Questions tagged [symbolic]
For questions about symbolic computation, as opposed to numerical computations.
324
questions
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0
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Spurious DSolve Solution
Bug introduced in 8.0.4 or earlier, persisting through 13.2.
DSolve quickly returns solutions to the following PDE (which is the homogeneous portion of the PDE in ...
- 61.5k
7
votes
1
answer
580
views
Symbolic calculation with generators and relations
Is it possible to do the following in Mathematica:
Define an algebra $A$ via generators and relations and multiply some tensors in $A\otimes A$ (and of course simplify the relations via the relations)...
user55170
7
votes
2
answers
2k
views
Why doesn't FullSimplify simplify expressions with DiracDelta?
I want to simplify a complicated expression with some Dirac delta distributions, but FullSimplify does not do what I want. Specifically, I want
...
- 135
7
votes
1
answer
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Derivative of real antisymmetric matrix in mathematica
Is it possible to find the derivative of components of a real antisymmetric matrix using index notation? Eg: I have a very large real antisymmetric matrix. Then from Matrix Cookbook, we know the ...
- 1,225
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votes
1
answer
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How to decompose a complex expression containing repeated subexpressions? [duplicate]
Suppose I have an expression like
...
- 7,213
4
votes
2
answers
782
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Polynomial expansion of operator
I am new to Mathematica, I am trying to generate the polynomial function of a operator. So for example, the operator $L $ is $\frac{\partial f}{\partial x}+\frac{\partial f}{\partial y} $, and I want ...
- 153
3
votes
1
answer
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views
Inverse Laplace transform of this complicated function
I have been solving a coupled PDE system analytically and I need to find the inverse Laplace transform of $(1)$ and get $T(x,y)$. $s$ is the Laplace domain variable and $\alpha, \beta, \gamma, T_{fi}, ...
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2
votes
1
answer
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DSolve gets stuck on system of differential equations with unassigned variable
Hopefully someone can help me with this problem. I'm running a fairly simple script that involves some matrix operations and ends with a fairly nasty system of differential equations:
...
28
votes
3
answers
2k
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Symbolic integration error
fixed in 10.1 (windows)
I'm running Mathematica 10.0.0 and encountered a disturbing error in the symbolic integration of a rather simple function
...
- 935
25
votes
2
answers
8k
views
Non-commutative algebra
I'm constantly dealing with non-commutative algebras. ** is inbuilt, non-commutative and associative. That's good :-) But it is not distributive. Rats.
...
- 1,043
23
votes
5
answers
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views
Why this real integral yields imaginary results?
This integral yields -1-4Iπ/3 in Mathematica:
Integrate[(y - y^2 + x - x^2 + 2*x*y)/(1 - x - y), {x,0,1}, {y, 0, 1}]
Since ...
- 685
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votes
2
answers
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How to assume all variables in my code are reals
I won't have any occasion to have any imaginary number in my code. If there are any, that is an error.
So allowing the imaginary case simply hinders the equation manipulation and simplification.
I ...
- 345
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votes
4
answers
5k
views
How to calculate the volume of a convex hull?
Given a spatial curve represented by a parametric equation, is it possible in Mathematica 9 to calculate symbolically (or at least numerically) the volume of its convex hull?
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votes
1
answer
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views
Mathematica 9 can't integrate this function but earlier versions could
Integrate[ ArcTan[x]/(1 + x) Log[(1 + x^2)/2], {x, -1, 1}]
I used Mathematica 9.0.1 on Windows7 32bit, Mathematica 9 cannot compute this, but Mathematica 8 gives ...
- 5,642
10
votes
2
answers
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views
How to simplify an expression with special functions to zero
The following is a well-known Bessel function identity:
$$J_{-n}(z)=(-1)^n J_n(z),\qquad n\in\mathbb Z$$
To check this, I used the following code and the result is as what I expected.
...
- 103
9
votes
1
answer
1k
views
Define an operator with the distributive property
I would like to define the ⊕ operator with distributive, associative, and commutative properties - so that Mathematica can symbolically simplify expressions I use ...
- 111
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votes
1
answer
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How to Make a change of variables
I have the following expresion
$$\hat{M}^2=-\left[\frac{1}{\sin\beta}\frac{\partial}{\partial\beta}\sin\beta\frac{\partial}{\partial\beta}+\frac{1}{sin^2\beta}\left(\frac{\partial^2}{\partial\alpha^2}...
