Questions tagged [expression-manipulation]

How to manipulate expressions structurally, not necessarily complying with the rules of algebra.

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Calculate density of states for 1D system

The density of states for a 1D system can be written as: $D\left(\omega\right)=\frac{L}{\pi}\frac{1}{d\omega\left(k\right)/dk}$ I have some expressions for $\omega\left(k\right)$: ...
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Substituting values from an association thread into a table of expressions

I have asked a question here. Yet I am trying to do the same procedure with AssociationThread Suppose I have the following function which is a normal distribution: <...
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1answer
51 views

Substituting elements of lists into an expression

Suppose I have the following lists, as = {1, 2, 3, 4}; bs = {10, 20, 30, 40}; and the following expression: ...
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1answer
53 views

Crown a list of two sublists with ErrorBar without losing list structure

I have a list with two sublists of numbers, e.g. Sigmaf = {{1,2,3},{3,4,5}}; ... and I would like to crown each number with ...
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1answer
82 views

Split Expression Into Constant And Non-Constant Summands

I have a partially t-dependent matrix which I want to split into its t-dependent and its t-...
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191 views

Replace a randomly chosen part of an expression

Given an arbitrary Mathematica expression, how can I choose a random part of the expression and replace it with another symbol of my choosing? For example, given $a x^3 +2y\cos(x)- \tanh(x^{y+3})/(x^...
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142 views

Fixed Point Iteration - Finding Iteration Functions

When we use Solve, it attempts to solve the system for the variables, for example Solve[x^3 + 4 x^2 - 10 == 0, x] If we want to use Fixed Point Iteration to ...
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1answer
85 views

Extracting coefficients from a sum of exponential functions

I'm dealing with a sum of exponential functions with different exponents ...
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1answer
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Problem with recursive relations

Continuing the topic of my previous questions (link1 and link2), let me ask one more question. I have problems with the following code: ...
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check if one expression can be transformed into another

My question is how to use Mathematica to check if one expression can be transformed into another: Example 1: $ax^2+bx+c$ into $K\cdot(x+\alpha)^2+\beta$, and then show me $K(a,b,c)$ and so on. ...
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1answer
58 views

Replace a family of coefficients by a function in a sum

I would like to do something very simple, i.e. replace the coefficients in a sum by a function: c[1] + c[2] + c[3] /. {c[s] -> (s + 1)/(2 (2 s + 1))} ...
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2answers
65 views

Symbolic nest expressions

I'm trying to understand how to use symbolic expressions as arguments. The following example represents my problem: ...
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1answer
39 views

using pattern matching to separate coefficients and functions

I want to find out the coefficients and functions from an expression and possibly save them in separate files with same order. I have the following toy example: ...
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2answers
96 views

Collect with linear combinations

Is there a way to collect coefficients on specific linear combinations of variables? Consider the example below: ...
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Expanding complex expression and replacing variables in the result

When I'm finished expanding my expression I would like the result to be expressed again in terms of the original variables (like α, S1, T1, T2). I've tried replace, ...
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Computations with OptimizedExpressions without completely expanding them

I have to manipulate huge expressions that are rational functions of many (∼30) variables with integer coefficients. Storing them just as a ratio of two polynomials would be impractical. But they can ...
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39 views

Rearranging expressions by DragAndDrop

I see that the DragAndDrop option for editing is not supported anymore. However, I think this could be a really useful feature, for instance to rearrange the terms of an expression in the form we ...
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1answer
35 views

Applying function to both coefficients and variables in Collect

I am dealing with expressions schematically of the form expr = c[1] G[1] + c[3,8] G[3,8] + ... + c[3] G[1] + ... where the Gs are fixed objects, and the cs some ...
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55 views

Fast way to apply permutations in large list?

I have one Polynomial in the form of FF[x1,x2,x3,x4,x5,x6,x7,x8], where xi pick numbers from ...
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1answer
52 views

Optimizing an equation - show the length of an equation, including operators

A simple, but I think useful question to know the answer for. How can I quickly count the length in my equation, including +,-, and so on? For example, $x^2+1$ has a length of 4.
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3answers
103 views

How to hold the expression when using ToExpression with TeXForm

I know {1, 1} // Apply[Defer@*Plus] can return 1+1 But if I want hold the form from TeXForm,what should I do? ...
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Lexicographical Search and Conjugate

I bid you a good day. I want Mathematica to plug this assumed solution into the left hand side of a differential equation. Then collect terms of powers of $\alpha$. $\psi (x,y)=\alpha f_1(y)e^{i x}+...
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1answer
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Testing expressions with === (SameQ) between original expression and after Factor[], Expand[] and FullSimplify[] [closed]

a=16x^4 y^5 (81-z^4)-54xy^2 (81-z^4) Out[30]= -54 xy^2 (81-z^4)+16 x^4 y^5 (81-z^4) b=Factor[a] Out[31]= 2 (27 xy^2-8 x^...
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1answer
64 views

How do I apply complicated algebraic/trigonometric manipulations to nested expressions?

Consider the expression $$ a\sin(x)-a\sin\left(\frac{x}{a}\left(a+\frac{ay}{x}\right)\right) \label{a}\tag{1} $$ which can be rewritten as $$ \sin(x)-\sin\left(x+y\right) \label{b} \tag{2} $$ and ...
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63 views

How do I build a position index of a general held expression to arbitrary depth?

