Solving a cubic equation using trigonometry, but with a2 term? « Next Oldest | Next Newest »

 ▼ snaggs Member Posts: 110 Threads: 17 Joined: Aug 2011 09-29-2011, 01:44 AM Hi, I read and entered this program here, after finding his Quadratic solver using ACOSH nice to use. "Solving a cubic equation using trigonometry" by Thomas Klemm http://www.hpmuseum.org/cgi-sys/cgiwrap/hpmuseum/archv020.cgi?read=180771 A general cubic equation can be transformed to the following form using a substitution;  ``` 00 { 31-Byte Prgm } 00 { 34-Byte Prgm } 01>LBL "CuEq" 01>LBL "CuEqH" 02 2 02 2 03 / 03 / 04 X<>Y 04 X<>Y 05 -3 05 3 06 / 06 / 07 / 07 / 08 LASTX 08 LASTX 09 SQRT 09 SQRT 10 / 10 / 11 LASTX 11 LASTX 12 X<>Y 12 X<>Y 13 ASIN 13 ASINH 14 3 14 3 15 / 15 / 16 SIN 16 SINH 17 * 17 * 18 2 18 -2 19 * 19 * 20 END 20 END ``` However, it doesn't work if you have an a2 term, unless I've made a typo. Having to do substitution before using the program seems to defeat the purpose. Daniel. ▼ Dieter Senior Member Posts: 653 Threads: 26 Joined: Aug 2010 09-29-2011, 07:19 AM Sure there is no a2 term: That's why it says "A general cubic equation can be transformed to the following form using a substitution". ;-) For more details see below. There are well-known standard methods for solving cubic equations. Just take a look at de.wikipedia.org - as well as the last link ("Leitfaden") on that page for a step-by-step solution. The entry on en.wikipedia.org is has some more details on the numerics. Having read all this you may finally proceed to the actual algorithm. ;-) For instance by using Cardano's method as described on de.wikipedia.org. This is the method you will probably use. Edit 1: Oops, I was a bit too fast. ;-) I didn't notice you're not Thomas so you probably don't read German. However, the mentioned Cardano method first reduces the cubic equation to a simplified form without "a2 term" and then this reduced equation is solved. The latter part is already done by the program you got. So you just have to provide the initial reduction (or transformation, as Thomas said) the way it is described in the wikipedia articles. The rest is already there. Edit 2: All this has already been discussed in the thread you mentioned. Please read messages 3 - 5 there. ;-) Dieter Edited: 29 Sept 2011, 8:49 a.m.

 Possibly Related Threads... Thread Author Replies Views Last Post [HP Prime] Tips for Solving Differential Equations More Efficiently Chris Pem10 8 1,935 11-21-2013, 08:25 PM Last Post: Chris Pem10 Equation Library/App for the Prime Harold A Climer 3 1,169 10-30-2013, 10:14 AM Last Post: CompSystems Equation Library on the PRIME Harold A Climer 0 703 10-26-2013, 10:01 AM Last Post: Harold A Climer HP-PRIME CAS SOLVING fabrice48 8 1,960 10-19-2013, 01:21 PM Last Post: Han Meltiple Equation Solver PRIME Vs. HP 50G Harold A Climer 5 1,255 10-07-2013, 05:11 PM Last Post: CR Haeger HP Prime Solving Nonlinear System of Equations for Complex Results Helge Gabert 11 2,752 09-30-2013, 03:44 AM Last Post: From Hong Kong EOT--TI N-Spire Equation Limit Matt Agajanian 2 917 09-22-2013, 12:37 PM Last Post: Matt Agajanian Does Prime Have a Multiple Equation Solver? Norman Dziedzic 2 890 09-20-2013, 09:43 AM Last Post: Norman Dziedzic Equation of the parabola given three points Gerson W. Barbosa 27 4,643 09-18-2013, 01:58 PM Last Post: Gerson W. Barbosa Quadratic & Cubic Regression RPN progs Matt Agajanian 9 2,055 09-17-2013, 11:37 AM Last Post: Jeff O.

Forum Jump: