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Polynomials of degree one, two or three are respectively linear polynomials, quadratic polynomials and cubic polynomials. [8] For higher degrees, the specific names are not commonly used, although quartic polynomial (for degree four) and quintic polynomial (for degree five) are sometimes used. The names for the degrees may be applied to the ...
In graph theory, the Möbius ladder M n, for even numbers n, is formed from an n-cycle by adding edges (called "rungs") connecting opposite pairs of vertices in the cycle. It is a cubic, circulant graph, so-named because (with the exception of M 6 (the utility graph K 3,3), M n has exactly n/2 four-cycles [1] which link together by their shared edges to form a topological Möbius strip.
In the case of a non-cyclic cubic field K this index formula can be combined with the conductor formula D = f 2 d to obtain a decomposition of the polynomial discriminant Δ = i(θ) 2 f 2 d into the square of the product i(θ)f and the discriminant d of the quadratic field k associated with the cubic field K, where d is squarefree up to a ...
In computational complexity theory, QMA, which stands for Quantum Merlin Arthur, is the set of languages for which, when a string is in the language, there is a polynomial-size quantum proof (a quantum state) that convinces a polynomial time quantum verifier (running on a quantum computer) of this fact with high probability.
This can be proved as follows. First, if r is a root of a polynomial with real coefficients, then its complex conjugate is also a root. So the non-real roots, if any, occur as pairs of complex conjugate roots. As a cubic polynomial has three roots (not necessarily distinct) by the fundamental theorem of algebra, at least one root must be real.
A set of graphs isomorphic to each other is called an isomorphism class of graphs. The question of whether graph isomorphism can be determined in polynomial time is a major unsolved problem in computer science, known as the graph isomorphism problem. [1] [2] The two graphs shown below are isomorphic, despite their different looking drawings.
In a tetrahedral molecular geometry, a central atom is located at the center with four substituents that are located at the corners of a tetrahedron.The bond angles are arccos(− 1 / 3 ) = 109.4712206...° ≈ 109.5° when all four substituents are the same, as in methane (CH 4) [1] [2] as well as its heavier analogues.
This polynomial is further reduced to = + + which is shown in blue and yields a zero of −5. The final root of the original polynomial may be found by either using the final zero as an initial guess for Newton's method, or by reducing () and solving the linear equation. As can be seen, the expected roots of −8, −5, −3, 2, 3, and 7 were ...