2nd Order Polynomials With Quaternion Coefficients

summary:

A polynomial can be shifted the input line with quaternion coefficients. This is an example of a subtle shift, but it would be trivial to make much more radical changes to the polynomial.

description:

The yellow line is the input, the red line a 2nd order polynomial with real coefficients, and the green line is the same polynomial with quaternion coefficients. The coefficients are only subtly different as shown in the animation. The green line is never quite in line with the yellow/red line.

command:
q_graph -out poly_2_q_coeffients -dir poly -box 6 -command 'q_add_n -3 -3 -3 -3 .005 .005 .005 .005 1000 | q_poly -n 2 -c "1 0.1 0 0" -n 1 -c "3 0 .2 0" -n 0 -c "-2 .01 .01 .01"' -color green -command 'q_add_n -3 -3 -3 -3 .005 .005 .005 .005 1000 | q_poly -n 2 -c 1 -n 1 -c 3 -n 0 -c -2' -color red -command 'q_add_n -3 -3 -3 -3 .005 .005 .005 .005 1000' -color yellow
math
equation:

Input: (-3, -3, -3, -3) to (2, 2, 2, 2)
Ouput: $(1, 0.1, 0, 0) q^2 + (3, 0, .2, 0) q - (-2, .01, .01, .01)$

tags
Math Tag:
polynomials
Programming Tag:
command line quaternions