Talk:Cubic equation

message: I'm a bit unhappy with this page as it stands. The standard trigonometric substitutions are not given; was there some reason for this? Shouldn't the Chebyshev cube root be given its own page? Also, it ought to be pointed out that in practice these equations are solved by iteration methods. Xanthoxyl 16:31, 23 June 2006 (UTC)
thread_title: Suitability of page for general audience

message: I notice that the disputed tag was removed.  However, the page still isn't correct for the simple example I gave above:
:x^3 - x = x (x^2 - 1) = x (x - 1) (x + 1)
which has roots 0, -1, and 1.  According to the revised page's notation, this has: \alpha_3 = 1,  \alpha_1 = -1, and  \alpha_2 = \alpha_0 = 0.  Then, according to the page, \Delta = -4 < 0, and the equation should have "one real roots and a pair of complex conjugate roots."
:That's my mistake. I was confused by the fact that MathWorld uses different sign conventions for the discriminant on their web site. Sorry. -- Jitse Niesen 13:38, 24 Jan 2005 (UTC)
replies: text: What would you say to my putting the coefficients the other way around, to correspond to how algebraists most often write them, putting the sign of the discriminant to be what algebraists usually want, checking everything, and removing the disputed tag? Gene Ward Smith 00:03, 25 Jan 2005 (UTC)
replies: text: Please go ahead. I'm a bit surprised that you want to put the coefficients the other way around, but I'm sure you know best. If you prefer to use the t from Chebyshev radicals in the first section instead of the determinant, that's fine with me as well. When I asked you to provide some references, I meant the old-fashioned kind: books and papers. I did not want to question your knowledge, it's just that I'm a mathematician myself and I have often quite a bit of trouble getting all the signs right; I know many of my colleagues have similar problems and I presumed the same goes for you. I hope this clarifies the matter. -- Jitse Niesen 13:10, 25 Jan 2005 (UTC)
thread_title: Continued accuracy dispute

message: I'm getting these TeX errors, dunno if its because of the power failure but some of the other <math>s seem to work. 203.218.37.45 15:20, 19 April 2006 (UTC)
thread_title:  TEX 

message: ----Proposal The idea is to replace existing articles with unique Cubic & Quartic equation as follows:
A.	Merged history paragraphs giving a credit for cubic to Tartaglia (Cardano’s contribution is suspicious, at least exaggerated) as well as for quartic to Ferrari. 
B.	Tartaglia’s – Ferrari’s method for resolving cubic and quartic equations containing mentioned lecture should replace all the others (Lagrange resolvents and Chebyshev radicals are included under trigonometric and hyperbolic substitutions, depressed cubic is replaced with Primeval one).
C.	The graph actualy presents Marginal case V: 4Y = (X + 1)3 – 9(X + 1) = O. Therefore it should be replaced with more representative one given in Primeval form 4y = 4x3 ± 3x – g = 0 (containing all off cubics where F ≠ 0) that can be splited into: Basic parabola  (y = x3) and either Green (if F > 0) or Red (if F < 0) Straight line (4y = ± 3x) shifted up for ¼g.  Real solution(s) is x-coordinate of the cut(s) of these functions.  Two characteristic examples are to be chosen (common S = 1.5 & R2 = ± 62). 8X3 + 36X2 – 162X – 729 = 0 → S = 1.5,  E = + 373248, F = + 5184, R = + 6, g = 1 = 4x3 – 3x or x3 = y = (1 + 3x)/4 → x0 = 1,  x1 = x2 = – 0.5, X0 = 6×1 – 1.5 = 4.5 &  X1 = X2 = 6×(– 0.5) – 1.5 = – 4.5 8X3 + 36X2 + 270X – 1350 = 0 → S = 1.5, E = + 1469664, F = – 5184, R = + 6, g = 3.9375 = 4x3 + 3x  or x3 = y = (3.9375 – 3x)/4 → x0 = 0.75,  X0 = 6×0.75 – 1.5 = 3 but X1 and X2 are conjugate numbers. 
x-Drawing Ratio: 6cm = 1, 4cm = 1 for y. The conversion from x & y to X & Y coordinates:  6cm = R (1cm = 1 for upper examples due to R = 6) should be taken as X-Drawing Ratio, Y-axis shifted either right if S > 0 or left if S < 0 (1.5cm right for upper examples), 
X-ais mirrored if E < 0.
----
The lecture is prepared by means of Microsoft Equation 3.0 and Word Drawing tool. Therefore it was impossible to paste here neither this drawing nor Geometrical interpretation. I apologize for this inconvenience to Wikipedians asking them to assist. If you (Wikipedia editorial) find it interesting don’t hesitate to contact me for details like: \mbox{ Normalized form of Primeval Cubic: }\cfrac{x^3}{\tfrac{1}{4}g} \mp\ \cfrac{x}{\tfrac{1}{3}g} = 1 
89.111.252.148 16:54, 17 March 2007 (UTC)
replies: text: Yes, a merge of cubic function into cubic equation seems to be appropriate to me. There is not much information in cubic function. It should be easily combined.  --MathMan64 00:43, 10 November 2007 (UTC)
thread_title:  Merger proposal 

