whuber

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Consultant (environmental stats a specialty) and teacher.

	14,111 reputation	bio	website	quantdec.com	visits	member for	1 year, 5 months
12676 badges		location			seen	Jun 5 at 22:21

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Mar 5	reviewed	Reopen Why does compiling a function with ConstantArray give an error when used in parallel?
Mar 5	revised	*What is the value Re[Sqrt[1+I2x]]?* added 8 characters in body
Mar 5	comment	*What is the value Re[Sqrt[1+I2x]]?* Concerning those voting for the duplicate: could you indicate how that would produce the solution $\sqrt{1+\sqrt{1+\left(x/2\right)^2}}$? (I had to manually derive this.)
Mar 5	reviewed	Reopen How do I get a plot with a certain size?
Mar 5	comment	Mathematica vs Sigmaplot (Non LinearModelFit) @rcollyer Ease of fitting can be a concern, but achieving constancy of variance and/or a linear model are more fundamental than that, because they are related to how one interprets the model and the quality of predictions or estimates made with it. Philosophy (such as Occam's Razor) and experience are part of the basis for such advice, which cannot be fully justified mathematically (nor contradicted mathematically, either). BTW, I am surprised that "_at_rc" doesn't work: pinging is supposed to recognize prefixes. Thanks for the heads-up about that.
Mar 5	comment	Erfc Not Returning Results Specified in Documentation There does appear to be some kind of a typo, but it is curious that the given answer in the docs looks like it should correspond to somewhere between $16$ and $17$ decimal places--almost exactly the native precision. It seems there might be something else going on here.
Mar 5	reviewed	Approve suggested edit on Why can't Mathematica solve these non-linear equations?
Mar 5	comment	Why can't Mathematica solve these non-linear equations? In spirit this is the same question as mathematica.stackexchange.com/questions/20606/…. It suffers from exactly the same problem: you cannot hope to find a closed symbolic solution to an equation in which the unknown(s) appear as exponents (as $l_2$ does on the rhs) unless there is some magical cancellation (which there is not here).
Mar 5	comment	Erfc Not Returning Results Specified in Documentation Wrapping the command in `N` will help when you remove the decimal point after the $30$. Ask for $407$ digits.
Mar 5	revised	Contour plots of a two-variable function depicting the values of its integral added 233 characters in body
Mar 5	revised	Plot a 2D vector path onto a surface added 425 characters in body
Mar 5	answered	Contour plots of a two-variable function depicting the values of its integral
Mar 4	comment	Contour plots of a two-variable function depicting the values of its integral It looks like you may have over-generalized this question into something meaningless. These "contours" are not well defined. First, surely you mean to refer to regions, because these are not contour integrals; they are 2D integrals. Also, with few exceptions, for any given $\alpha_j$ there will be a large set of regions, having differing boundaries $C_j$, which yield the same value of the integral. Do you intend that $f$ be constant on each $C_j$?
Mar 4	comment	Can mathematica resolve this equation? @belisarius I'm afraid I don't understand what you mean by "state" a solution. The question I read here is "Am I using these functions incorrectly?" (BTW, if by the use of quotations you mean to suggest our use of "primitive" may be unusual or idiosyncratic, please be assured that is not the case: it is a standard, well-known term.)
Mar 4	reviewed	Leave Open How is the Mathematica kernel structured internally, and how does evaluation work?
Mar 4	comment	Can mathematica resolve this equation? I don't believe my comment answers the question stated, which is whether `Exists` and `Resolve` have been "incorrectly" used. The question does explicitly presume the lack of all solutions, and your answer does challenge the basis of that presumption--which I think is a valid thing to do--so I commented only in order to address that tangential issue.
Mar 4	comment	How can I obtain the function described by given set of central moments? (1) Not all probability distributions are determined by central moments; moreover, some sets of moments give rise to more than one probability distribution. (2) You are not free to fix a finite set of central moments and vary the rest: there are relationships among them all that must be satisfied. This suggests you consider alternative characterizations of distributions. But which ones would be appropriate? As to that, you have provided us no clues. Perhaps you could tell us what your problem is rather than stating it in such abstraction that we have little chance of helping you?
Mar 4	comment	Can mathematica resolve this equation? The lack of any solution might not be "obvious," but Fermat's method of descent works well here. If we start with a primitive solution $(x,y,z)$ and reduce it mod $3$, we see easily that $x$ and $z$ are multiples of $3$: `Solve[x^2 - 3 y^2 == 2 z^2, {x, y, z}, Modulus -> 3]`. Dividing out by $3$ and reducing the new equation mod $3$ shows that $y$ also is a multiple of $3$: `Solve[3 xp^2 - y^2 == 6 zp^2, {xp, y, zp}, Modulus -> 3]`. This contradicts the assumption that we had a primitive solution, whence there can be no solutions.
Mar 4	comment	Plot a 2D vector path onto a surface @rm-rf A script or macro is a good idea. It would be ideal to do it directly within MMA, though!
Mar 4	comment	Plot a 2D vector path onto a surface This is very clever. Because it is offered without much explanation, it may be worth pointing out that the technique is specific to this particular problem. It will not work for general paths (such as those that are self-intersecting or do not form loops), because these cannot be extended to 2D coordinate systems. It is necessary that the image of the path be a submanifold of $\mathbb{R}^2$, in which case one can use a coordinate system for a tubular neighborhood.