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

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1
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1answer
183 views

Using NMinimize Properly

I'd like to find the point on a Bezier curve that's closest to some other point. The tricky thing is that because Bezier curves can loop around, the distance function can have multiple local minima ...
2
votes
1answer
124 views

Why the EuclideanDistance of these 2 exact points generates the warning N::meprec?

The two points are: pts = {{1/4 (-1 - Sqrt[5]), Sqrt[5/8 - Sqrt[5]/8]}, {1/4 (-1 - Sqrt[5]), -Sqrt[5/8 - Sqrt[5]/8]}}; EuclideanDistance @@ pts ...
2
votes
2answers
91 views

How to make a function work on symbols in a specific context

Let us say we have two sets of symbols $(x, y, z)$ with the same names that live in two different contexts: ...
3
votes
3answers
246 views

How to find the numbers $a$, $b$, $c$, $d$ of the function?

I want to find four numbers $a$, $b$, $c$, $d$ of the function $f(x)= \dfrac{a x + b}{c x + d}$ satisfying the conditions $f(-6)=4$, $f(-5)=5$, $f(1)=3$ and $f(2)=2$. I tried ...
19
votes
1answer
205 views

How to get Cases to wrap results in an arbitrary head?

A number of functions provide for results to be wrapped in an arbitrary head. This is very important in cases where the results should not be evaluated. Take ...
0
votes
0answers
49 views

Phase Unwrap List Of Points: Implementing continuous phase/Arg function for List of Points [duplicate]

I am looking for a function to unwrap phase of a list of points as done here for the continuous case. I have the Re/Im data as my input and would like the unwrapped phase as the output. Does anyone ...
10
votes
5answers
517 views

How to find first list element that differs from average of N previous elements by more than a given amount?

Given a list of real numbers, I need to write a function that returns the value of the first element in the list that differs from the mean of the previous $N$ elements by greater than $P$ standard ...
10
votes
4answers
1k views

How to find the domain and range of an implicit function?

For example, we have this curve: $$ x^2 + y^2 = 1 $$ Is there a function in Mathematica for finding out that the ranges for $x$ and $y$ are both [-1, 1]? What ...
3
votes
1answer
275 views

NestList with a list inside?

I'm new to Mathematica, and was looking for more efficient ways to implement the Do loop below. a, ...
2
votes
1answer
131 views

User-defined Distance Functions with extra parameters [duplicate]

The Nearest function accepts a customized distance function. For example, a simple case that works well is ...
1
vote
1answer
75 views

Why is a function I defined in a package not visible when I load the package? [duplicate]

I made a package containing some functions in the following way. ...
6
votes
2answers
223 views

Not FullDefinition for Save. MachineID not Protected?

Is there a way to set what symbols's definitions I do not want to store? Consider the following code: ...
1
vote
1answer
209 views

Map a function conditional on elements at multiple relative positions in a list

I figure this question has many solutions, and if an answer already exists it would be nice just to be referred to it. I need a function that 'maps' over my list and produces a list of equal length ...
0
votes
1answer
62 views

Errors in evalauting an expression

I have the following: Constants: b3b = 2; G = (1/eps^2); a1 = 3; a3 = 4; xc = 0.3; Functions: ...
8
votes
3answers
215 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 ...
4
votes
5answers
331 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
197 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
232 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
140 views

Understanding output of multivariable integration

I'm new to Mathematica and I'm trying to integrate this function: ...
0
votes
1answer
80 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
149 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
224 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
225 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
186 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
245 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
203 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
173 views

Inverse function

What probably could be the inverse of following function? ...
7
votes
2answers
418 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
64 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
198 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. ...
26
votes
4answers
385 views

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

In ListPlot and Interpolation, the option InterpolationOrder->0 uses two different ...
4
votes
1answer
392 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
270 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
160 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
222 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
203 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
122 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
84 views

Ordering under assumptions

I have a three-element list which contains inverses of a function u, like so: ...
2
votes
1answer
99 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
vote
0answers
874 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
311 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 ...
21
votes
1answer
385 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" ...
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
115 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
204 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
817 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
320 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
71 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
669 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 ...