Quadratic

It could be argued that the simplest kind of number fields (viz., quadratic fields) were already studied by Gauss, as the discussion of quadratic forms in Disquisitiones arithmeticae can be restated in terms of ideals and norms in quadratic fields.

An integer a is a quadratic residue modulo p if it is congruent to a perfect square modulo p and is a quadratic nonresidue modulo p otherwise.

Avoiding loss of significance Although the quadratic formula provides what in principle should be an exact solution, it does not, from a numerical analysis standpoint, provide a completely stable method for evaluating the roots of a quadratic equation.

Even if a field does not contain a square root of some number, there is always a quadratic extension field which does, so the quadratic formula will always make sense as a formula in that extension field.

For example, the quadratic formula (which is the solution of the quadratic equation ) appears as: The formula is printed in a way a person would write by hand, or typeset the equation.

For instance, one could define a general quadratic function by declaring : ; here, the variable x designates the function's argument, but a, b, and c are parameters that determine which particular quadratic function is being considered.

Further properties Expectation of a quadratic form One can take the expectation of a quadratic form in the random vector X as follows: Kendrick, David, Stochastic Control for Economic Models, McGraw-Hill, 1981.

More precisely, the polynomial X 2 − r is irreducible over GF(p) if and only if r is a quadratic non-residue modulo p (this is almost the definition of a quadratic non-residue).

Namely, Cℓ can be considered as a functor from the category of vector spaces with quadratic forms (whose morphisms are linear maps preserving the quadratic form) to the category of associative algebras.

Quadratic curves For quadratic Bézier curves one can construct intermediate points Q 0 and Q 1 such that as t varies from 0 to 1: * Point Q 0 (t) varies from P 0 to P 1 and describes a linear Bézier curve.

Quadratic programming (QP) is a special type of mathematical optimization problem —specifically, the problem of optimizing (minimizing or maximizing) a quadratic function of several variables subject to linear constraints on these variables.

Reduced quadratic equation It is sometimes convenient to reduce a quadratic equation so that its leading coefficient is one.

The quadratic formula covering all cases was first obtained by Simon Stevin in 1594. citation In 1637 René Descartes published La Géométrie containing the quadratic formula in the form we know today.

Zhang and Heidel citation citation showed that, at least for dissipative and conservative quadratic systems, three-dimensional quadratic systems with only three or four terms on the right-hand side cannot exhibit chaotic behavior.

Quadratic Capital Management LLC increased its position in Schwab U.S. TIPS ETF by 1.1% during the fourth quarter.

Under the quadratic voting system, lawmakers log on each spring to a website and anonymously use digital tokens to vote for the bills they think should get a piece of the state budget.

With this money, three solar powerplants were built on the roofs of typical quadratic soviet buildings with large and flat roofs.

A bar at the top keeps track of the budget of voice credits, while the circles fill up, and the top bar draws down, at the quadratic rate as the survey respondent exchanges credits for votes.

In mathematical terms, the relationship between Aβ42 and tau is best described by a quadratic equation rather than the current linear one, which attempts to make a curve "fit" onto a straight line.

All quadratic equations will have two solutions in the complex number system, but need not have any in the real number system.