Questions tagged [symbolic]
For questions about symbolic computation, as opposed to numerical computations.
1,407
questions
1
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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 ...
- 115
3
votes
1
answer
137
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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,
$$\operatorname{u}(x,y,t)=\operatorname{u}(\xi) e^{...
- 459
3
votes
1
answer
133
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Symbolic solution for steady-state heat equation i.e. Laplace equation inside cylinder
I want to symbolically solve the following boundary value problem in my textbook. It's steady-state heat conduction equation i.e. Laplace equation inside a cylinder
$$
\left\{\begin{array}{l}
\Delta u=...
- 535
4
votes
2
answers
106
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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
2
answers
288
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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:
...
- 21
0
votes
1
answer
105
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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
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1
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78
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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 ...
1
vote
1
answer
73
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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 ...
- 175
3
votes
3
answers
177
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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....
- 41
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0
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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:
...
2
votes
1
answer
80
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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 ...
- 21
0
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0
answers
28
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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 ...
- 593
3
votes
1
answer
45
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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 ...
- 1,721
2
votes
1
answer
107
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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 ...
- 1,307
1
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1
answer
31
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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 <...
- 819
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0
answers
32
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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 ...
- 1,721
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1
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80
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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 ...
- 123
0
votes
0
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87
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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 ...
- 2,760
1
vote
1
answer
57
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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
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40
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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
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2
answers
61
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0
votes
2
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80
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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)$$
I try to enter this, but Mathematica can't figure it out....
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2
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2
answers
96
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How to find that this be always real number
I don't know how to find out this is be real number for l[y]?
...
- 391
0
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1
answer
77
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Symbolic solution of first order differential equation
Is it possible to get simbolical solution of this differential equation:
$$\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,...
6
votes
2
answers
262
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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}, \...
- 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
...
- 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
...
- 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:
...
- 625
2
votes
2
answers
177
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2
votes
1
answer
74
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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
- 111
0
votes
0
answers
65
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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 <...
- 381
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 ...
- 4,124
1
vote
1
answer
148
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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 ...
- 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 ...
- 1,365
3
votes
1
answer
191
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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}...
- 1,365
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1
answer
76
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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 ...
- 3
1
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2
answers
100
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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?
...
- 1,365
0
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0
answers
44
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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
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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 ...
- 43
2
votes
2
answers
72
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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)
...
- 219
1
vote
2
answers
47
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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 ...
- 11
4
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2
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347
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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:
...
- 649
2
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2
answers
154
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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+...
- 21
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0
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40
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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 ...
- 71
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1
answer
53
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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 ...
- 1,032
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1
answer
97
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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. ...
- 71
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1
answer
83
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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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0
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63
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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
answer
67
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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 ...
- 13
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1
answer
70
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Issue with the output of pure functions
I am getting the operator & in outputs of pure functions. e.g. with the following code
...
- 1