Suppose a is a root of polynomial P, with multiplicity m > 1.

Suppose that the interpolation polynomial is in the form

Suppose we interpolate through n + 1 data points with an at-most n degree polynomial p ( x ) ( we need at least n + 1 datapoints or else the polynomial cannot be fully solved for ).

Suppose also another polynomial exists also of degree at most n that also interpolates the n + 1 points ; call it q ( x ).

Suppose we want to compute the characteristic polynomial of the matrix

Suppose we have the following polynomial with integer coefficients.

It is known that no non-constant polynomial function P ( n ) with integer coefficients exists that evaluates to a prime number for all integers n. The proof is: Suppose such a polynomial existed.

Suppose K is a Galois extension of the rational number field Q, and P ( t ) a monic integer polynomial such that K is a splitting field of P. It makes sense to factorise P modulo a prime number p. Its ' splitting type ' is the list of degrees of irreducible factors of P mod p, i. e. P factorizes in some fashion over the prime field F < sub > p </ sub >.

Suppose f is the cubic polynomial vanishing on the three lines through AB, CD, EF and g is the cubic vanishing on the other three lines BC, DE, FA.

Suppose John Jones, who, for 1960, filed on the basis of a calendar year, died June 20, 1961.

Suppose Lauren comes looking for us??

If two players tie for minority, they will share the minority shareholder bonus. Suppose Festival is the chain being acquired.

) Then X < sub > i </ sub > is the value ( or realization ) produced by a given run of the process at time i. Suppose that the process is further known to have defined values for mean μ < sub > i </ sub > and variance σ < sub > i </ sub >< sup > 2 </ sup > for all times i. Then the definition of the autocorrelation between times s and t is

* Suppose that the exchange rates ( after taking out the fees for making the exchange ) in London are £ 5

Suppose the bank sells its IT installations for 40 million USD.

Suppose that we had a general decision algorithm for statements in a first-order language.

Suppose the formula for some given function is known, but too complex to evaluate efficiently.

It is frequently stated in the following equivalent form: Suppose that is continuous and that u is a real number satisfying or Then for some c ∈ b, f ( c ) = u.

Suppose an array A with elements indexed 1 to n is to be searched for a value x.

Suppose, for example, that two particles interact.

Suppose, for concreteness, that we have an algorithm for examining a program p and determining infallibly whether p is an implementation of the squaring function, which takes an integer d and returns d < sup > 2 </ sup >.

Suppose, for example, we are interested in the set of all adult crows now alive in the county of Cambridgeshire, and we want to know the mean weight of these birds.

Suppose, for example, we are interested in the set of all adult crows now alive in the county of nederlands best country, and we want to know the mean weight of these birds.

Suppose that the person doing job B is actually interested in having job A done for him.

Suppose that whenever P ( β ) is true for all β < α, then P ( α ) is also true ( including the case that P ( 0 ) is true given the vacuously true statement that P ( α ) is true for all ).

:: “ Suppose that a sheriff were faced with the choice either of framing a Negro for a rape that had aroused hostility to the Negroes ( a particular Negro generally being believed to be guilty but whom the sheriff knows not to be guilty )— and thus preventing serious anti-Negro riots which would probably lead to some loss of life and increased hatred of each other by whites and Negroes — or of hunting for the guilty person and thereby allowing the anti-Negro riots to occur, while doing the best he can to combat them.

Suppose then that a female is speaking continuously for an hour.

Suppose for environmental reasons we needed to replace the chlorinated solvent, chloroform, with a solvent ( blend ) of equal solvency using a mixture of two non-chlorinated solvents from this table.

Suppose further, because this is necessary to the alleged case for our nuclear weapon as the defence of last resort, that, as in 1940, the United States was standing aloof from the contest but that, in contrast with 1940, Britain and the Warsaw Pact respectively possessed the nuclear weaponry which they do today.

Suppose T = 2 sec (~ lunar distance ) then delta-phi = 8000 radians, i. e. ( 8000 * 180 )/ Pi.

Suppose that A, B, and C are the matrices representing the transformations T, S, and ST with respect to the given bases.

Suppose we have an n-dimensional oriented Riemannian manifold, M and a target manifold T. Let be the configuration space of smooth functions from M to T. ( More generally, we can have smooth sections of a fiber bundle over M .)

Suppose the rod rotates at a constant rate so that the mass moves at speed v. Then the kinetic energy T of the mass is:

Suppose that x < sup > i </ sup > are local coordinates on the base manifold M. In terms of these base coordinates, there are fibre coordinates p < sub > i </ sub >: a one-form at a particular point of T * M has the form p < sub > i </ sub > dx < sup > i </ sup > ( Einstein summation convention implied ).

Given a circle k, with a center O, and a point P outside of the circle, we want to construct the ( red ) tangent ( s ) to k that pass through P. Suppose the ( as yet unknown ) tangent t touches the circle in the point T. From symmetry, it is clear that the radius OT is orthogonal to the tangent.

Suppose some theory T implies an observation O ( observation meaning here the result of the observation, rather than the process of observation per se ):

First proof: Suppose forms a basis of ker T. We can extend this to form a basis of V:.

Suppose the set of objects is T =

Suppose G is a finitely generated group ; and T is a finite symmetric set of generators

Suppose that an L-formula True ( n ) defines T *.

Suppose that ( X, T ) is a topological space and that Σ is at least as fine as the Borel σ-algebra σ ( T ) on X.

Suppose X is a Tychonoff space, also called a T < sub > 3. 5 </ sub > space, and C ( X ) is the algebra of continuous real-valued functions on X.

If is closed, densely defined and continuous on its domain, then it is defined on B < sub > 1 </ sub >.< ref > Suppose f < sub > j </ sub > is a sequence in the domain of T that converges to.

Suppose X is the T × K matrix of explanatory variables resulting from T observations on K variables.

Suppose a pendulum is swinging with a particular period T. For such a system, it is advantageous to perform calculations relating to the swinging relative to T. In some sense, this is normalizing the measurement with respect to the period.

Suppose the available data consists of T iid observations

Suppose that S and T are two first-order theories.

Suppose that it takes twice as much capital per unit of output to produce trucks than it does to produce lasers, so that the capital cost per unit equals $ 20, 000 for trucks ( T ) and $ 10, 000 for lasers ( L ), where these coefficients are initially assumed not to change.

Suppose that T is a bounded operator on the normed vector space X.