Questions tagged [symbolic]

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

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6
votes
1answer
165 views

Laplace transform of a rectangle function

I defined a rectangle function as below: rect[t_, T_] := (Sign[t] - Sign[t - T])/2 The laplace transform should be $$ \frac{1-e^{-sT}}{s} $$ But the code below ...
1
vote
0answers
84 views

Element: True,False,Maybe,,,

I have a question about Element[] Element[3/2,Rationals] True OK ...
0
votes
1answer
65 views

Simple nested sum giving ridiculous answer [closed]

I have produced a minimum working example of the issue I'm facing. I would like to evaluate the following symbol sum, with $n\geq0$: $$\sum_{k=0}^n \sum_{m=0}^{2(n-k)} x^m$$ If I evaluate this sum ...
2
votes
1answer
90 views

`Series` gives wrong result

The following code shows that Series gives different results depending on whether one simplifies the expression in the first place. Let's assume all variables real. ...
4
votes
3answers
215 views

How to simplify this formula?

$$ \int \frac{1}{\sqrt{1-2 x^3}} \, dx $$ Integrate[1/Sqrt[1 - 2 x^3], x]// FullSimplify The result is very complex. Then I want to differentiate it with the ...
5
votes
1answer
123 views

Implement abstract algebraic structure

I would like to implement algebraic structures in Mathematica such as groups, algebras, Lie-algebras, Hopf-algebras, ... In particular, after initialising such a structure, I would like to have ...
1
vote
3answers
658 views

How would I solve this math problem on Mathematica?

$(3t^2 + 5t + a ) (4t^2 + bt - 2) = 12t^4 +26t^3 - 8t^2 - 16t + 6$ What is a + b? The answer would be: $6=-2a$ $a=-3$ $-16t=(5t\cdot-2)+a\cdot bt\Longrightarrow-16t=-10t+(-3)bt\Longrightarrow b=...
1
vote
1answer
54 views

Refine Max[#] with assumptions breaks with more elements

Can someone please explain the following phenomenon to me? I am using Refine to evaluate a symbolic Max expression with a ...
0
votes
0answers
34 views

PlanarAngle symbolic equalities return contradictory results

PlanarAngle[OO->{A,B}]==PlanarAngle[OO->{B,A}]/.{OO->{0,0},A->{1,0},B->{1,1}} False ...
2
votes
1answer
70 views

Using chain rule to calculate a second-order partial derivative in spherical polar co-ordinates

I have a function $f$ and I am supposed to calculate its second-order partial derivative first in cartesian co-ordinates, which is fine. However, I am stuck while solving the problem in spherical ...
0
votes
1answer
91 views

How to calculate integration with undefined functions?

There are two functions inside the integral symbol, one is related to the independent variable and the other is independent of the independent variable. Both are the derivative and Tload is a ...
4
votes
1answer
124 views

How to get DAE representation from equations?

Update2: Thank you for all of your answers. I would like to clarify the question as I did a bit of research on DAE representations and their applications in software. There are 2 representations used ...
0
votes
0answers
30 views

TagSet::sym Error using Subscript [duplicate]

I am a beginner to Mathematica and I am trying to get it to solve some equations of a function (vector) $B$ of three components, but first I want it to know that the derivates with respect to one ...
3
votes
1answer
51 views

Is there a global parameter that limits the number of variables handled by Simplify?

It seems that Simplify is unable to handle (at least some) expressions involving 22 or more variables. Consider the code snippet below: ...
4
votes
1answer
129 views

Simplify is not simplifying a compound inequality as expected

The Simplify command is having trouble verifying a compound inequality, even while it correctly handles the two corresponding single inequalities. I'm starting ...
5
votes
2answers
243 views

A fast way to expand symbolic products

My goal is to expand a product, where the factors are sums of symbols such as: $a_1 \times a_2 \times \ldots \times a_n$, where $a_i = b_1 + b_2 + \ldots + b_m$. The desired final expression is ...
5
votes
1answer
80 views

I can't get DSolve to work on coupled equations

In trying to solve a geodesic equation, I have these coupled equations: ...
0
votes
1answer
64 views

Finding ODE series solution coefficients

I am trying to solve an ODE by subbing in a series form and then looking individually at the coefficients of different powers of the variable. I'm looking at a general form of equation: $$\frac{\...
9
votes
1answer
334 views

Deep learning outperforms in symbolic integration and ODE?

