the area of algebraic number theory, a cubic field is an algebraic number field of degree three. If K is a field extension of the rational numbers Q of...

two fields are equal. In this case, the extension is a trivial extension. Extensions of degree 2 and 3 are called quadratic extensions and cubic extensions...

In algebra, a cubic equation in one variable is an equation of the form a x 3 + b x 2 + c x + d = 0 {\displaystyle ax^{3}+bx^{2}+cx+d=0} in which a is...

rank 1 exactly when the number field is a real quadratic field, a complex cubic field, or a totally imaginary quartic field. When the unit group has rank...

crystals: Primitive cubic (abbreviated cP and alternatively called simple cubic) Body-centered cubic (abbreviated cI or bcc) Face-centered cubic (abbreviated...

field holds an estimated 1,800 trillion cubic feet (51 trillion cubic metres) of in-situ natural gas and some 50 billion barrels (7.9 billion cubic metres)...

a positive or negative number is adjoined to Q. In the case of cubic fields, a cubic integer polynomial P irreducible over Q will have at least one real...

Cubic Corporation is an American multinational defense and public transportation equipment manufacturer. It operates two business segments: Cubic Transportation...

called the order of the curve (n = 1 for linear, 2 for quadratic, 3 for cubic, etc.). The first and last control points are always the endpoints of the...

next totally real cubic field (of discriminant 1957) has class number two. The polynomials defining the totally real cubic fields that have discriminants...

gas field are around 171.5 trillion cubic feet (4.9×1012 cubic metres), and production is stated to be around 11 billion cubic feet (311,000,000 cubic metres)...

del Pezzo surfaces. A central feature of smooth cubic surfaces X over an algebraically closed field is that they are all rational, as shown by Alfred...

mathematical field of graph theory, a cubic graph is a graph in which all vertices have degree three. In other words, a cubic graph is a 3-regular graph. Cubic graphs...

parametrize orders in cubic fields. Their work was generalized in (Gan, Gross & Savin 2002, §4) to include all cubic rings (a cubic ring is a ring that...

reserves were increased by 251.3 billion cubic metres (8.87 trillion cubic feet). 86% of the natural gas in the field is methane. Up to 8% of the natural gas...

smallest is (49,169,289). 49 is the smallest discriminant of a totally real cubic field. 49 and 94 are the only numbers below 100 whose all permutations are...

4 feet 8+1⁄2 inches (1.435 m) 1436 = discriminant of a totally real cubic field 1437 = smallest number of complexity 20: smallest number requiring 20...

\left|{\frac {-{\sqrt {5}}+1}{2}}\right|\ \right].} The regulator of the cyclic cubic field Q ( α ) {\displaystyle \mathbb {Q} (\alpha )} , where α is a root of...

These are ten in number; therefore the cubic curves form a projective space of dimension 9, over any given field K. Each point P imposes a single linear...

unit of volume. It is equal to 1 cubic decimetre (dm3), 1000 cubic centimetres (cm3) or 0.001 cubic metres (m3). A cubic decimetre (or litre) occupies a...

000-cubic-metre-per-day (250,000 bbl/d) refinery in Mesaieed to process oil from Al Shaheen. This plan has been postponed. The Al-Shaheen field also...

and which can be rewritten as a cubic function of the molar volume. Equations of state are generally applied in the fields of physical chemistry and chemical...

prime 621 = 33 × 23, Harshad number, the discriminant of a totally real cubic field 622 = 2 × 311, nontotient, Fine number, Fine's sequence (or Fine numbers):...

Petroleum Limited. Sui gas field was discovered in 1952, its current production is 8.5 million cubic metres (300 million cubic feet) per day at standard...

South Pars / North Dome Gas-Condensate field, which holds an additional 450 trillion cubic feet (13 trillion cubic metres) of recoverable natural-gas reserves...

In algebra, a resolvent cubic is one of several distinct, although related, cubic polynomials defined from a monic polynomial of degree four: P ( x )...

quadratic fields are monogenic, already among cubic fields there are many that are not monogenic. The first example of a non-monogenic number field that was...

prices. In June 2022 the gas field caught fire again. The Urengoyskoye conventional gas field has over ten trillion cubic meters (1013 m3) in total deposits...

reserves reaching over 800 billion cubic metres (28 trillion cubic feet). The Tangguh field is operated by BP Berau Ltd. on behalf of other production sharing...

metres (5,600 ft) deep. The Tamar field is considered to have proven reserves of 200 billion cubic metres (7.1 trillion cubic feet) of natural gas, while the...