Questions tagged [symbolic]

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

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1 answer
70 views

Why Solve is not working? [closed]

I'm new here and I'm a newbie also with Mathematica, so probably this an easy and stupid question. If you have suggestion on how can I learn at least the basics of the language, I appreciate it. I'm ...
16 votes
2 answers
2k views

Solving quintic in radicals

I need to find an explicit expression in radicals for the real root of the quintic equation ...
0 votes
1 answer
34 views

Partial Trace with KroneckerProduct

I have some symbolic expression of the form X=KroneckerProduct[A,B]+KroneckerProduct[G,F]+... How can I define a partial trace for this, i.e. a function f: ...
0 votes
0 answers
80 views

Solve a symbolic expression

I'm working with the Hoek Brown plastic yield surface to model soil/rock materials. The yield surface is given by: Were sig1 and sig3 are the maximum and minimum principal stresses. sigc, m, s and n ...
0 votes
1 answer
71 views

Collecting coefficients of non-commutative products from an expression

I am trying to manipulate a Hamiltonian with non-commutative operators, $a_j,a_j^\dagger$. After some algebra using NCAlgebra package in Mathematica, I have an expression like, $$H = C_1 (b**a) + C_2 (...
1 vote
1 answer
35 views

Derivative of quadratic form in NCAlgebra

I installed the NCAlgebra package in the hope that it contains enough rules for symbolic work with most branch-matrix expressions. ...
0 votes
0 answers
82 views

Plotting rotational heat capacity [closed]

I am trying to plot heat capacity of a diatomic molecule using partiton function. https://en.wikipedia.org/wiki/Diatomic_molecule#Rotational_energies . The plot varible is ...
2 votes
1 answer
187 views

Noncommutative tensor product

I am using Mathematica 8. Is there any way to make a noncommutative tensor product calculation? For instance, I have the following relations : $XY=YX; \ Xt=qtX; \ Yt=qtY$. Is there any way to make a ...
0 votes
0 answers
38 views

How to analytically solve for an intersection of two functions on an interval?

I would like to analytically solve for the intersection of two functions on a given interval and store the solution as a function (of parameters) for later use. How can I tell Mathematica to look for ...
2 votes
2 answers
58 views

Collecting terms in an expression using a specific pattern

I have the following expression: ...
5 votes
2 answers
254 views

How to pose simultaneous trigonometric equations problem in a way solvable by mathematica

Context: A camera at O has an image of a rectangular object ABCD. From the 2D coordinates of the image + the projection matrix of the camera I can calculate the direction vectors $\hat {A}, \hat{B}, \...
0 votes
1 answer
72 views

Symbolic solution of first order differential equation

Is it possible to get simbolical solution of this differential equation: $$\dfrac{\mathrm{d}}{\mathrm{d}z}(x_0x_1) = -\dfrac{8}{r_i-z(r_i-1)}\dfrac{\mathrm{d} x_0}{\mathrm{d}z} $$ where if $z=1: x_0=1,...
0 votes
2 answers
77 views

Assumptions in Integration for positive real values [closed]

I want to evaluate the following integral in Mathematica. $$ \int_0^\infty \frac{a^{-t}-b^{-t}}{t} dt = \ln \left(\frac{\ln b}{\ln a} \right)$$ I try to enter this, but Mathematica can't figure it out....
1 vote
2 answers
79 views

How to find that this be always real number

I don't know how to find out this is be real number for l[y]? ...
1 vote
0 answers
50 views

Dimension of the dot product - symbolic calculation

With the following code $Assumptions = {a \[Element] Matrices[{2, 2}]}; Dimensions[{{1, 0}, {0, 0}}.a.{{1, 0}, {0, 0}}] I get as an answer ...
4 votes
3 answers
137 views

Equalities for trace with symbols

Mathematica does not seem to know basic rules for computation with trace when one uses symbols; e.g. FullSimplify[Tr[A.B] == Tr[B.A]] gives as output ...
2 votes
2 answers
172 views

Difficulty evaluating integral with Boole

I am trying to evaluate ...
5 votes
2 answers
2k views

Solving a heat equation problem

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: Consider the equation $\qquad u_t = u_{xx} - 9 u_x$, $0\...
1 vote
0 answers
221 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: ...
2 votes
2 answers
145 views

Symbolic Integration of a Specific Integral

I'm trying to compute the integral $$\int_{\delta n!/n}^{1/n}\int_{\alpha_{n-1}}^{1/n} \cdots \int_{\alpha_2}^{1/n} \frac{1}{x_2\cdots x_n}dx_2\cdots dx_n$$ where $$\alpha_k = \frac{\delta n!}{n^{n-k+...
2 votes
1 answer
70 views

How to convert an expression of several variables into an operator

Given the expression How can I define the following operator like g[u_, v_] := eq1 The correct definition is
0 votes
0 answers
57 views

FullSimplify crashes kernel

I'm trying to simplify an enormous analytic expression as much as possible. When I use Simplify, I get a half-decent result in about 20 seconds. However when I use <...
7 votes
3 answers
457 views

Zero result from a positive integral

Bug introduced in 12.2 or earlier and persisting through 13.0.1. How to calculate the following symbolic integral in MMA? Every variable is real. Although the integrand is always positive, MMA (mine ...
1 vote
1 answer
145 views

Solving equation set with vectors

I have six unit vectors in real $3$D space v1,v2,v3,v4,v5,v6; Represent the dot product between some of the vectors as the Cos ...
0 votes
1 answer
104 views

Symbolic partial differentiation of a Lagrangian function including a summation

I'm using Mathematica to double-check that I correctly derived first order conditions for the models I'm researching. Before I get started, I wanted to actually teach myself how to use Mathematica, ...
8 votes
1 answer
134 views

Order of boundary condition inside DSolve matters?

Bug introduced in 11.1.1 or earlier, fixed in 12.3.1 or earlier. Consider the following example: ...
4 votes
3 answers
674 views

How can I calculate the sum of this series?

Backslide introduced after 9.0.1, persisting through 13.0. How can I calculate the sum of this series? $\sum_{n=1}^{\infty} \ln \left(1+\frac{1}{n^{2}}\right)$ The sum of this series has been proved ...
9 votes
4 answers
409 views

Limit problem no longer works in Mathematica 11.1.0

Backslide introduced in 11.1, fixed in 11.2. In Mathematica 11.0, the following limit, Limit[Power[Sqrt[((1 - 4 n)/(3 n + 2))^(3 n)]^2, (n)^-1], n -> ∞] gave ...
7 votes
4 answers
119 views

a Sum that no longer evaluates

Backslide introduced in 7.0, fixed after 11.0, in or before 12.3. At http://forums.wolfram.com/mathgroup/archive/2000/Sep/msg00318.html and http://forums.wolfram.com/mathgroup/archive/1999/Jul/...
1 vote
2 answers
99 views

MomentOfInertia help

Radius and angle must be assigned in order to get the result. When radius and angle are variables, how to get the result? ...
1 vote
1 answer
91 views

Alternatives to NumericQ that allow symbols to be considered numeric

I am writing a program in which I am using NumericQ. I am trying to allow symbols to also be considered Numeric, so I have been using NumericQ[a]=True for all of ...
3 votes
1 answer
186 views

Calculating a surface integral

How to calculate the following surface integral using MichaelE2's DoubleContourIntegral (How can I evaluate surface integral in Mathematica?), $$\iint_{\Sigma} x^{2}...
1 vote
1 answer
126 views

Ordinary differential equation with variable (polynomial) coefficients -form of solution

If you have a differential equation with polynomial coefficients then quite remarkably Mathematica can find a solution. For example for the second order differential equation $ y''(t)+b y'(t)+\left(\...
0 votes
1 answer
72 views

