Search Results for "complex"

...A hash table is used to do fast variable and function lookup (they are entries in the same table). Collisions are handled in the hash table by making each entry a linked list. Written as C++ classes using the STL libraries <complex> and <vector>. The Numerical Recipes routines zroots and laguer rewritten in C++ find the complex roots of a polynomial with complex coefficients. Exact quartic and cubic too. FFT that zero pads to 2^m 3^n, for dimensions up to 10.

C++ code to perform the Lorentz boosts and rotations of special relativity using complex quaternions The interface is a complex quaternion console-based calculator with operations + - * / ^ and functions for Lorentz boosts and rotations. THEORY Complex quaternions have form q = A + B * I + C * J + D * K with A, B, C, D complex I * I = -1 , J * J = -1 , K * K = -1, I * J = K, J * I = -K , J * K = I,K * J = -I, K * I = J, I * K = -J Transpose T takes I into -I, J into -J, K into -K (q1 q2)T = q2T q1T Star complex conjugates A, B, C, D Bar is product of T and Star, Norm(q) = qTq Norm(q1*q2)=Norm(q1)*Norm( q2) q in H1 iff q qT = qT q = 1 4-vector X=t + i*x*I +i*y*J + i*z*K XPRIME = q X Bar(q) for q in H1 Form with real scalar, imaginary spatial is preserved Bar(X) = X and Bar(XPRIME )= XPRIME Norm(XPRIME) = Norm(X) = t*t - x*x - y*y - z*z q=cos(theta/2)+K*sin(theta/2) rotates by theta about z q=cosh(alpha/2)+i*I*sinh(alpha/2) boosts by alpha along x

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