Examples of using Integer coefficients in English and their translations into Portuguese
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Use integer coefficients or integer division.
Suppose we have the following polynomial with integer coefficients.
In the ring Z of all polynomials with integer coefficients, the ideal generated by 2 and X is a prime ideal.
To prove the above assertion let us first consider the set of all polynomials with integer coefficients.
Numbers that are not roots of any polynomial with integer coefficients are called transcendent numbers.
Numerical coefficients andvalues are calculated with precision 27-36 digits 36 digits for integer coefficients.
The roots of monic polynomial with integer coefficients are called algebraic integers. .
Algebraic functions are functions that can be expressed as the solution of a polynomial equation with integer coefficients.
Algebraic numbers appear as solutions to polynomial equations(with integer coefficients) and may involve radicals and certain other irrational numbers.
A variant of the Alexander polynomial, the Alexander-Conway polynomial,is a polynomial in the variable z with integer coefficients Lickorish 1997.
Conway's version is a polynomial in z with integer coefficients, denoted∇( z){\displaystyle\nabla(z)} and called the Alexander-Conway polynomial also known as Conway polynomial or Conway-Alexander polynomial.
Like a determinant,the hyperdeterminant is a homogeneous polynomial with integer coefficients in the components of the tensor.
Addition, exponentials, logarithms Algebraic functions===Algebraic functions are functions that can be expressed as the solution of a polynomial equation with integer coefficients.
Algebraic numbers are numbers which are solutions to polynomial equations with integer coefficients, such as√2, which is a solution to x2-2 0.
Also it is sufficient to assume P is a polynomial over Q{\displaystyle\mathbb{Q}}and multiply P by the appropriate denominators to yield integer coefficients.
A Diophantine equation is a(usually multivariate) polynomial equation with integer coefficients for which one is interested in the integer solutions.
Every lattice in formula_1 can be generated from a basis for the vector space by forming all linear combinations with integer coefficients.
A typical use case is the sum of a rational number and a polynomial with integer coefficients, yielding a polynomial with rational coefficients. .
In mathematics, a Diophantine equation is an equation of the form P(x1,…, xj, y1,…, yk)=0(usually abbreviated P(x, y)=0) where P(x, y)is a polynomial with integer coefficients.
The general cubic equation a x 3+ b x 2+ c x+ d 0{\displaystyle ax^{ 3}+ bx^{ 2} +cx+d=0} with integer coefficients has three solutions in the complex plane.
An element x of F is an algebraic integer if andonly if the characteristic polynomial pA of the matrix A associated to x is a monic polynomial with integer coefficients.
This criterion is not applicable to all polynomials with integer coefficients that are irreducible over the rational numbers, but it does allow in certain important cases for irreducibility to be proved with very little effort.
The simplest example of a lattice is the integer lattice ℤn of all points with integer coefficients; its determinant is 1.
A Diophantine equation is a more general case of Fermat's Last Theorem;we seek the integer roots of a polynomial in any number of variables with integer coefficients.
In mathematics, the Alexander polynomial is a knot invariant which assigns a polynomial with integer coefficients to each knot type.
A number is said to be irrational when it cannot be represented by a fraction of two integers, andtranscendent if it is not a zero of any non-zero polynomial function of integer coefficients.
Hilbert's tenth problem was to determine whether a given polynomial Diophantine equation with integer coefficients has an integer solution.
Analogously, the first Chern class classifies smooth complex line bundles on a space, andthe group of line bundles is isomorphic to the second cohomology class with integer coefficients.
We deal with rational quadratic forms and integral quadratic forms,with rational and integer coefficients respectively.
This is just as general as considering polynomials with rational number coefficients because one can multiply by the denominators of rational coefficients to get integer coefficients.