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For statements with several variables, substitution is a common technique to replace one variable with an equivalent expression that does not use this variable. For example, if one knows that y = 3 x {\displaystyle y=3x} then one can simplify the expression 7 x y {\displaystyle 7xy} to arrive at 21 x 2 {\displaystyle 21x^{2}} .
In mathematics, an n th root of a number x is a number r (the root) which, when raised to the power of the positive integer n, yields x: = ⏟ =.. The integer n is called the index or degree, and the number x of which the root is taken is the radicand.
While polynomial functions are defined for all values of the variables, a rational function is defined only for the values of the variables for which the denominator is not zero. The rational fractions include the Laurent polynomials, but do not limit denominators to powers of an indeterminate.
Difficult integrals may also be solved by simplifying the integral using a change of variables given by the corresponding Jacobian matrix and determinant. [1] Using the Jacobian determinant and the corresponding change of variable that it gives is the basis of coordinate systems such as polar, cylindrical, and spherical coordinate systems.
Predicate logic, originally called predicate calculus, expands on propositional logic by the introduction of variables, usually denoted by x, y, z, or other lowercase letters, and by sentences containing variables, called predicates. These are usually denoted by an uppercase letter followed by a list of variables, such as P(x) or Q(y,z).
a simplifier, which is a rewrite system for simplifying mathematics formulas, a memory manager, including a garbage collector, needed by the huge size of the intermediate data, which may appear during a computation, an arbitrary-precision arithmetic, needed by the huge size of the integers that may occur,
Algebraic operations in the solution to the quadratic equation.The radical sign √, denoting a square root, is equivalent to exponentiation to the power of 1 / 2 .The ± sign means the equation can be written with either a + or a – sign.
In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator.
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