- 139
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1
answer
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How to assign up-values for `Derivative`?
I have defined several custom analytic functions. Here is the simplest example:
ln[x_, a_?NumericQ] := Piecewise[{{Log[x], Re[a] > 0}, {-Log[1/x], True}}]
...
- 19.7k
7
votes
4
answers
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views
Transform Piecewise[] into sum of indicators
I'm interested in transforming a piecewise defined function into a sum of indicator functions, ultimately with the aim to be better able to integrate them.
As an example I would like to transform the ...
- 83
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votes
1
answer
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views
Problems with DSolve and NDSolve for Dirichlet problem on an annulus
To solve the Dirichlet problem on an annulus, I do the following in 12.2 on Windows 10 Pro
...
- 26.4k
6
votes
1
answer
1k
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Does the Im function work with symbolic arguments?
Does the Im function work with symbolic arguments?
...
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votes
1
answer
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Definite and Indefinite integral give different results for piecewise function
I have the following function:
$$
f(q,y)=
\begin{cases}
\tfrac{11720+p}{37791360} & -11720<p<-7720 \\
0 & \text{True}
\end{cases}
$$
where $p = 443\ y-777600\ \sin^{-1}\left(\frac{q \...
- 435
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votes
1
answer
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views
Symbolic integration in the complex plane
Context
While answering this question, I defined (symbolic and numerical) path integrations as follows
...
- 22.9k
2
votes
2
answers
618
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Symbolic linear algebra gradients/matrix calculus
Can Mathematica generate symbolic expressions for gradients?
For example, if $x_1$ and $x_2$ are two points, could I get Mathematica to generate expressions similar to the following?
$\frac{\partial ...
- 123
2
votes
0
answers
144
views
Implementing the symbolic identity matrix $I$
I am working with symbolic tensors within Mathematica and I wanted to ask if there is a way to have a symbolic identity tensor.
2
votes
2
answers
2k
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Dropping Higher Order Terms in symbolic evaluation
I have a series of symbolic manipulations (along with some coefficients).
As a sample, here is one of the intermediate forms
...
- 1,867
25
votes
3
answers
604
views
Backslide of Limit
Backslide introduced in 9.0, and persisting through 12.0.
A friend of mine showed me this example:
Limit[Sum[Sin[Pi*k/n]/(n + 1/k), {k, 1, n}], n -> Infinity]
...
- 66.2k
20
votes
1
answer
1k
views
Incorrect result from Integrate
Bug introduced in 8.0 and fixed in 10.0
I attempted to calculate the following integral:
...
- 11.9k
20
votes
1
answer
607
views
What does "suitable for symbolic manipulation" in the documentation mean?
This question is related to this other one I posted on Stack Overflow some time ago. There, in a beautiful answer, acl (with some unhumble editing done by me) showed that the derivative of ...
- 116k
18
votes
1
answer
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How to represent a continuous monotonic phase of Airy functions?
Note: In this question I am concerned only with real-valued variables and functions.
DLMF, §9.8 Airy Functions, Modulus and Phase, formula $9.8.4$ defines the phase of Airy functions:
$$\theta(x)=\...
- 7,213
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votes
2
answers
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Why do certain values in ArcSin not fully evaluate?
This is a continuation of: Why do certain fractional values in TriangleWave not evaluate?
The analysis by R.M and rasher revealed that problem to reduce to the behavior of:
...
- 272k
17
votes
2
answers
2k
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Solving quintic in radicals
I need to find an explicit expression in radicals for the real root of the quintic equation
...
- 7,213
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votes
3
answers
1k
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Does anyone have experience with performing symbolic regression using Mathematica?
I understand that there is at least one Mathematica package, DataModeler commercially available for symbolic regression. I'm seeking any observations with this or any other similar tool.
I'm ...
- 1,407
15
votes
1
answer
542
views
Why does Mathematica think this series doesn't converge?
Bug introduced in 10.0 and fixed in 11.1
(reported as CASE:3790525)
Here's a simple series:
Sum[t^k DiscreteDelta[k]/k!,{k,0,Infinity}]
Mathematica says that ...