There comes a new paper on arXiv (arXiv 1912.01412, Deep Learning for Symbolic Mathematics by Guillaume Lample, François Charton) claiming that a deep learning model outperforms Mathematica a lot in ...
2
votes
1answer
139 views

How can I use a unit vector notation found in physic texts?

In physics (I'm thinking of Taylor's Classical Mechanics or Griffith's Classical Electrodynamics) it is common to use "hat" vectors to denote unit vectors like $\hat{x}$ or $\hat{r}$. If I wanted to ...
1
vote
1answer
64 views

Expectation and direct integration give different results [closed]

I have an integral I want to compute: $\qquad \int_{\mathbb R^4} e^{-(x_1+x_2+x_3+x_4)} \left( 1-x_1-x_3 \right) dx$ To me, this should be equivalent (modulo some scaling factor) to computing the ...
0
votes
1answer
42 views

Speeding up differentiation of a complicated expression

I'm a beginner to Mathematica in the spirit that I cannot write the most optimized codes for a particular task. In the following snippet, I have a function $\Phi(\eta(Ee,y,z),\alpha(y,Ee,z),\xi(\kappa,...
0
votes
0answers
17 views

Symbolically invert block matrix [duplicate]

In Mathematica, if I write something like: Inverse[{{a, b}, {c, d}}] I get the inverse: ...
0
votes
3answers
108 views

Function which returns a symbolic jump between two ordinates, e.g. $[f(a,b,c)]^+_- = f(a^+,b^+,c^+)-f(a^-,b^-,c^-)$

I want to create a function in Mathematica which accomplishes the following: $$[f(a,b,c)]^+_- = f(a^+,b^+,c^+)-f(a^-,b^-,c^-)$$ where $f$ is any function (has 3 arguments above but this need not be ...
0
votes
0answers
27 views

How to display partial derivatives correctly after making a change of variables

I am currently looking into a way of being able to easily non-dimensionalise differential equations (such as the Navier-Stokes equation) in Mathematica, so that I can then seek an asymptotic expansion ...
1
vote
0answers
70 views

Solving a heat equation problem(DSolve)

I'm brand new to Mathematica. I am trying to solve a heat equation problem, but I keep getting back the input on the output line. The problem: In: ...
0
votes
1answer
90 views

Double integration of an exponential function which includes a Csch function and complex numbers

Mathematica couldn't solve following using just integrate function. I checked on interpolating as well, that also turned to be a dead end. Can someone help me with evaluating this integral? If it ...
0
votes
2answers
105 views

How to evaluate Integrate[Exp[Csch[(x - τ)]^2], {x, 0, x}]

I have been trying to integrate the following and Mathematica couldn't integrate it. Can someone help me on this? ...
0
votes
2answers
104 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 ...
0
votes
0answers
40 views

Symbolic Subset Sum Problem

I am interested in solving the following problem with Mathematica, but I do not know if it can be done or how it could be done. Given a finite set of terms $M=\{a_i(p_1, \ldots,p_m) \}_{i=1}^n$, ...
4
votes
1answer
143 views

Pattern matching expressions that have been simplified

I run into this type of issue frequently when trying to apply known identities to complicated expressions: some of my expressions will have their forms simplified by mathematica in such a way that ...
3
votes
1answer
116 views

DSolve gives the wrong solution for an inhomogeneous differential equation

I have the following inhomogeneous differential equation (sorry, I cannot come up with a simpler example) ...
1
vote
0answers
62 views

Evaluating another symbolic sum

Here I asked about a symbolic sum, and received three very insightful replies (from: მამუკა ჯიბლაძე, Carl Woll and Dr. Wolfgang Hintze) which did the trick. (Thank you again!) Currently I am trying ...
2
votes
2answers
90 views

