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An algebraic equation is an equation involving polynomials, for which algebraic expressions may be solutions. If you restrict your set of constants to be numbers, any algebraic expression can be called an arithmetic expression. However, algebraic expressions can be used on more abstract objects such as in Abstract algebra.
Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication.
The number 3 is a constant term. [1] After like terms are combined, an algebraic expression will have at most one constant term. Thus, it is common to speak of the quadratic polynomial + +, where is the variable, as having a constant term of .
A term is a constant or the product of a constant and one or more variables. Some examples include ,,, The constant of the product is called the coefficient. Terms that are either constants or have the same variables raised to the same powers are called like terms. If there are like terms in an expression, one can simplify the expression by ...
Algebraic numbers are all numbers that can be defined explicitly or implicitly in terms of polynomials, starting from the rational numbers. One may generalize this to " closed-form numbers ", which may be defined in various ways.
In universal algebra and mathematical logic, a term algebra is a freely generated algebraic structure over a given signature. [1] [2] For example, in a signature consisting of a single binary operation, the term algebra over a set X of variables is exactly the free magma generated by X.
[1] [2] The terms mathematical constant or physical constant are sometimes used to distinguish this meaning. [3] A function whose value remains unchanged (i.e., a constant function). [4] Such a constant is commonly represented by a variable which does not depend on the main variable(s) in question.
The term obtained by replacing in a term t the subterm at a position p by a new term u is commonly denoted by t[u] p. The term t [ u ] p can also be viewed as resulting from a generalized concatenation of the term u with a term-like object t [.] ; the latter is called a context , or a term with a hole (indicated by "."; its position being p ...