Possible (and useful) adequate equivalence relations include rational, algebraic, homological and numerical equivalence. They are called "adequate" because dividing out by the equivalence relation is functorial, i.e. push-forward (with change of co-dimension) and pull-back of cycles is well-defined. Codimension one cycles modulo rational equivalence form the classical group of divisors.
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Any regular local ring is a complete intersection ring, but not conversely. A ring R is a set-theoretic complete intersection if the reduced ring associated to R, i.e., the one obtained by dividing out all nilpotent elements, is a complete intersection. As of 2017, it is in general unknown, whether curves in three-dimensional space are set- theoretic complete intersections.
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In cultivation L. cardinalis requires rich, deep soil which remains reliably moist year-round. It has gained the Royal Horticultural Society's Award of Garden Merit. This plant is easily propagated by seed and dividing out the young plants which form around the older mature plants each year. Although the plant is generally considered a perennial, they may be short lived.
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A section of DNA; the sequence of the plate-like units (nucleotides) in the center carries information. Genes are pieces of DNA that contain information for the synthesis of ribonucleic acids (RNAs) or polypeptides. Genes are inherited as units, with two parents dividing out copies of their genes to their offspring. Humans have two copies of each of their genes, but each egg or sperm cell only gets one of those copies for each gene.
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Some polynomials, such as , do not have any roots among the real numbers. If, however, the set of accepted solutions is expanded to the complex numbers, every non-constant polynomial has at least one root; this is the fundamental theorem of algebra. By successively dividing out factors , one sees that any polynomial with complex coefficients can be written as a constant (its leading coefficient) times a product of such polynomial factors of degree 1; as a consequence, the number of (complex) roots counted with their multiplicities is exactly equal to the degree of the polynomial. There may be several meanings of "solving an equation".
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Propagation can occur with fresh seeds, although they are slow to germinate, or through dividing out suckers. In the wild, the most suitable environment for growth occurs in areas of Southeast Asian lowland peat swamp forests with the following characteristics: good soil drainage, high sand content in the soil, a thin peat layer in the soil, a low carbon to nitrogen ratio (C/N) in the soil, low acid, and nutrient levels in the soil and water but relatively high organic substance levels. The palm grows well in full sun or shade but needs humid conditions and well-draining soil. However, it also tolerates flooding and can grow in standing water as its native habitat is peat swamp forests.
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An electric potential (also called the electric field potential, potential drop, or the electrostatic potential) is the amount of work needed to move a unit of electric charge from a reference point to a specific point in an electric field without producing an acceleration. Typically, the reference point is the Earth or a point at infinity, although any point can be used. In classical electrostatics, the electrostatic field is a vector quantity which is expressed as the gradient of the electrostatic potential, which is a scalar quantity denoted by V or occasionally φ, equal to the electric potential energy of any charged particle at any location (measured in joules) divided by the charge of that particle (measured in coulombs). By dividing out the charge on the particle a quotient is obtained that is a property of the electric field itself.
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