I have an expression which I would like to make a position index of, which for sake of argument will be this: expr = f[q + g[x, y, z]]; Since it's not a list, ...
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1answer
48 views

Extracting argument of a specific functions in a large expression

I have a large expression, for example Cos[x]Sin[y]Sqrt[1+z]/(1+x^2)-1/(1+y) I wish to extract the argument inside Sqrt ...
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55 views

Finding a selected expression

How can I find all expressions matching the one I am selecting? This features exists in Matlab and is quite helpful: Just trying to make my debugging easier. Thanks!
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How to do an arbitrary expression growth in Mathematica?

I want to write a function that can be used to grow an expression from a seed or another existing expression based on part specification. ...
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3answers
620 views

Split expression into list of terms

I'm looking for a nice way to split an expression into a list of the terms (i.e. the addends). The desired behavior in: ...
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45 views

Canceling factors from numerator and denominator with complex number

I have the following expression: $\text{expr} = i \frac{\sqrt{a-b}}{\sqrt{b-a}}x$. Clearly simplifying expression gives $\text{expr}=x$ by cancelling the numerator and denominator. However, I am not ...
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74 views

Any differences between Activate[…] vs ReplaceAll[…,Inactive[f_]-f>]?

I can activate an expression with Inactive objects such as expr = Inactive[f][Inactive[f][x], y] + Inactive[f] by applying <...
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1answer
66 views

Manipulate MeshRegion as normal Mathematica expression

A MeshRegion seems to function quite differently from any other Mathematica expression. One cannot take a Part of it. Nor can I ...
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1answer
96 views

How can I show that the equation holds?

Suppose we have the following data: $ r=\frac{vk}{h^2}$ $u[i,j]$ is a function of two variables with $i,j$ integers. $\frac{u[i,j+1]-u[i,j]}{k}=v\frac{u[i+1,j]-2u[i,j]+u[i-1,j]}{h^2}$ Then I would ...
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Assert no unevaluated function applications

Background Suppose I have begun a fresh kernel session, and I have defined the following function alone: F[x_, y_] := x + y; One expected use of ...
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33 views

Making substitution to an expressions with a list of numerical data [closed]

Suppose I have an expression similar to this: y=23.23*(h[x]^2)*(D[h[x],x])*(D[h[x],{x,3}])/(13.2+Cos[0.245x]) The actual expression is a lot more complicated, but ...
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3answers
90 views

Select variable and its derivatives

A simple question: I have this equation: ...
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3answers
341 views

isolating a specific variable to one side in an equation

I am trying to do a simple operation of manipulating an equation of multiple variables (say, $x,y,z$), so that I can get one of the these variables on the LHS and everything else on the RHS. It should ...
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3answers
88 views

Remove imaginary part from expression on an interval

Let us have a expression: ...
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7answers
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Which operation combines {f,g,h,…} and y[u,v,w,…] to get y[f[u],g[v],h[w],…]?

I have a list of functions myFuncs = {f,g,h} which I'd like to map over an expression expr = y[u,v,w] to obtain ...
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3answers
332 views

How to make arbitrary transpositions of associations and datasets

Is there a general Transpose for Dataset/Association that will transpose arbitrary levels, ...
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4answers
107 views

ReplaceList doesn't apply rules down to subparts

Somewhat related to a previous question, I'm experimenting with ReplaceList to get the list of all possible transformations we can obtain by applying a rule to an expression. But I don't manage to ...
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1answer
68 views

How to test if $ⅈ$ is in an expression?

From this answer https://mathematica.stackexchange.com/a/9773/68791 and according to the documentation: FreeQ[list,form] test whether form occurs nowhere in ...
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59 views

General rule to rewrite function and argument into a new symbol

I am trying to convert Mathematica output into equations I can plug into C. I am presently trying to convert expressions of the form Derivative[1,0,0][f][t,x,y] ...
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1answer
78 views

Collect integer and non-integer powers at the same time

Imagine we have an expression that contains both integer ($y$, $y^3$, $y^8$ etc.) and non-integer powers ($y^{1+\alpha}$, $y^{2\,\alpha}$, $y^{2+3\,\alpha}$) of the variable $y$, where $\alpha\in\...
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2answers
126 views

Expand in series an equation of two variables

I am sorry if this has been asked, I don't really know how to formulate the search to find it. We have some system of equations (that are equal to zero), for example (not sure how to enter ...
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How can I force the output of a computation to be as compact as possible, yet complete, by using functions?

I am computing some derivatives in Wolfram Mathematica 11.3. The functions that I have to differentiate (with respect to the state variables) are the equations of motion of a rocket in the atmosphere. ...
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1answer
221 views

How to make a function linear

I have a linear function, say f, and an expression like f[3x^2 - 8 a y^2 + 4 z b] where I know that ...
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1answer
46 views

How can I calculate the union of a tagged set? [closed]

I want to calculate: Union[envelope[1], envelope[2], envelope[3], envelope[4], envelope[5], envelope[6], envelope[7], envelope[8], envelope[9], envelope[10]] ...
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2answers
84 views

Suppress arguments in output for pretty print

I would like to define a rule that suppress any arguments of a function for visibility. I tried: rule = f_[x__] -> f While this works well with individual ...
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1answer
46 views

Matrix multiplication of function

Suppose I had a 2-by-2 matrix with each entry a function, e.g., {{#1&,#2&},{#1 + #2 &, -#1 + #2 &}} and a vector of functions, e.g.,...

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