Questions about the use of built-in Mathematica functions, including pure functions.

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1
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1answer
165 views

Expansion of functions in the real domain

When I try FullSimplify[FunctionExpand[x^(1/12)(1/12) LerchPhi[x,1,1/12]]] I have a nice answer with many complex numbers. Is there any way to have the ...
2
votes
1answer
236 views

Inverse on a restricted domain

I have a function, whose domain is [0,1]. The function is f = Piecewise[{{Exp[-β * (-Log[#])^α], 0 < # <= 1}}, #]& with ...
3
votes
1answer
222 views

plotting hypergeometric functions

Does anyone know why a plot of a hypergeometric function turns out differently in Mathematica than in Maple? The function I'm plotting between x=-30 and +30 is: ...
1
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0answers
123 views

CDF with numerous independent manipulate objects

I have been working on my senior project that involves the creation of a CDF with multiple Manipulateexpressions. I need to protect my code so I have been trying to ...
0
votes
1answer
90 views

Ordering under assumptions

I have a three-element list which contains inverses of a function u, like so: ...
2
votes
1answer
101 views

Replace inverse function

I'm solving an expression like so: Solve[u[x] == u[a] + u[b], x] Mathematica returns {{x->(u^(-1))[u[a]+u[b]]}} If I ...
1
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0answers
965 views

How to Output Chi-Squared Statistics when using NonLinearModelFit

I am using NonLinearModelFit for some curve fitting and I was wondering if NLM is able to output chi-squared/leastsquared statistics from the best-fit parameters and confidence intervals. From my ...
13
votes
2answers
322 views

Clever use of DownValues, or failure to understand the “Mathematica Way.”

I needed to look at the changes in the values of about 4000 items from one year to the next. I have a table with identifiers and values for each year. Not all of the items are in each list. The ...
22
votes
1answer
430 views

Why does list assignment with a packed array result in unpacked values?

Bug introduced in 5.2 or earlier and fixed in 10.1.0 This is another question on the design choices in Mathematica. I understand that without direct reply from the developers it may not be ...
0
votes
1answer
106 views

Is there such a command like FindZero[f[x],{x,1}]?

I´d like to find the zeros of a function. I know I could find them by Solve[f[x] == 0, x] but that gives me only the x-coordinates. I want to get both the ...
2
votes
1answer
118 views

How can I define a function taking two distinguishable sets of options?

It commonly happens that one wants to define some function foo which in turn calls some other function (e.g., Plot) that can ...
9
votes
2answers
206 views

How can I make Which format its output?

Functions like Piecewise have cool, easy-to-read formatting. In the same vein, I think it would be wonderful if the Which ...
28
votes
2answers
836 views

Is there a name for #1@#2&?

Why does the pure function # @ #2 & have no name? I'm asking because sometimes I find inelegant to write expressions like ...
1
vote
1answer
92 views

Techniques To AutoReplace Browse

Let's say I have a function of the form. Test[File_,text_] What would be the most automated way and flexible way to generate an input cell of the form, such ...
2
votes
1answer
337 views

Problem with Covariance Matrix Output in NonlinearModelFit

I am running NonlinearModelFit based off of some simulated data and trying to fit to a function with more than one parameter. Eventually, I would like to fit to 5 ...
1
vote
0answers
79 views

what is the difference between these definitions? [duplicate]

I define 2 functions: g[s_][x_,y_] := the gaussian (1) g1[s_,x_,y_] := the gaussian (2) I get the same answer using ...
1
vote
1answer
779 views

Computing the fundamental matrix and its monodromy matrix

Assume $\dot x(t)=v(x,t)$ is a $T$-periodic, with respect to $t$ dynamical system. That is: $x\in\mathbb R^n,\quad t\in\mathbb R,\qquad v(x,t+T)=v(x,t)$. Let $x_0$ be a smooth periodic solution in ...
3
votes
0answers
93 views

Finding the argument set for internal functions in Mathematica v9.0

I've recently run into a problem with importing TIF stacks in Mathematica: Slow import of multigigabyte TIF image stacks On the advice of Simon Woods and others, I've been looking into the behavior ...
0
votes
1answer
205 views

Calling functions which take their arguments interactively

Lets say I have a file named test.m containing some functions. ...
9
votes
1answer
300 views

solve ODE with divergencies

The solutions of the second order differential equation $$\frac{1}{\eta}\frac{d}{d\eta}\left(\eta \frac{df}{d\eta}\right)+\left(1-\frac{s^2}{\eta^2}\right)f-f^3=0$$ is shown in Fig. 5.2 below, for ...
0
votes
1answer
70 views

Extracting function variables from a list [duplicate]

Evaluating the following func[x_, y_] := x^2 + y^2 listn = {{a, b}, {c, d}, {e, f}}; Map[func[##] &, listn, {1}] yields {func[{a, b}], func[{c, d}], ...
7
votes
3answers
348 views

Find names of the functions defined in a file

Lets say I have a file named file.m that contains: test[] := ( Print["test"] ) How would I go about extracting the function ...
1
vote
4answers
2k views

Solve trigonometric equation

I'm looking for a solution (graphic, numeric or analytic) for a function of the form: $$a^2\tanh(x)=\tan(ax),\quad a ≥ 1,\ x > 0$$ preferably using Mathematica. Any advice?
4
votes
2answers
668 views

How can I find the range of my function

I am trying to find the range of (3 Sin[x] - 3)/(2 Cos[x] + 10), I tried this, ...
3
votes
1answer
509 views

How do I draw a credible velocity vs. time graph using Locators?

