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  2. Degree of a polynomial - Wikipedia

    en.wikipedia.org/wiki/Degree_of_a_polynomial

    Therefore, the polynomial has a degree of 5, which is the highest degree of any term. To determine the degree of a polynomial that is not in standard form, such as (+) (), one can put it in standard form by expanding the products (by distributivity) and combining the like terms; for example, (+) = is of degree 1, even though each summand has ...

  3. Inverse curve - Wikipedia

    en.wikipedia.org/wiki/Inverse_curve

    The degree is exactly 2n unless the original curve passes through the point of inversion or it is circular, meaning that it contains the circular points, (1, ±i, 0), when considered as a curve in the complex projective plane. In general, inversion with respect to an arbitrary curve may produce an algebraic curve with proportionally larger degree.

  4. Five points determine a conic - Wikipedia

    en.wikipedia.org/wiki/Five_points_determine_a_conic

    In Euclidean and projective geometry, five points determine a conic (a degree-2 plane curve), just as two (distinct) points determine a line (a degree-1 plane curve).There are additional subtleties for conics that do not exist for lines, and thus the statement and its proof for conics are both more technical than for lines.

  5. Determinant - Wikipedia

    en.wikipedia.org/wiki/Determinant

    In mathematics, the determinant is a scalar-valued function of the entries of a square matrix.The determinant of a matrix A is commonly denoted det(A), det A, or | A |.Its value characterizes some properties of the matrix and the linear map represented, on a given basis, by the matrix.

  6. General position - Wikipedia

    en.wikipedia.org/wiki/General_position

    In algebraic geometry and computational geometry, general position is a notion of genericity for a set of points, or other geometric objects. It means the general case situation, as opposed to some more special or coincidental cases that are possible, which is referred to as special position. Its precise meaning differs in different settings.

  7. Homogeneous function - Wikipedia

    en.wikipedia.org/wiki/Homogeneous_function

    In mathematics, a homogeneous function is a function of several variables such that the following holds: If each of the function's arguments is multiplied by the same scalar, then the function's value is multiplied by some power of this scalar; the power is called the degree of homogeneity, or simply the degree.

  8. Dimension of an algebraic variety - Wikipedia

    en.wikipedia.org/wiki/Dimension_of_an_algebraic...

    The degree of the Hilbert polynomial of A. The degree of the denominator of the Hilbert series of A. This allows, through a Gröbner basis computation to compute the dimension of the algebraic set defined by a given system of polynomial equations. Moreover, the dimension is not changed if the polynomials of the Gröbner basis are replaced with ...

  9. Angle - Wikipedia

    en.wikipedia.org/wiki/Angle

    In three-dimensional geometry, "clockwise" and "anticlockwise" have no absolute meaning, so the direction of positive and negative angles must be defined in terms of an orientation, which is typically determined by a normal vector passing through the angle's vertex and perpendicular to the plane in which the rays of the angle lie.