This book presents a rigorous look at how rational functions of coefficients behave under transformation. It connects foundational concepts to methods for building finite, irreducible systems and understanding when forms are invariant, covariant, or semi‑invariant. The discussion blends classical ideas with Hilbert’s theorems and practical techniques for binary and higher quantics.

Learn how absolute and non‑absolute orthogonal concomitants are formed and distinguished
See how invariants, covariants, and syzygies interact through finite base systems
Understand the role of the modulus, annihilators, and transvectants in invariant theory
Gain perspective on the finiteness results and reconstruction methods for covariants

Ideal for readers of advanced algebra who want a clear, structured treatment of invariants, covariants, and their applications in quantic systems.

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