quantic
Noun: A quantic is a homogeneous polynomial in two or more variables. This means it is an algebraic expression where each term has the same total degree (the sum of the exponents of the variables in that term).
The term quantic is a specialized mathematical term. It is used to classify and discuss polynomials with specific symmetrical properties due to their homogeneity. * The expression x² + 2xy + y² is a quantic of degree two. * In classical invariant theory, the properties of a quantic under linear transformations were studied. * The cubic quantic ax³ + bx²y + cxy² + dy³ has four coefficients.
- Binary quantic: A quantic in exactly two variables (e.g., and ).
- Ternary quantic: A quantic in exactly three variables (e.g., , , and ).
- The degree of a quantic is a key descriptor (e.g., a quadratic quantic, a quintic quantic).
- Form: In modern algebra, the term "form" (as in , , ) is more commonly used than "quantic." A "binary cubic form" is equivalent to a "binary cubic quantic."
- Homogeneous polynomial
- Algebraic form
The term quantic is largely historical and is found in older mathematical literature, particularly in 19th-century works on invariant theory. In contemporary mathematics, the more general term "homogeneous polynomial" or the specific "[degree] form" is preferred.
- a homogeneous polynomial having at least two variables