Components of vector in symbol computation

I want to define a $3d$ vector $\gamma^{j}_{i}$ (here $i$ is the space node index, and $j$ is the time node index, in other words, suppose we have a time-space grid, and $\gamma$ is the vector ...
0 votes
0 answers
44 views

How to plot Piecewise function using symbols as axis

I want to make a plot of V(r) vs r with my x-axis being in units of R, and my y-axis in units of q/(4πqεR). I used discrete values of q and R to get the plot to work but I would prefer if they could ...
1 vote
2 answers
108 views

How to get the integrated result of "KT/C" of a 2nd order system

this is a noise transfer function of a RLC-2nd-order system. what I expected result is k*t/cap: the symbolic solve inlcludes many ...
1 vote
1 answer
198 views

how to define unit vectors in mathematica

I'm struggling a little bit trying to understand how to address this problem, I would like to do this in mathematica: is just that I don't know how to do the dot product between $\mathbf{J}$ and $\...
2 votes
2 answers
71 views

How to get special solution with DSolve?

I am trying to solve the following ODE with DSolve, but can't obtain a special solution (which I know exists simply by looking at the equation: f[x]=1) ...
1 vote
2 answers
47 views

need dimension of solution space of system of non-linear complex equations

I've been trying to do this in Mathematica for several days but I'm getting almost nowhere. I need to know the dimension of the solution space of each of the two systems of nonlinear complex equations ...
4 votes
2 answers
333 views

How do I get other representations of the Gamma function?

In my studymaterial I see different definitions of the Gamma function In Mathematica it is for example: ...
0 votes
0 answers
40 views

Result of expansion changes based on when I define a quantity

I have code where I evaluate a series expansion symbolically. I want to do the same thing without explicitly specifying the point before the expansion. Naively, I think this should not change my ...
1 vote
1 answer
52 views

Efficient way to simplify `E^(x (Log[a]/x + Log[b]/x))` to `a b`

I would have expected PowerExpand to simplify expressions like E^(x (Log[a]/x + Log[b]/x)) to the expected outcome ...
0 votes
1 answer
83 views

How does Mathematica take a Series expansion at Infinity?

I have a program that requires a series expansion at infinity and at a finite horizon, and I have posted two questions about simplifying these expressions or obtaining the series expansion recently. ...
0 votes
1 answer
73 views

Simplifying a symbolic matrix-inverse

I have an $8\times8$ symbolic matrix, $G$. It contains mostly real parameters but a few complex ones too. Mathematica computes (actually pretty fast) its inverse $G^{-1}$. The problem is that the ...
40 votes
4 answers
2k views

Some indefinite integrals evaluate in 11.2 but not in 11.3 - what can be done?

Bug introduced in 11.3 and fixed in 12.0.0 Reported to Wolfram: [CASE:4032137] These integrals evaluate in version 11.2 on windows but when I tried them under version 11.3 they returned unevaluated.,...
3 votes
0 answers
61 views

Can I solve a differential equation with the (ir)regular Coulomb wavefunctions?

When I evaluate DSolve[w''[ρ]] + (1 - (2 η)/ρ) w[ρ] == 0, w[ρ], ρ] Mathematica returns me a solution in terms of the Hypergeometric1F1 and HypergeometricU ...
4 votes
3 answers
254 views

Transforming implicit solutions of an ODE involving InverseFunction to an explicit form

When I DSolve a nonlinear differential equation: ...
1 vote
1 answer
67 views

How to replicate the result of symbolic limit?

I am trying to check whether the limit mentioned in the equation (3.5) of this textbook (page 14 of the PDF) does really simplify into the claimed expression. I am trying to simplify this limit in ...
0 votes
1 answer
69 views

Issue with the output of pure functions

I am getting the operator & in outputs of pure functions. e.g. with the following code ...
0 votes
2 answers
145 views

Convergence of a complete elliptic integral

How to prove that the following integral assuming $k^2 < 1$ $$\int_{0}^{1} \frac{d x}{\sqrt{1-x^2}\sqrt{1-k^2 x^2}}$$ is convergent? ...

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