solverCan 0.1.4

Mathematical Function Solver from Dataset

# solverCan Mathematical Function Solver from Dataset by Emrecan Bayhan. Find equations from raw data using forward differences and derivative ratio analysis.

solverCan

Mathematical Function Solver from Dataset by Emrecan Bayhan

Find equations from raw data using forward differences, derivative ratio analysis, and piecewise polynomial approximation.

Installation

pip install solverCan

Quick Start

import solverCan

y = [14, 13, 14, 17, 22, 29, 38, 49, 62, 77]
result = solverCan.auto(y)
print(result['equation'])       # f(x) = x^2 - 4*x + 17
print(result['compute'](15))    # 182.0

Methods

1. Polynomial

r = solverCan.plynm(y)
print(r['equation'])        # f(x) = x^2 - 4*x + 17
print(r['degree'])          # 2
print(r['coefficients'])    # [17, -4, 1]

2. Exponential

y = [50000.0, 51522.73, 53091.83, 54708.71, 56374.84,
     58091.71, 59860.87, 61683.9, 63562.46, 65498.22]
r = solverCan.expo(y)
print(r['equation'])        # f(x) = 48512.25*exp(0.03*x) + 10.36

3. Trigonometric (Piecewise)

y = [200, 217.02, 232.95, 247.47, 260.31, 271.19, 279.9, 286.26,
     290.12, 291.42, 290.12, 286.26, 279.9, 271.19, 260.31, 247.47,
     232.95, 217.02, 200]
x = list(range(0, 95, 5))
r = solverCan.trig(y, x=x)
print(r['equation'])        # Two pieces

4. Trigonometric (Single Equation)

r = solverCan.trigOneEq(y, x=x)              # auto iterations
r = solverCan.trigOneEq(y, x=x, max_iter=2)  # fixed 2 iterations
print(r['equation'])
print(r['iterations'])

5. Irrational (Piecewise)

y = [24.0, 26.5858, 31.2679, 38.0, 46.7639,
     57.5505, 70.3542, 85.1716, 102.0, 120.8377]
r = solverCan.irrational(y)
print(r['equation'])

6. Irrational (Single Equation)

r = solverCan.irrationalOneEq(y)
r = solverCan.irrationalOneEq(y, max_iter=3)  # fixed iterations

7. Auto (Best Method)

r = solverCan.auto(y)
print(r['method'])          # Polynomial (degree 2)
print(r['equation'])
for name, info in r['all_results'].items():
    print(f"  {name}: {info['method']} (max dev: {info['max_deviation']:.4f}%)")

Visualization

Comparison Table

solverCan.table(y, r['compute'])

Comparison Graph

solverCan.compare_graph(y, r['compute'])
solverCan.compare_graph(y, r['compute'], title="My Analysis")
solverCan.compare_graph(y, r['compute'], save_as="output.png")

Custom X Values

x = [0, 5, 10, 15, 20]
y = [100, 250, 380, 470, 520]
r = solverCan.auto(y, x=x)

Prediction

r = solverCan.auto(y)
print(r['compute'](15))     # Predict at x=15
for x in range(11, 21):
    print(f"  x={x}: {r['compute'](x):.4f}")

Result Fields

All methods return a dict:

Field	Description
r['equation']	Equation string
r['compute'](x)	Predict value at x
r['method']	Method name
r['coefficients']	Polynomial coefficients (plynm, OneEq)
r['degree']	Polynomial degree (plynm)
r['parts']	Exponential parts (expo)
r['pieces']	Piecewise segments (trig, irrational)
r['iterations']	Iteration count (OneEq)
r['all_results']	All methods comparison (auto)

How It Works

1. Forward Differences — Detects polynomial degree via CV analysis
2. Gauss Elimination — Solves linear system for polynomial coefficients
3. Derivative Ratios — Constant ratio = exponential function (e^ax)
4. Iterative Correction — Find f1, compute residual, find f2, sum together
5. Piecewise Splitting — Split at deviation breakpoints, fit each segment

Citation

If you use solverCan in your research, please cite:

Bayhan, E. (2026). solverCan: A Mathematical Function Solver from Dataset Using 
Forward Differences, Derivative Ratio Analysis, and Iterative Residual Correction. 
Zenodo. https://doi.org/10.5281/zenodo.19167599

Author

Emrecan Bayhan Email: [e-mail]