message: The external link reference:
Dave Auckly, Solving the quartic with a pencil American Math Monthly 114:1 (2007) 29--39
is about quartics and not cubics.
Before the "Lagrange resolvents" section it states:
"...or two real roots (a single and a double root.)"
What does this mean? Id D=0 and there are 2 roots [aside that there should be 3 roots for a cubic] how can there be 2 real roots of a single and double root?
I think this statement needs clarification.  —Preceding unsigned comment added by 212.20.240.70 (talk) 16:22, 20 January 2009 (UTC)
thread_title:  cited reference and D section 

message: , I have reverted your edit several times for two reasons. The first one, is that it is not useful, and often confusing to introduce in a section some symbols that are not used in the same section. The second reason, is that it is very confusing to give the same name (here \Delta) to two different things (here the discriminants of two different cubics). However, reading your explanation, it appeared that the formulation  of the beginning ot the next section was incorrect: the use of "the polynomial" and "the discriminant" seemed to refer to things previously defined and was therefore ambiguous, since there are two polynomials and two discriminants defined in the previous section. So, I have put "a polynomial" and "its discriminant". With this modification, \Delta is perfectly defined by the sentence, and I hope that will convince you. D.Lazard (talk) 15:51, 19 April 2021 (UTC)
thread_title:  Naming discriminants 

message: May I append and algorithm written in Python or is it inappropriate? 
I use the General cubic formula, so I would insert it at the end of section 'General cubic formula'.  — Preceding unsigned comment added by Betaminus (talk • contribs) 09:49, 26 May 2021 (UTC)
replies: text: A program written in Python would certainly not useful in this article: not all readers knows Python. Readers who know Python are supposed to be able to write simple programs in this language. Translating the formula into a Python program is an easy exercise for beginners in Python programming. This is of no value in this article that is not about Python. D.Lazard (talk) 11:37, 26 May 2021 (UTC)
replies: text: Thank you for your guidance. Betaminus (talk) 16:25, 26 May 2021 (UTC)
thread_title:  Algorithm 

message: In section Cubic equation#Characteristic 2 and 3 one can read «This allows computing the multiple root». OK, if the polynomial has a multiple root. But NOT OK, if it does not have. E.g. if the derivative is a constant. What then? Or let f(X) := X^3+tX+q \in \mathbb F_2(t)[X] with non-constant derivative X^2+t ? I assume there is no multiple root of f(X)=0 . What does this knowledge help me to find the non-multiple roots ? –Nomen4Omen (talk) 15:29, 10 February 2022 (UTC)
thread_title:  Characteristic 2 and 3​ 

message: This article includes the phrase, "Babylonian (20th to 16th centuries BC)".  That just can't be right, but I don't know what it should be.  AWCzarnik (talk)  — Preceding undated comment added 04:58, 17 July 2022 (UTC)
thread_title: This just can't be right

message: Equations (85) - (91) of Wolfram MathWorld's CubicFormula webpage develop the roots of the reduced cubic using Lagranges theory. I checked the algebra of equation (91).
A Fourier transform is not referenced, just algebra.
Janet Heine Barrett, in her article "The Roots of Early Group Theory in the Works of Lagrange" (2017) , references the algebra needed to transform a reduced cubic equation into a Lagrange resolvent equation. [op. cit., page 7]. As suggested, I checked the algebra. 72.89.23.208 (talk) 15:17, 21 November 2022 (UTC)
thread_title:  Application of Lagrange resolvent roots 

message: There is still an error in the sign of the discriminant in the Cardano section. In the section defining the discriminant, the discriminant for the depressed cubic is asserted to be
:-\left(4\,p^3+27\,q^2\right).
However, in the section on Cardano's formula, the discriminant \Delta has the opposite sign. It is important to make the signs consistent because of the section relating the sign of the discriminant \Delta to the number of real roots.Thomas Hales (talk) 00:20, 24 May 2023 (UTC)
replies: text: In , it is not said that \Delta is the discriminant. Nevertheless, I have added a footnote for clarifying this. D.Lazard (talk) 08:12, 24 May 2023 (UTC)
thread_title: Sign of the discriminant

message: What did I do wrong? 121.210.212.82 (talk) 10:47, 2 September 2023 (UTC)
replies: text: This is explained in the edit summary: . D.Lazard (talk) 11:31, 2 September 2023 (UTC)
replies: text: I worked so hard on it! 121.210.212.82 (talk) 12:27, 2 September 2023 (UTC)
replies: text: Doesn't matter. If it's wrong, it's wrong; if it's badly formatted, it's badly formatted; if it's poorly written, it's poorly written. Please stop trying to insert it.--Jasper Deng (talk) 08:20, 3 September 2023 (UTC)
thread_title:  Why was my change reversed by D.Lazard?