simplex-primal 1.0

Primal Simplex Method solver with exact rational arithmetic (Big-M)

simplex-primal

A pure-Python implementation of the Primal Simplex Method for Linear Programming.

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Features:

• ✅ Exact rational arithmetic - no floating-point drift, thanks to fractions.Fraction
• ✅ Big-M method for artificial variables ($>=$ and $=$ constraints)
• ✅ Supports MIN and MAX objectives
• ✅ Handles $<=0$ and unrestricted ($R$) variables via substitution
• ✅ Full iteration-by-iteration snapshots for teaching / debugging
• ✅ Zero third-party dependencies (stdlib only)

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Quick Start:

from simplex_primal import solve

# Maximise f = 5x1 + 4x2
# subject to:
#   6x1 + 4x2 <= 24
#    x1 + 2x2 <= 6
#   x1, x2 >= 0

result = solve(
    c=[5, 4],
    A=[[6, 4], [1, 2]],
    b=[24, 6],
    constraint_types=["<=", "<="],
    var_types=[">=0", ">=0"],
    opt="MAX",
)

print(result["status"])        # "optimal"
print(result["x_opt"])         # [Fraction(3,1), Fraction(3,2)]
print(result["f_opt"])         # Fraction(21,1)
print(result["sol_text"])      # formatted solution + verification

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Installation

pip install simplex-primal

pip install git+https://github.com/cosminelulul/simplex-primal.git

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References:

Coursework from Faculty of Applied Sciences, University POLITEHNICA of Bucharest.

1. Curs_1_CO - PL(1) (S. Bibic).pdf
2. Curs_2_CO - PL(2) (S. Bibic).pdf
3. Cursul_3_CO - PL(3) (S. Bibic).pdf
4. Seminar_1_CO - PL(1) (S. Bibic).pdf
5. Seminar_2_CO - PL(2) (S. Bibic).pdf