In mathematics, an algebraic equation, also called polynomial equation over a given field is an equation of the form

where P and Q are (possibly multivariate) polynomials over that field. For example

is an algebraic equation over the rationals.

Two equations are equivalent if they have the same set of solutions. In particular the equation Failed to parse (Missing texvc executable; please see math/README to configure.): P = Q

. It follows that the study of algebraic equations is equivalent to the study of polynomials.

An algebraic equation over the rationals can always be converted to an equivalent one in which the coefficients are integers. For example, multiplying through by 42 = 2·3·7 and grouping its terms in the first member, the algebraic equation above becomes the algebraic equation

Although the equation

is not an algebraic equation in four variables (x, y, z and T) over the rational numbers (because sine, exponentiation and 1/T are not polynomial functions). It is an algebraic equation in the three variables x, y, and z over Q((T)), the field of formal Laurent series in T over the rational numbers. Indeed, the coefficients

The Basics ( /ˈbæzɪtʃ/ BAZZ-ich) are a three-piece band from Melbourne, Australia, formed by Wally De Backer and Kris Schroeder in 2002. Their style has been described as anything from 'indie-pop' to 'rock'n'roll' to 'pop-rock', though their records show they span a wide range of genres, including reggae, ska, country, and electro-pop. They are "recognised as one of Australia's hardest-working bands".

With close to 1000 shows in their ten-year career, their live performances are well-known for their sense of humour and energy.

The Basics were formed after Kris met Wally at a party in Melbourne. The event was to see off the young aspiring producer, who was about to depart for Los Angeles, and together with a number of musician friends, the two jammed on some blues-rock standards. Later that night, they bonded over a mutual love of The Beatles, 70s and 80s cartoon theme songs and old Sierra adventure games.

Initially, they played around Melbourne as an acoustic guitar/drums combo, starting at The Opposition in Frankston and the House of Fools in Footscray, where in late 2002 they met Michael Hubbard and later invited him to join them on electric guitar. Though lacking any real experience with the instrument, Kris willingly purchased his first bass guitar, and the trio was born. During this time, the group start performing songs with more complicated three-part harmony.