Questions tagged [symbolic]
For questions about symbolic computation, as opposed to numerical computations.
1,396
questions
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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 ...
- 1,626
2
votes
1
answer
99
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 ...
- 1,287
1
vote
1
answer
29
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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 <...
- 807
0
votes
0
answers
29
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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 ...
- 1,626
0
votes
1
answer
73
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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 ...
- 111
0
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0
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82
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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
48
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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.
...
- 1,626
0
votes
0
answers
39
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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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58
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0
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2
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77
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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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1
vote
2
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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]?
...
- 381
0
votes
1
answer
72
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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,...
5
votes
2
answers
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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}, \...
- 103
1
vote
0
answers
50
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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
137
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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
35
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
174
views
2
votes
1
answer
71
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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
58
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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
7
votes
3
answers
464
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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 ...
- 4,006
1
vote
1
answer
146
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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 ...
- 270
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 ...
- 1,365
3
votes
1
answer
187
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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
0
votes
1
answer
72
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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
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vote
2
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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 ...
- 1
1
vote
2
answers
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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
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)
...
- 219
1
vote
2
answers
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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
votes
2
answers
336
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:
...
- 649
2
votes
2
answers
146
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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
answers
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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
1
vote
1
answer
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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
0
votes
1
answer
85
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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
0
votes
1
answer
74
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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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votes
0
answers
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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 ...
- 31
1
vote
1
answer
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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 ...
- 13
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1
answer
69
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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
...
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4
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3
answers
256
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Transforming implicit solutions of an ODE involving InverseFunction to an explicit form
When I DSolve a nonlinear differential equation:
...
- 97
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votes
2
answers
147
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?
...
- 1,365
0
votes
2
answers
82
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A problem when solving an equation with symbolic variables
I asked a question a couple days ago and received a solution that worked for me at the time. But now I am seeing that the proposed solution fails for some other cases I need.
For example, if I just ...
- 207
15
votes
1
answer
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Integration Bug?
Bug introduced in 8 and persisting through 13.0
Mathematica 11.2.0.0 Home edition on MacBook Pro OS X 10.10.5 (Yosemite).
...
- 847
2
votes
1
answer
205
views
1
vote
0
answers
73
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Selecting specific solutions from a differential equation using DSolve with difficult boundary conditions
Let's suppose I want to solve Laplace's equation in Axial Symmetry:
$$
\nabla^2\psi=\partial^2_{\rho}\psi+\partial^2_{z}\psi+\frac{1}{\rho}\partial_{\rho}\psi=0,
$$
for some function $\psi=\psi(\rho,z)...
0
votes
1
answer
52
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rewriting the solutions of symbolic 3rd and 4th order polynomials
I have symbolic third and fourth-order polynomials which read.
$F_{3}= x^3+p x +q,$
$F_{4}= x^4+p_{0} x^2 +q_{0} x + r_{0}.$
Using the Mathematica, I can find the roots of these polynomials using
<...
- 295
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votes
2
answers
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How to guide Eliminate or GroebnerBasis to reduce a set of simple odes to a single ode (which can be done by Laplace Transform)
Recently, I am trying to use Eliminate or GroebnerBasis to simplify a system of ODEs. I don't want the solution of ODEs. What I ...
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1
answer
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Spotting and condensing expressions in output
I am running some symbolic scripts to generate a model problem. One of my outputs is
This is generated by the Mathematica code
or, in Mathematica format (owing to the fancy lettering and formatting ...
- 155
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1
answer
44
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How can I use ComplexExpand and PowerExpand for Log of complex symbols?
How can I simplify Log[ x + I y] or Log[ r Exp[ I phi]
into Log[r] + I Log[ phi]
where r = Abs[x + I y] and Phi = Arg[x + I y]
using ComplexExpand, PowerExpand, etc...
};
2
votes
1
answer
35
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CoefficientRules numericizing parameters
I ran into a problem with CoefficientRules behaving differently with exact and numerical coefficients, where in the numerical case it behaves as if the entire ...
- 21
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vote
0
answers
64
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“Largest” symbolic common factor of an integer sequence (not simply GCD)
Suppose, I have a finite fragment of a quickly increasing sequence of integers $\{a_n\}$ that is too complex, unusual, or irregular for FindSequenceFunction to find ...
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