Like any constant value, the value 0 can be considered as a (constant) polynomial, called the zero polynomial.It has no nonzero terms, and so, strictly speaking, it has no degree either.…

If both are nonzero, then must be negative and must be positive.

The remainder will have been nonzero if and only if c was zero.As a result, an FSM with two counters can simulate four counters, which are in turn simulating two stacks, which are simulating a Turing machine.…

In special relativity, an object that has nonzero rest mass cannot travel at the speed of light.As the object approaches the speed of light, the object's energy and momentum increase without bound.…

Magic Lunchbox are an original rock band from Sydney, Australia.They have released three albums and one EP, most recently through Nonzero Records.…

Let S be the restriction of scalars of G m over the field extension C/R.This is a real torus whose real points form the Lie group of nonzero complex numbers.Restriction of scalars gives a canonical embedding of S into GL 2, and composition with determinant gives an algebraic homomorphism of tori from S to G m, called the norm.…

D, on the other hand, is necessarily a nonzero natural number and cannot be measured.Hence most physicists would not deem it a dimensionless physical constant of the sort discussed in this entry.…

It turns out that the only normed division algebras over the reals are R, C, H, and O. These four algebras also form the only alternative, finite-dimensional division algebras over the reals (up to isomorphism).Not being associative, the nonzero elements of O do not form a group.They do, however, form a loop, indeed a Moufang loop.…

Therefore the only product terms that have a nonzero average are those where the frequency of voltage and current match.In other words it is possible to calculate real (average) power by simply treating each frequency separately and adding up the answers.…

Each set contains a nonzero, and possibly infinite, number of elements.

A ring in which every nonzero element has a multiplicative inverse is a division ring; likewise an algebra in which this holds is a division algebra.As mentioned above, the reciprocal of every nonzero complex number is complex.…

This is likewise true in a skew field (which for this reason is called a division ring).However, in other rings, division by nonzero elements may also pose problems.For example, the ring Z/6Z of integers mod 6.…

We are free to choose components as infinitesimally small as we wish as long as they remain nonzero.

If a = b = 0, then the sum of the series is 0.If either a or b is nonzero, then the series diverges and has no sum in the usual sense.…

These phenomena are known more specifically as the Seebeck effect (converting temperature to current), Peltier effect (converting current to temperature), and Thomson effect (conductor heating/cooling).While all materials have a nonzero thermoelectric effect, in most materials it is too small to be useful.However, low-cost materials that have a sufficiently strong thermoelectric effect (and other required properties) could be used in applications including power generation and refrigeration.…

A ring is called reduced if it has no nonzero nilpotent.Thus, a ring is reduced if and only if its nilradical is zero.…

More generally, for any distribution over high-dimensional, real-valued vectors, if two particular elements of the vector are perfectly correlated (or perfectly anti-correlated), those two elements will become stuck, and Gibbs sampling will never be able to change them.The second problem can happen even when all states have nonzero probability and there is only a single island of high-probability states.…

An ideal in the ring (with unity) is prime if the factor ring is an integral domain.A nonzero principal ideal is prime if and only if it is generated by a prime element.Prime elements should not be confused with irreducible elements.…

This is because a logical operator must treat any nonzero value the same.

However the proof given above cannot be used when is a GCD domain, since it uses irreducible factors, which need not exist in such, Here is a proof that is valid in this context.We proceed by induction on the total number of nonzero terms of and combined.If one of the polynomials has at most one term, the result is obvious; this covers in particular all cases with fewer than 4 nonzero terms.…