Questions tagged [symbolic]

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

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A piecewise inequality not simplified to True

In = Simplify[-a + Piecewise[{{-b, t > c}}] < 0, {a > 0, b > 0, c > 0}] Out = Piecewise[{{-b, t > c}}] < a Why the result is not evaluated to ...
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How to achieve the transformation using DSolveChangeVariables introduced in Mathematica 13.1?

I have a PDE (1D Schrödinger equation) as follows: $$iu_t-\frac12 u_{xx}-\left(|u|^2-A\right)u=0$$ Applying the following transformations to the PDE, $$\operatorname{u}(x,y,t)=\operatorname{u}(\xi) e^{...
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1 answer
133 views

Symbolic solution for steady-state heat equation i.e. Laplace equation inside cylinder

I want to symbolically solve the following boundary value problem in my textbook. It's steady-state heat conduction equation i.e. Laplace equation inside a cylinder $$ \left\{\begin{array}{l} \Delta u=...
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4 votes
2 answers
106 views

ComplexExpand no longer assumes Derivative[__][__][__] as real

Bug introduced after 11.3, in or before 12.3, persisting through 13.0. Consider the following sample: {Re, Im}[u'[t]] // Through // ComplexExpand In v9.0.1 ...
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2 votes
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288 views

How do I implement convolution integrals symbolically (not numerically)? [closed]

I'm working to symbolically solve convolution integrals i.e., using symbolic equations and not numerical methods of integration. The general form of the convolution I'm working to solve is as follows: ...
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1 answer
105 views

Small question about the output form of the derivative

I have an expression: D[D[Subscript[T, 1][x[t], y[t], x'[t]] + Subscript[T, 2][x[t], y[t], y'[t]], x'[t]], t] The result is: $y'(t) T_1{}^{(0,1,1)}\left(x(t),y(t),...
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2 votes
1 answer
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Loop over multiple variables with readable code

I've seen similar posts to this, but not with as many variables. I need to loop over 8 variables, with only two values each(1 and 2), so I can loop over the 16 possible input and output states, and ...
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1 vote
1 answer
73 views

RSolve with integer and boolean variable

I have a recurrence relation with two variables $i, b$ where $i \in \{0, \ldots, n-1\}$ for some parameter $n \in \mathbb{N}$; and $b\in \{0,1\}$. I tried to solve it using RSolve, but the function ...
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3 votes
3 answers
177 views

Equating coefficients of two expressions

I have two symbolic Expressions and the both contain the same functions, as follows: $$ 3.12592+5.96272 \cos (2 \theta )+5.15739 \cos (4 \theta )+4.00413 \cos (6 \theta )+2.72961 \cos (8 \theta )+2....
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Scaling a variable multiplied by power series is not giving expected output

I have a power series getting multiplied by a variable, which gets scaled by the small parameter used in the power series. As an example, in the following dummy series: ...
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2 votes
1 answer
80 views

Can't simplify expression with square roots of square roots

I'm very new to Mathematica, and I've been using it to evaluate some symbolic expressions in my research that are too complicated to do by hand. However, some of them don't simplify when it is obvious ...
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Notation package problem [duplicate]

I am using Mathematica 12.3.1 on Windows 10. I am trying to load the Notation package: Needs["Notation`"] and I get the following: It seems the package ...
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3 votes
1 answer
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Terms of expressions with non-commutative multiplication that meet the given criteria

There is the following expression: expr=a^3**x**Transpose[x]**y+x+y**Transpose[y]**x**a^3+x**Transpose[y] It is necessary to apply the ...
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2 votes
1 answer
107 views

Introduce formal symbols indexed by natural numbers

I'm going to describe a toy example here which I'm hoping with some help, I can then soup up into the more complex application I have in mind. Suppose the input is a list of lists, and for now take ...
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1 vote
1 answer
31 views

Getting the same result from Integrate as Probability

I'm trying to solve a Baysian inference problem (although the details are not all that important for this question) I define two probability distributions P and <...
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0 answers
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Noncommutative multiply - expand expression - And then assembly back without `NCAlgebra`

The topic Noncommutative multiply- expand expression discussed how to expand parentheses in an expression using the Distribute command and using non-commutative ...
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1 answer
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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 ...
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0 answers
87 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 ...
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1 vote
1 answer
57 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. ...
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0 votes
0 answers
40 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 ...
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2 votes
2 answers
61 views

Collecting terms in an expression using a specific pattern

I have the following expression: ...
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  • 357
0 votes
2 answers
80 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....
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2 votes
2 answers
96 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]? ...
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0 votes
1 answer
77 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,...
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6 votes
2 answers
262 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}, \...
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  • 113
1 vote
0 answers
51 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 ...
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  • 625
4 votes
3 answers
138 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 ...
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  • 625
0 votes
1 answer
37 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: ...
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  • 625
2 votes
2 answers
177 views

Difficulty evaluating integral with Boole

I am trying to evaluate ...
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  • 131
2 votes
1 answer
74 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
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0 votes
0 answers
65 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 <...
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8 votes
3 answers
479 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 ...
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1 vote
1 answer
148 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 ...
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  • 268
4 votes
3 answers
680 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 ...
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  • 1,365
3 votes
1 answer
191 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}...
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0 votes
1 answer
76 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 ...
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1 vote
2 answers
100 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? ...
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  • 1,365
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 ...
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1 vote
2 answers
109 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 ...
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  • 43
2 votes
2 answers
72 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) ...
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  • 219
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 ...
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4 votes
2 answers
347 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: ...
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2 votes
2 answers
154 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+...
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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 ...
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1 vote
1 answer
53 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 ...
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  • 1,032
0 votes
1 answer
97 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. ...
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0 votes
1 answer
83 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 ...
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3 votes
0 answers
63 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 ...
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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 ...
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  • 13
0 votes
1 answer
70 views

Issue with the output of pure functions

I am getting the operator & in outputs of pure functions. e.g. with the following code ...
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