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To use REDC to compute the product of 7 and 15 modulo 17, first convert to Montgomery form and multiply as integers to get 12 as above. Then apply REDC with R = 100, N = 17, N′ = 47, and T = 12. The first step sets m to 12 ⋅ 47 mod 100 = 64. The second step sets t to (12 + 64 ⋅ 17) / 100.
The class of doubly stochastic matrices is a convex polytope known as the Birkhoff polytope.Using the matrix entries as Cartesian coordinates, it lies in an ()-dimensional affine subspace of -dimensional Euclidean space defined by independent linear constraints specifying that the row and column sums all equal 1.
Spaces within a formula must be directly managed (for example by including explicit hair or thin spaces). Variable names must be italicized explicitly, and superscripts and subscripts must use an explicit tag or template. Except for short formulas, the source of a formula typically has more markup overhead and can be difficult to read.
MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD symbolic engine allowing access to symbolic computing abilities.
Q ← 0 for i from m to 0 do Q ← point_double_repeat(Q, w) if d i > 0 then Q ← point_add(Q, d i P) # using pre-computed value of d i P return Q This algorithm has the same complexity as the double-and-add approach with the benefit of using fewer point additions (which in practice are slower than doubling).
Example of bilinear interpolation on the unit square with the z values 0, 1, 1 and 0.5 as indicated. Interpolated values in between represented by color. In mathematics, bilinear interpolation is a method for interpolating functions of two variables (e.g., x and y) using repeated linear interpolation.
The gray rhombus is a primitive cell. Vectors a 1 {\displaystyle \mathbf {a} _{1}} and a 2 {\displaystyle \mathbf {a} _{2}} are primitive translation vectors. The honeycomb point set is a special case of the hexagonal lattice with a two-atom basis. [ 1 ]
In log-linear analysis there is no clear distinction between what variables are the independent or dependent variables. The variables are treated the same. However, often the theoretical background of the variables will lead the variables to be interpreted as either the independent or dependent variables.