Questions tagged [symbolic]
For questions about symbolic computation, as opposed to numerical computations.
1,397
questions
2
votes
1
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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 ...
- 21
0
votes
0
answers
27
views
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
38
views
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 ...
- 1,636
2
votes
1
answer
103
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 <...
- 819
0
votes
0
answers
30
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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 ...
- 1,636
0
votes
1
answer
74
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 ...
- 111
0
votes
0
answers
83
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 ...
- 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.
...
- 1,636
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 ...
- 77
2
votes
2
answers
58
views
0
votes
2
answers
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....
- 1
1
vote
2
answers
80
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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
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,...
5
votes
2
answers
256
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}, \...
- 103
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
...
- 625
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
...
- 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
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
- 111
0
votes
0
answers
58
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 <...
- 381
7
votes
3
answers
466
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 ...
- 4,006
1
vote
1
answer
146
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 ...
- 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
views
Calculating a surface integral
How to calculate the following surface integral using MichaelE2's DoubleContourIntegral (How can I evaluate surface integral in Mathematica?),
$$\iint_{\Sigma} x^{2}...
- 1,365
0
votes
1
answer
72
views
Components of vector in symbol computation
I want to define a $3d$ vector $\gamma^{j}_{i}$ (here $i$ is the space node index, and $j$ is the time node index, in other words, suppose we have a time-space grid, and $\gamma$ is the vector ...
- 3
1
vote
2
answers
99
views
MomentOfInertia help
Radius and angle must be assigned in order to get the result. When radius and angle are variables, how to get the result?
...
- 1,365
0
votes
0
answers
44
views
How to plot Piecewise function using symbols as axis
I want to make a plot of V(r) vs r with my x-axis being in units of R, and my y-axis in units of q/(4πqεR). I used discrete values of q and R to get the plot to work but I would prefer if they could ...
- 1
1
vote
2
answers
108
views
How to get the integrated result of "KT/C" of a 2nd order system
this is a noise transfer function of a RLC-2nd-order system.
what I expected result is k*t/cap:
the symbolic solve inlcludes many ...
- 43
2
votes
2
answers
72
views
How to get special solution with DSolve?
I am trying to solve the following ODE with DSolve, but can't obtain a special solution (which I know exists simply by looking at the equation: f[x]=1)
...
- 219
1
vote
2
answers
47
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need dimension of solution space of system of non-linear complex equations
I've been trying to do this in Mathematica for several days but I'm getting almost nowhere. I need to know the dimension of the solution space of each of the two systems of nonlinear complex equations ...
- 11
4
votes
2
answers
336
views
How do I get other representations of the Gamma function?
In my studymaterial I see different definitions of the Gamma function
In Mathematica it is for example:
...
- 649
2
votes
2
answers
146
views
Symbolic Integration of a Specific Integral
I'm trying to compute the integral $$\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+...
- 21
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 ...
- 71
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 ...
- 1,032
0
votes
1
answer
87
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. ...
- 71
0
votes
1
answer
77
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 ...
- 169
3
votes
0
answers
62
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 ...
- 31
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 ...
- 13
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
...
- 1
4
votes
3
answers
256
views
Transforming implicit solutions of an ODE involving InverseFunction to an explicit form
When I DSolve a nonlinear differential equation:
...
- 97
0
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
views
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
275
views
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
206
views
1
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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
views
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
5
votes
2
answers
142
views
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 ...
- 969
0
votes
1
answer
35
views
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
1
vote
1
answer
44
views
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...
};
