In mathematics, an algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number).[1] For example, 3x2 − 2xy + c is an algebraic expression. Since taking the square root is the same as raising to the power 1/2, the following is also an algebraic expression:
An algebraic equation is an equation involving only algebraic expressions.
By contrast, transcendental numbers like π and e are not algebraic, since they are not derived from integer constants and algebraic operations. Usually, π is constructed as a geometric relationship, and the definition of e requires an infinite number of algebraic operations.
A rational expression is an expression that may be rewritten to a rational fraction by using the properties of the arithmetic operations (commutative properties and associative properties of addition and multiplication, distributive property and rules for the operations on the fractions). In other words, a rational expression is an expression which may be constructed from the variables and the constants by using only the four operations of arithmetic. Thus,
is a rational expression, whereas
is not, i.e. this is an irrational expression.
A rational equation is an equation in which two rational fractions (or rational expressions) of the form
are set equal to each other. These expressions obey the same rules as fractions. The equations can be solved by cross-multiplying. Division by zero is undefined, so that a solution causing formal division by zero is rejected.
^Morris, Christopher G. (1992). Academic Press dictionary of science and technology. Gulf Professional Publishing. p. 74. algebraic expression over a field.
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In mathematics, an algebraicexpression is an expression built up from constant algebraic numbers, variables, and the algebraic operations (addition, subtraction...
In mathematics and computer science, computer algebra, also called symbolic computation or algebraic computation, is a scientific area that refers to the...
empirical sciences. Algebra is the branch of mathematics that studies algebraic operations and algebraic structures. An algebraic structure is a non-empty...
that a binary expression tree can represent are algebraic and boolean. These trees can represent expressions that contain both unary and binary operators...
equations that involve nth roots and, more generally, algebraicexpressions. This makes the term algebraic equation ambiguous outside the context of the old...
on variables, algebraicexpressions, and more generally, on elements of algebraic structures, such as groups and fields. An algebraic operation may also...
theory, an algebraic data type (ADT) is a kind of composite type, i.e., a type formed by combining other types. Two common classes of algebraic types are...
expressed as algebraic equations. In mathematics, a basic algebraic operation is any one of the common operations of elementary algebra, which include...
computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in a way...
an algebraic function is a function that can be defined as the root of an irreducible polynomial equation. Algebraic functions are often algebraic expressions...
mathematical expression by an equivalent one, that is simpler (usually shorter), for example Simplification of algebraicexpressions, in computer algebra Simplification...
constant term (sometimes referred to as a free term) is a term in an algebraicexpression that does not contain any variables and therefore is constant. For...
In algebra, an algebraic fraction is a fraction whose numerator and denominator are algebraicexpressions. Two examples of algebraic fractions are 3 x...
side of an equation, which is not the case with symbolic algebra. Syncopated algebraicexpression first appeared in Diophantus' Arithmetica (3rd century...
solution in radicals or algebraic solution is a closed-form expression, and more specifically a closed-form algebraicexpression, that is the solution of...
equation involving only algebraicexpressions in the unknowns. These are further classified by degree. Linear equation – algebraic equation of degree one...
relational calculus expression, the relational algebra is meant as an imperative language: the sub-expressions of a relational algebraicexpression are meant to...
segment which joins the point to nearest point on the line. The algebraicexpression for calculating it can be derived and expressed in several ways....
expression formed from algebraic numbers using any combination of the basic arithmetic operations and extraction of nth roots gives another algebraic...
polynomial. A rational fraction is the quotient (algebraic fraction) of two polynomials. Any algebraicexpression that can be rewritten as a rational fraction...
method is a special case of a more general method for multiplying algebraicexpressions using the distributive law. The word FOIL was originally intended...
between two nearby points. When the curve is given as the graph of an algebraicexpression, calculus gives formulas for the slope at each point. Slope is thus...
gate. The gate is also used in subtractors and comparators. The algebraicexpressions A ⋅ B ¯ + A ¯ ⋅ B {\displaystyle A\cdot {\overline {B}}+{\overline...
elementary algebra. The distinction is rarely made in more recent writings. Algebraic structures are defined primarily as sets with operations. Algebraic structure...
414213562\ldots } All nth roots of rational numbers are algebraic numbers, and all nth roots of integers are algebraic integers. The term "surd" traces back to Al-Khwarizmi...
that is an algebraicexpression, with a finite number of operations involving just those coefficients (i.e., can be solved algebraically). This can be...
make it a commutative algebra. These operations are defined according to the ordinary rules for manipulating algebraicexpressions. Specifically, if p =...
results. The algebraic notation used to represent the XNOR operation is S = A ⊙ B {\displaystyle S=A\odot B} . The algebraicexpressions ( A + B ¯ ) ⋅...
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