Questions tagged [symbolic]

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

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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
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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 ...
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1 vote
1 answer
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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 <...
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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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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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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
48 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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  • 1,626
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39 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
58 views

Collecting terms in an expression using a specific pattern

I have the following expression: ...
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  • 335
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....
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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]? ...
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1 answer
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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,...
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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}, \...
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1 vote
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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 ...
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  • 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 ...
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  • 625
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1 answer
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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
174 views

Difficulty evaluating integral with Boole

I am trying to evaluate ...
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  • 131
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
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0 answers
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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 <...
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7 votes
3 answers
464 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
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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 ...
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  • 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 ...
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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}...
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0 votes
1 answer
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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 ...
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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? ...
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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
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 ...
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  • 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) ...
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  • 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 ...
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  • 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: ...
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  • 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+...
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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
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 ...
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0 votes
1 answer
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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. ...
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0 votes
1 answer
74 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
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 ...
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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
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 ...
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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: ...
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  • 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? ...
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  • 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 ...
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  • 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). ...
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  • 847
2 votes
1 answer
205 views

Solving equations with symbolic variables

I have the equations ...
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  • 207
1 vote
0 answers
73 views

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)...
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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 <...
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  • 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 ...
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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 ...
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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... };
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2 votes
1 answer
35 views

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 ...
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  • 21
1 vote
0 answers
64 views

“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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