- 7,152
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votes
5
answers
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Does $x>0$ imply that $x\in\mathbb{R}$?
Let’s assume I input
Assuming[x > 0, expression]
Is it assumed by Mathematica that $x$ is a real number? Or that the real part of $x$ is positive? Something ...
- 1,585
13
votes
1
answer
324
views
1 is not the SameQ as Null, but why might 1 be Equal to Null?
The command
SameQ[1, Null]
returns
False
which is what I would expect, but the command
...
- 1,415
13
votes
1
answer
407
views
Symbolic computations with already assigned variables
For example I have assigned some variables that could defined in terms of each other. Then I for some reason need to derive some formula using this variables. How to show the result of this ...
- 7,881
12
votes
2
answers
791
views
Surprises simplifying simple polynomials
I came across some somewhat surprising behavior of Simplify today, on something very simple. Let's take two cubic polynomials that we know have the same value:
<...
- 18.5k
11
votes
1
answer
1k
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Expanding derivatives of hypergeometric functions
Sometimes Mathematica expresses results of integration or summation in terms of symbolic derivatives of Hypergeometric2F1 function, and cannot further simplify ...
- 7,213
10
votes
3
answers
556
views
Use both values of $\pm$ in equations
Is there an elegant way to use $\pm$ in equations, without having to make a text change and substitution using an Or function?
For instance, I would like this ...
- 41.2k
9
votes
3
answers
2k
views
Mathematica gives wrong answer for an integral
Bug introduced in 9.0 or earlier, persisting through 13.2 or later
When I execute the following,
Integrate[ Exp[-w^2 + I w^3], {w, -∞, ∞}]
I get
...
PJR
9
votes
2
answers
998
views
How to symbolically differentiate an infinite series without evaluating the series itself
I'm dealing with finite sums of infinite series. Each of the infinite series possesses a different starting index, i.e. each of the series begins at n = 0, n = 1, or n = 2. As a result, it's important ...
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9
votes
3
answers
418
views
DSolve—different solutions for same set of equations using different symbols?
I happen to find that DSolve can give different solutions, even a different number of solutions, for a set of differential equations just by making a change in the ...
- 1,229
9
votes
3
answers
3k
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RowReduce for symbolic matrices
I'd like to invoke RowReduce on some matrices with a time parameter.
For example consider
A = {{1, 0}, {0, t}}
If ...
- 91
8
votes
1
answer
409
views
Obtaining both Solutions of Linear, Second-Order ODE using DSolve
Bug introduced in 10.4 or earlier and persisting through 11.3
Reported as CASE:3849226.
While attempting to provide a general answer for question 138321, I obtained a result,
...
- 61.5k
8
votes
3
answers
1k
views
Symbolic integration in real domain only ( assumptions and ComplexExpand don't work)
Integrate[m^2/((x - m^2)^2 + y^2), m]
mathematica gives me a complex-valued reuslt, but maple 17 gives me what I want.
I tried using assumptions, but it doesn't ...
- 1,323
8
votes
2
answers
360
views
Two-dimensional Laplacian coupled with another equation leading to a BVP with integral bc(s)
I have the two-dimensional Laplacian $(\nabla^2 T(x,y)=0)$ coupled with another equation. The Laplacian is defined over $x\in[0,L], y\in[0,l]$. On manipulating the second equation (which I have ...
- 297
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votes
1
answer
811
views
Simplification of double symbolic sums containing a DiscreteDelta without explicit summation range
I am trying to get Mathematica to automatically do simplifications like the following:
$$\sum\limits_{q}^{q\in qV}\sum\limits_{q'}^{q'\in q'V}{f(q)g(q')\delta(q-q')}=\sum_{q}^{q\in qV}{f(q)g(q)}.$$
...
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8
votes
2
answers
255
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Finding sub-expressions that simplify larger formula
If I use FullSimplify on a large formula it will consequently return a much smaller expression. However, suppose I notice the simplified expression can benefit from ...
- 2,675
7
votes
2
answers
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Evaluating a surface integral
I'm trying to compute the integral $$\int_S x^2+z^2\,{\rm d}S,$$where $S$ is the surface $$S\colon~
\frac{x^2}{2} + \frac{y^2}{3} + \frac{z^2}{2} = 1, \quad y \geq 0.$$
One possible parametrization ...
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