):
    frequency = {}
    for k in range(10):
        frequency[k] = digitCount(n, k)
    return frequency

print(digit_frequency(1000))
# {0: 189, 1: 301, 2: 300, 3: 300, ...}

### Large Number Calculations

from pywayne.maths import karatsuba_multiplication

# Very large numbers
x = 123456789012345678901234567890
y = 9876543210987654321098765432109876

# Use Karatsuba for efficiency
product = karatsuba_multiplication(x, y)

### Notes

get_all_factors returns sorted unique factors
digitCount counts from 1 to n inclusive
karatsuba_multiplication is optimized for large integers (hundreds+ of digits)
For small integers, standard multiplication * may be faster due to overhead
## Trust
- Source: tencent
- Verification: Indexed source record
- Publisher: wangyendt
- Version: 0.1.0
## Source health
- Status: healthy
- Item download looks usable.
- Yavira can redirect you to the upstream package for this item.
- Health scope: item
- Reason: direct_download_ok
- Checked at: 2026-05-07T16:05:26.014Z
- Expires at: 2026-05-14T16:05:26.014Z
- Recommended action: Download for OpenClaw
## Links
- [Detail page](https://openagent3.xyz/skills/maths)
- [Send to Agent page](https://openagent3.xyz/skills/maths/agent)
- [JSON manifest](https://openagent3.xyz/skills/maths/agent.json)
- [Markdown brief](https://openagent3.xyz/skills/maths/agent.md)
- [Download page](https://openagent3.xyz/downloads/maths)