resolvent cubic造句

例句与造句

1. In some cases, the concept of resolvent cubic is defined only when is a quartic in depressed form that is, when 0 } }.
2. Note that the fifth definitions below also make sense and that the relationship between these resolvent cubics and are still valid if the characteristic of is equal to.
3. It is not a resolvent invariant for, as being invariant by, in fact, it is a resolvent invariant for the dihedral subgroup, and is used to define the resolvent cubic of the quartic equation.
4. In Galois theory, this map, or rather the corresponding map, corresponds to associating the Lagrange resolvent cubic to a quartic, which allows the quartic polynomial to be solved by radicals, as established by Lodovico Ferrari.
5. This is stuck in directly between " This suggests using a . . . " and " . . . resolvent cubic whose roots may be variously described as a discrete Fourier transform or a Hadamard matrix transform . . ."
6. It's difficult to find resolvent cubic in a sentence. 用resolvent cubic造句挺难的
7. A striking application of such a family is in which gives a geometric solution to a quartic equation by considering the pencil of conics through the four roots of the quartic, and identifying the three degenerate conics with the three roots of the resolvent cubic.
8. The reducible quadratics, in turn, may be determined by expressing the quadratic form as a matrix : reducible quadratics correspond to this matrix being singular, which is equivalent to its determinant being zero, and the determinant is a homogeneous degree three polynomial in and and corresponds to the resolvent cubic.
9. Waring proved the main theorem on symmetric functions, and specially considered the relation between the roots of a quartic equation and its resolvent cubic . " M閙oire sur la r閟olution des 閝uations " ( " Memoire on the Solving of Equations " ) of Alexandre Vandermonde ( 1771 ) developed the theory of symmetric functions from a slightly different angle, but like Lagrange, with the goal of understanding solvability of algebraic equations.
10. The above solution shows that a quartic polynomial with rational coefficients and a zero coefficient on the cubic term is factorable into quadratics with rational coefficients if and only if either the resolvent cubic "'( " " ) "'has a non-zero root which is the square of a rational, or is the square of rational and 0 } }; this can readily be checked using the rational root test.
11. A couple years back I figured out how to solve an equation of the form f ( g ( x ) ) = 0 if I know how to solve f, and how to solve an equation of the form g ( x ) + C for arbitrary constant C . But for the Quartic, the middle terms had to have a certain relation, by doing a change of variables of the form y-\ lambda = x, I can transform any Quartic into the correct form, this involves solving a Cubic, the Resolvent Cubic in fact . talk ) 00 : 34, 29 July 2009 ( UTC)