The Museum of HP Calculators

HP Forum Archive 20

 Solving a cubic equation using trigonometry, but with a2 term?Message #1 Posted by snaggs on 29 Sept 2011, 1:44 a.m. 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; $x^{3}+px+q=0$ 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.

 Re: Solving a cubic equation using trigonometry, but with a2 term?Message #2 Posted by Dieter on 29 Sept 2011, 7:19 a.m.,in response to message #1 by snaggs 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.

Go back to the main exhibit hall