Sentence examples for defined by equations from inspiring English sources

But, with the creation of an abstract theory of fields, it was natural to want a theory of varieties defined by equations with coefficients in an arbitrary field.

He had studied algebraic functions that is, loci defined by equations of the form f x, y) = 0, where f is a polynomial in x whose coefficients are polynomials in y.

The study of algebraic geometry was amenable to the topological methods of Poincaré and Lefschetz so long as the manifolds were defined by equations whose coefficients were complex numbers.

where L and N are defined by Equations (3) and (4), respectively.

In this paper, the classical NCC defined by Equations 2, 3 and 4 is used.

where A is defined by Equations 28-29 and ψ controls the rate of convergence.

This velocity gradient-defined lid base is then used to find the thermal lid base defined by Equation 35.

Parameter defined by equation (13).

C is defined by Equation (5).

where b is defined by Equation 4.

where Φ is defined by equation (3.2).