Questions tagged [symbolic]

For questions about symbolic computation, as opposed to numerical computations.

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2answers
106 views

Defining a list without knowing the number of elements

Let $N$ be a natural number $\ge 1$. I have two questions: How can I define a list with variables $p_1,...,p_n$? How can I define an element $a\in\mathbb{C}$ such that $a⁶=(-1)^n?$
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0answers
217 views

How to get Mathematica to evaluate trig function derivatives in a expression

I am working on a problem that results in expressions with trig functions and their derivatives along with several other functions and derivatives. At one point, the subtraction of two expressions ...
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0answers
50 views

Why does Mathematica take an aeon to solve an inequality?

I gave Mathematica this inequality to solve: ...
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1answer
90 views

Need help with computing symbolic derivatives [duplicate]

Imagine you are trying to get an equation of motion (in my case, the Lagrangian of a coupled drives CE108 system). In such a case, you need to symbolically define certain derivatives as themselves, ...
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0answers
94 views

How to symbolically represent N-dimensional matrix? [duplicate]

Considering the following simple problem: Given $A$ an n x n matrix, $B$ an n-dimensional column vector, find the gradient: $$\nabla _B((A B) . (A B))$$ The solution is obviously $2(A + A^T) B$, ...
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0answers
45 views

Symbolic differentiation of an arbitrary function [duplicate]

I often work with expressions in one or more arbitrary function, and would like to get simplified expressions for their derivatives. For example I would like to define the normal to a graph as ...
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0answers
114 views

Question arising from research into relation between Pi and its convergents

I am researching my conjecture (-1)^n*(Pi−A002485(n)/A002486(n))=(Abs(m)*2^j)^(-1)*Integrate[(x^l*(1-x)^(2*(j+2))*(k+(m+k)*x^2))/(1+x^2),{x,0,1}] (1) where ...
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2answers
2k views

How can I isolate a variable?

I'm new to Mathematica. I'm having trouble using Reduce to isolate the variable hab in the inequality below (Mathematica has ...
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1answer
291 views

Defining the derivative of a Hermitian inner product symbolically [duplicate]

I have various $\mathbb{C}^{n}$ valued function $f[z,\overline{z}],g[z,\overline{z}]$ with $z \in \mathbb{C}$ and I wish to represent their Hermitian inner product and furthermore the derivative of ...
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0answers
40 views

Symbolic multivariable calculus with undetermined number of variables [duplicate]

$y$ is a function of $n$ independent variables $x_1, \dots, x_n$ where $n$ is unknown. How do I calculate $\partial y/\partial x_k$ with Mathematica? For example, $$y=f(x_1,\dots,x_n)=\sum_{i=1}^n {...
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0answers
41 views

Mathematica can't simplify disguised expression [duplicate]

When I simplify the following quartic polynomial with a linear constraint; Simplify[x y z a + x y z b , a + b + c == 0] // Expand I get what to me seems like the ...
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0answers
36 views

Series Manipulation [duplicate]

How do I get Mathematica to realize that it should simplify the expression Sum[f[t],{t,1,Infinity}]-Sum[f[t],{t,2,Infinity}] to ...
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1answer
2k views

How to order a polynomial in descending powers of x? [duplicate]

This should be very simple, even silly If I ask this mathematica Expand [(x + 1) (x + 2) (x + 3)] Mathematica delivers me well ...
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0answers
273 views

Mathematical symbol and name for Symbolic Replacement

(Originally from math.SE, but might be better here) I'm searching for a mathematical symbol, that describes the symbolic replacement done for instance in Mathematica: ...
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0answers
207 views

Is there a way for me to get Mathematica show its steps? [duplicate]

I have seen similar questions but they were quite dated (3+ years). When performing, say an Integration, it would be beneficial to see the major steps such as variable substitution, change the order ...
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0answers
90 views

How do I simplify Interval[{x,x}] to x? [duplicate]

How do I simplify Interval[{x,x}] to x ? Simplify and ...
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0answers
173 views

Alternative to Series

Here is a sample of my code: ...
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0answers
707 views

Simplifying terms in a Sum expression

I have a sum in the form of pure function s = Sum[f[k], {k, 0, # - 1}] & of perhaps complicated terms f[k]. The terms <...
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0answers
197 views

A derivative encountered in matrix factorization using gradient descent

I want to factorize a matrix $a_{ij}$ as $$ a_{ij} = \sum_k u_{ik} v_{jk} $$ using variational method for some reason. That is, I want to minimize the cost function $$ F = \sum_{ij} b_{ij}^2 $$ with ...
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0answers
609 views

Symbolic tensor product calculation

I am trying to calculate the a symbolic tensor product $\langle \nabla f\otimes f,\nabla g\otimes g\rangle ^2+(\langle \nabla f\otimes g,\nabla f\otimes g\rangle +\langle \nabla g\otimes f,\nabla g\...
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0answers
65 views

Simplify symbolic expression in terms of constants [duplicate]

Say I have an expression $a+b+a\times b$ and I define $c:= a\times b$. How do I get Mathematica to write $a+b+a\times b$ in terms of $c$, i.e. $a+b+c$?
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0answers
71 views

Symbolic Calculations with formal matrices [duplicate]

I want to make calculations with matrices in the form (for lovers of statistical mechanics, is just the first step replica symmetry breaking) ...
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1answer
585 views

Eigensystem without Root objects

I'd like to find eigenvalues and eigenvectors of the parametric, 21x21, matrix below without Root objects. My matrix is: ...
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1answer
351 views

How to write a more concise `RowReduce` function that can deal with symbolic matrix?

I asked a similar question in this post before and understand the reason why RowReduce function can't reduce symbolic matrix. I wrote an ...
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1answer
118 views

How to do quick symbolic integration in Mathematica

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3answers
313 views

How do I convert the E^[…] notation back to Exp[…] notation?

How do I convert the E^[...] notation back to Exp[...] notation? Is there a simple command for this? It appears that ...
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1answer
86 views

How to replace one numerical constant with another?

I want to replace the symbol for the constant ∞ with some variable name such as "Inf" or another constant such as 1000.0 The constant infinity appears many times in the file.
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1answer
685 views

How to correctly calculate symbolic eigenvectors

I give a minimalistic example of my problem: I have a matrix: m[a_,b_]:={{0,-a+b},{b,0}}; I define the eigenvectors as: ...
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2answers
218 views

Can Minimize work faster and/or be parallelized?

Having executed ...
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1answer
274 views

How to symbolically integrate 2D exponential function? [duplicate]

Is it possible to symbolically solve a 2D integral of the following form $$\int d \vec{r}e^{-\frac{\left| \vec{r} - \vec{r}' \right|^2}{2c}}e^{-i \vec{k} \cdot \vec{r}} $$ where $\vec{r} = (x,y)$ and $...
-3
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1answer
658 views

Mathematica's steps towards the result of a definite integral

I am interested in this definite integral: $$ \eqalign{\int_0^\infty {x^2 \log(1-e^{-x})}\; dx\cr } $$ That is: ...
-3
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1answer
110 views

How to solve differential equation of this type?

So, I tried so solve the first equation, where I am looking for $p_2$, in Mathematica with next command: ...
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1answer
965 views

Symbolic Definite Integration

How do I perform Integrate[Sin[x]^2/(z^2 + R^2 - 2 zRCos[x])^(3/2), {x, 0, Pi}] where z and ...

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