HP-71B Enhanced Math LEX

[Albert Chan]

Thank you for the enhanced Math Lex

This is a cubic solver, AX³ + BX² + CX + D = 0, using the new ASINH.
Code shift and scale to match identity: sinh(3z) = 3 sinh(z) + 4 sinh(z)^3

Code:

10 DESTROY ALL @ COMPLEX A,B,C,D,E,F,G,H,K
20 INPUT "A,B,C,D ? ";A,B,C,D
30 E=3*A @ H=-B/E
40 E=((E*H+2*B)*H+C)/A
50 F=(((A*H+B)*H+C)*H+D)/A
60 K=SQRT(E/.75)
70 E=ASINH(-4*F/K^3)/3 @ G=(0,2*PI/3) @ F=E+G @ G=E-G
80 E=SINH(E) @ F=SINH(F) @ G=SINH(G)
90 DISP E*K+H @ DISP F*K+H @ DISP G*K+H

>RUN
A,B,C,D ? 1,-6,11,-6
(2,0)
(1,0)
(3,-0)

>RUN
A,B,C,D ? 1,2,3,4
(-1.65062919144,0)
(-.174685404282,1.54686888723)
(-.174685404282,-1.54686888723)