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

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7
votes
3answers
162 views

How can I break through Function's HoldAll attribute to force evaluation of a body element?

The question concerns creating a function. Let consider the following code With[{f = Function[t, Cos[t]]}, {First[#], f'[#]} & ] which returns ...
3
votes
5answers
304 views

How to generalize and speed up this program?

There is a vector whose length is $n*m$, we can part it into $n$ sections in order. I want to define a function to compare the $i$-th and $i+1$-th section and find the minimum. The program for $n=m=3$ ...
1
vote
1answer
138 views

BSplinefunction and its derivative

Hi I am trying to use curve fit some data using the BSplinefunction. I havent been using Mathematica long, so my questions might be quite basic. ...
2
votes
1answer
115 views

How to compute a discrete histogram of a list [duplicate]

I'm trying to compute the discrete histogram of a set of values. By histogram I mean the absolute frequency a value appears on the dataset, by discrete I mean the values are from a discrete set, e.g. ...
0
votes
1answer
110 views

Understanding output of multivariable integration

I'm new to Mathematica and I'm trying to integrate this function: ...
0
votes
2answers
72 views

Scope of expression in a user-defined function

I have the following code: fbasic = A + R + Z*Z *Z*Z; f[A_, Z_, R_] := fbasic + R; f[0, 2, 3] The answer I am getting is ...
0
votes
1answer
98 views

Defining functions with changing number of variables [duplicate]

I am working with a bunch of functions of the form fn[x1_,x2_,x3_,...,xn_] := x1x2+x2x3+...+xnx1 where $n$ changes. Is there a way to create these functions ...
4
votes
4answers
211 views

How to avoid writing $K$ loops?

I want to evaluate a mathematical function of $K$ variables each of variables varying between 1:N. One way to do this is writing $K$ loops and varying variables accordingly, as shown below: ...
2
votes
4answers
208 views

Find time since last 0 in list

When I have a list of data (measured per day), is it possible to define a function that gives the nr of days since the data has been 0? I tried working with...
1
vote
1answer
130 views

Create continuous function from list

I have a list of data (measured per day) that I want to use as imput for another equation (say f). The problem is that the input I need for f needs to be a continuous function of time. Is it possible ...
2
votes
2answers
193 views

Writing a function that returns a (usable) function

I am trying to create a function that returns Arnold's Cat Map of size n iterated k times. I can get something out of the Function command, but I can't figure out ...
1
vote
4answers
174 views

How to use If to select arguments min & max in Range?

I want to call Range[] with its arguments depending on a condition. Say we have ...
0
votes
2answers
151 views

Inverse function

What probably could be the inverse of following function? ...
7
votes
2answers
275 views

How can I define a sequence of functions?

I need to define a function fun, and then re-define this function iteratively. The code is given at the end. First, a function ...
0
votes
0answers
60 views

Defining functions in a loop [duplicate]

I have a symbolic solution to a linear system with respect to some variables a[i,j] which depend on a parameter t. sol=Solve[...,Table[a[i,j],{i,0,n},{j,0,n}]] I ...
1
vote
0answers
141 views

Positive integrand giving negative answer

I'm integrating a positive function f(t) times sin(t) from 0 to pi/5 and get -38. Actually f is slightly negative for a short time (smallest value ~ -0.0005), but far from enough to explain this. ...
22
votes
4answers
260 views

How can the behavior of InterpolationOrder->0 be controlled?

In ListPlot and Interpolation, the option InterpolationOrder->0 uses two different ...
4
votes
1answer
254 views

Counting the number of operations performed during a calculation

I need to know how can I count the number of operations performed during a calculation of a CompoundExpression. In some of these expressions there are ...
2
votes
1answer
220 views

Call Functions From File Without Modifying Context (Sandbox)

Let's say I have file named test.m containing test[arg1_] := ( Print[arg1];) What is the best technique for calling test like ...
1
vote
1answer
144 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 ...
1
vote
1answer
143 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
111 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
vote
0answers
94 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
74 views

Ordering under assumptions

I have a three-element list which contains inverses of a function u, like so: ...
2
votes
1answer
86 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 ...
0
votes
0answers
401 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 ...
11
votes
2answers
264 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 ...
19
votes
0answers
227 views

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

This is another question on the design choices in Mathematica. I understand that without direct reply from the developers it may not be possible to give a definitive and exhaustive answer to "why" ...
-1
votes
1answer
125 views

Totalling a list including negative values [closed]

I'm trying to use the Total function on a list that includes negative values, and can't seem to figure out how to stop Mathematica from getting hung up on those ...
0
votes
1answer
95 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
94 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
197 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 ...
1
vote
1answer
83 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
198 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 ...
0
votes
0answers
61 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 ...
0
votes
1answer
266 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 periodic solution, and in ...
3
votes
0answers
86 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
181 views

Calling functions which take their arguments interactively

Lets say I have a file named test.m containing some functions. ...
6
votes
1answer
226 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
56 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
300 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
716 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?
3
votes
2answers
371 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
274 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
138 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
79 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 ...
3
votes
1answer
339 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
173 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
71 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
390 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 ...