Let the open enemy to it be regarded as a Pandora with her box opened ; ;

Let every policeman and park guard keep his eye on John and Jane Doe, lest one piece of bread be placed undetected and one bird survive.

`` Let him be now ''!!

Let us assume that it would be possible for an enemy to create an aerosol of the causative agent of epidemic typhus ( Rickettsia prowazwki ) over City A and that a large number of cases of typhus fever resulted therefrom.

Let T be a linear operator on the finite-dimensional vector space V over the field F.

Let p be the minimal polynomial for T, Af, where the Af, are distinct irreducible monic polynomials over F and the Af are positive integers.

Let Af be the null space of Af.

Let N be a linear operator on the vector space V.

Let T be a linear operator on the finite-dimensional vector space V over the field F.

Let V be a finite-dimensional vector space over an algebraically closed field F, e.g., the field of complex numbers.

Let N be a positive integer and let V be the space of all N times continuously differentiable functions F on the real line which satisfy the differential equation Af where Af are some fixed constants.

Let Q be a nonsingular quadric surface bearing reguli Af and Af, and let **zg be a Af curve of order K on Q.

Let us take a set of circumstances in which I happen to be interested on the legislative side and in which I think every one of us might naturally make such a statement.

Let the state of the stream leaving stage R be denoted by a vector Af and the operating variables of stage R by Af.

Let this be denoted by Af.

Let it be granted then that the theological differences in this area between Protestants and Roman Catholics appear to be irreconcilable.

Let not your heart be troubled, neither let it be afraid ''.

The same God who called this world into being when He said: `` Let there be light ''!!

For those who put their trust in Him He still says every day again: `` Let there be light ''!!

Let us therefore put first things first, and make sure of preserving the human race at whatever the temporary price may be ''.

Let her out, let her out -- that would be the solution, wouldn't it??

Let k be a field ( such as the rational numbers ) and K be an algebraically closed field extension ( such as the complex numbers ), consider the polynomial ring kX < sub > n </ sub > and let I be an ideal in this ring.

Let F be a field and p ( X ) be a polynomial in the polynomial ring F of degree n. The general process for constructing K, the splitting field of p ( X ) over F, is to construct a sequence of fields such that is an extension of containing a new root of p ( X ).

Let P < sub > n </ sub > denote the vector space of real-valued polynomial functions of degree ≤ n defined on an interval.

Let L ( x ) be the interpolation polynomial in the Lagrange form for the given data points, then

Let k be an algebraically closed field and let P < sup > n </ sup > be a projective n-space over k. Let f ∈ k ..., x < sub > n </ sub > be a homogeneous polynomial of degree d. It is not well-defined to evaluate f on points in P < sup > n </ sup > in homogeneous coordinates.

Let V be an algebraic set defined as the set of the common zeros of an ideal I in a polynomial ring over a field K, and let A = R / I be the algebra of the polynomials over V. Then the dimension of V is:

Let A = K be the set of all polynomials over a field K and B be the set of all polynomial functions over K. Both A and B are algebras over K given by the standard multiplication and addition of polynomials and functions, respectively.

For example, let P be an irreducible polynomial with integer coefficients and p be a prime number which does not divides the leading coefficient of P. Let Q be the polynomial over the finite field with p elements, which is obtained by reducing modulo p the coefficients of P. Then, if Q is separable ( which is the case for every p but a finite number ) then the degrees of the irreducible factors of Q are the lengths of the cycles of some permutation of the Galois group of P.

Let f in F be an irreducible polynomial and f < nowiki >'</ nowiki > its formal derivative.

Let be another third degree polynomial satisfying the given boundary conditions.

) Let and be the roots of the characteristic polynomial

Let α ∈ GF ( p < sup > m </ sup >) be the root of a primitive polynomial of degree m over GF ( p ).

Let P be a polynomial of degree on complex numbers with derivative P ′.

Let α ∈ GF ( 2 < sup > 3 </ sup >) be a root of the primitive polynomial x < sup > 3 </ sup > + x < sup > 2 </ sup > + 1.

Let k be a field and M a finitely generated module over the polynomial ring

Let be a polynomial, and be a collection of sets such that contains-bit long sequences.

Let P ( x ) be a polynomial with coefficients in k, and be the set of its roots.

Let X be an affine algebraic variety embedded into the affine space k < sup > n </ sup >, with the defining ideal I ⊂ k. For any polynomial f, let in ( f ) be the homogeneous component of f of the lowest degree, the initial term of f, and let in ( I ) ⊂ k be the homogeneous ideal which is formed by the initial terms in ( f ) for all f ∈ I, the initial ideal of I.

Let be a polynomial with integer ( or p-adic integer ) coefficients, and let m, k be positive integers such that m ≤ k. If r is an integer such that

Let f ( z ) be a complex polynomial.