This is partly a math question, partly a Mathematica question. For educational purposes, I'm making a simple demonstration to create a velocity over time graph from six locators. On the basis of ...
3
votes
1answer
159 views

Circle as a function parameter

What I want to do is to find a circle which is tanget to the three big ones. I tried the code below: findSmallCircle[c1_Circle, c2_Circle, c3_Circle] := ...
0
votes
1answer
82 views

Function or script which maxes out the CPUs?

I've been using Mathematica for awhile now and have never come even close to maxing out my CPU cycles. Are there any functions which consume lots of CPU cycles? Right now I am running a script which ...
4
votes
1answer
1k views

What do the hashtags represent in the result of Solve, and how should I use them? [duplicate]

There is a function that I'm trying to get the inverse of. My function is a simple polynomial: Tn[T_] := 4/9 T^3/Tc^2 + 5/9 T Now I tried to find ...
0
votes
2answers
202 views

Is there a better way to approximate some graphs of integrals than interpolation?

I'm still pretty new to Mathematica so my apologies if this is a dumb question. I wanted to plot some integrals of functions for no particularly good reason, but the only decent way I could come up ...
0
votes
2answers
92 views

How would I add together any list of arguments as a pure function?

Let's say I have a list of arguments, of any length. How would I add them all together? f = Evaluate[Plus @@ Array[Slot, 3]] & f[1, 2, 3] This would add ...
2
votes
1answer
828 views

How to take the derivative w.r.t. an arbitrary function?

EDIT: The answer posted by @Jens works for built-in functions only. However I'm starting to wonder if this is related to my Mathematica install somehow. I have version 7. Here is an example in the ...
2
votes
1answer
849 views

How could I define a function as the solution of equations in Mathematica?

I have posed a specific question yesterday but it may be too trivial to answer. I think the question could be asked in a more general way so it is easier to answer. Then I could solve the original ...
1
vote
1answer
87 views

How can I transform parts of an Integer list to a String list

There is a sorted list of Integers. ilist = PadRight[Sort[ RandomSample[Range[1, 99999], 3], Less], 5] It should become string area codes like: ...
1
vote
0answers
25 views

valuation to a function using a list [duplicate]

What I want to do is to evaluate a function as shown below: LessQ[n_] := LessQ[n] = l[n] < 61 In some cases, when I am sure that on a list the ...
2
votes
1answer
141 views

making a function of fit results

I have 13*25 datasets consisting each of around 40 points. They are all linear I can easily fit them using fit function but my problem is when I want to call them I want them to be functions. I want ...
4
votes
1answer
290 views

How to check if a given expression is an “explicit algebraic number”?

The documentation for PossibleZeroQ says: With the setting Method...
5
votes
2answers
168 views

How to check an algebraic number for membership in a list

I need to check an algebraic number for membership in a list of algebraic numbers. The numbers can be expressed in different forms (combinations of radicals, Root ...
-1
votes
2answers
395 views

How do I generate a table of data points from a function and add random noise? [duplicate]

I am trying to generate a table of data for the function: ...
2
votes
2answers
234 views

Restarting an Animate animation after variable in Manipulate changes

I've been trying to restart an animation after variables change from Manipulate PopUpMenus. My animation takes the form: ...
1
vote
1answer
212 views

Derivative inside a function

I am trying a problem that should be simple: to create a function that contains a derivative. I need to do a more complex example, but even with the simplest I'm having trouble: Let's consider ...
7
votes
2answers
163 views

How do I invoke the default complexity function?

Documentation on ComplexityFunction says: With the default setting ComplexityFunction->Automatic, forms are ranked ...
1
vote
1answer
155 views

Recursive function taking functions as arguments

I'm trying to implement Lie brackets and derivatives of nth order. For doing this, I've stumbled upon something I don't understand. Here is an illustration: First I define the functions: ...
10
votes
1answer
435 views

Is it possible to find a limit of a sequence given by its recurrence relation?

I need to calculate a limit of a sequence given by its recurrence relation. I tried the following: ...
6
votes
3answers
339 views

How to get the correct answer when solve this equation?

I want to find the values of the parameter $m$ to the graph of the funtion $$x^4 - 2 m x^2 + m + 1$$ has three extremal points make an equilateral triangle. I tried ...
7
votes
2answers
145 views

Change some option of a function when calling it [duplicate]

Say I have defined some function like f[p_] := Plot[Sin[p*x], {x, 0, 2 Pi}] Now in most cases, I just need to specify the value of ...
4
votes
2answers
190 views

Using Element[]

Can the Element[] function only be used for the domains given in the documentation? I am trying to use it to determine if a value is contained in a previously defined list. Thanks!
-1
votes
1answer
275 views

How to define a pure function with a Module?

I was not able to use a self defined (using Module and For loops) piecewise function to fit data. It seems that the problem is that I have to define a pure function. I would like to learn how to ...
1
vote
1answer
152 views

Find a sequence of integers which give max in each step

I would like to write a program in Mathematica to look for the integer $n$ such that the following definition holds for any $1 < m < n $ $$\frac{f(n)}{f(m)}>1+\frac{\log(n/m)}{\log(n) ...
25
votes
1answer
267 views

What does Internal`InheritedBlock do?

What does the function Internal`InheritedBlock do? How is it different from the regular Block?
0
votes
1answer
66 views

Have the kernel load a user-defined function by default [duplicate]

I wrote a very simple function that I would like to act as if it were one of the default functions that came with Mathematica, so that you don't have to load or import any package before you make use ...