Get independent parameters from Solve for solving diophantine equation

I need to solve some diophantine equations, in some cases, results returned by Solve the included parameters are not all independent. For example, the flowing case ...
3
votes
1answer
162 views

Inverse Laplace transform of this complicated function

I have been solving a coupled PDE system analytically and I need to find the inverse Laplace transform of $(1)$ and get $T(x,y)$. $s$ is the Laplace domain variable and $\alpha, \beta, \gamma, T_{fi}, ...
0
votes
0answers
28 views

Relating `DSolve` solution to initial data for a PDE

The Liouville equation for a free particle is the PDE $$\frac{p P^{(1,0,0)}(x,p,t)}{m}+P^{(0,0,1)}(x,p,t)=0$$ For which Mathematica gives the solution in terms of the arbitrary function $$P(x,p,t)\...
8
votes
2answers
147 views

Closed form of product of Gamma function

Mathematica recognizes this closed form \begin{align} \prod_{k=1}^{n-1}\sin(\pi k/n) &= 2^{1-n}\,n \end{align} just fine: but fails on this one despite that this expression also has a known ...
12
votes
2answers
366 views

Evaluating a symbolic sum

I have read how Mathematica does not have an easy time with symbolic sums, but nevertheless would like to know if anyone can suggest an approach to help Mathematica along. For: ...
0
votes
1answer
43 views

How can I take the divergence of a symbolic vector? [duplicate]

I would like to compute expressions that have the following form: $$\left(\partial_{p_1} - \partial_{p_2}\right)^2 \left(\partial_{p_1} - \partial_{p_2}\right)^2 \frac{(p_1-p_2)\cdot(p_3-p_4)}{p_1^...
0
votes
1answer
59 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 ...
1
vote
0answers
71 views

Defining second derivative boundary condition using DEigensystem

I tried to solve a fourth-order eigenvalue problem with boundary conditions on high order derivative. For example, the following equation, $$\frac{\partial d}{\partial t}+\frac{\partial^4 d}{\...
0
votes
0answers
35 views

Is there a feasible computation?

I have to find the values of $p_1$ and $p_2$ which minimizes the expression $G$. However, when I took the partial differentiation of $G$ with respect to $p_1$ and $p_2$, the equations I obtained were ...
0
votes
0answers
32 views

Why can Mathematica detect a linear term in a series expansion only in special cases?

The series expansion Series[Sqrt[2 - 2 Cos[d k]], {k, 0, 5}] Is in odd powers of Abs[k], or more precisely ...
0
votes
1answer
97 views

Minimize fails to find a minimum [closed]

I am trying to find, analytically, the $\theta,\phi$ that minimize the function U($\theta,\phi$) ...
15
votes
0answers
200 views

Mathematica v12 Integration bug?

Bug introduced in 12.0 After upgrading to mathematica 12, this integral gives the wrong result, also with other types of similar integrals. ...
0
votes
0answers
30 views

Exact Solution to Maximum with constraint, no output

I am new to Mathematica. I am trying to solve a maximum problem with several constraints. Here is my input. ...
2
votes
2answers
80 views

Definite Integration with Exponental Heaviside Step Funtions

As part of an equation of state calculator that I am working on, I have to handle a virial expansion for the equation of state. As such I have to solve for the virial coefficent, $B(T)$, which is ...
3
votes
3answers
67 views

Assign Values from Array to Array [duplicate]

I am trying to simply do the following cVec = {a,b,c,d} From another expression, I obtain another vector, say, ...
0
votes
1answer
54 views

How to force Mathematica to give answer in certain functional form?

I want Mathematica to evaluate $$0=\psi (x) \left(\frac{k x^2}{2}-\text{En}\right)-\frac{\hbar ^2 \psi ''(x)}{2 m}$$ and give me answer in terms of the Hermite polynomials but it gives me result in ...
5
votes
1answer
71 views

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