Questions tagged [symbolic]
For questions about symbolic computation, as opposed to numerical computations.
229
questions with no upvoted or accepted answers
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How to speed up calculations on big symbolic matrices?
this is my first time posting something on a community of the StackExchange platform, so please feel free to correct me if I'm doing something wrong. :) Additionally you should probably know that I'm ...
- 121
11
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0
answers
346
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Improving the performance of a package for working with rational functions
As Mathematica gets slow for large symbolic calculations, the cost of putting terms over a common denominator (Together), in particular, gets too high. It occurred ...
- 661
10
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0
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317
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Possible Symbolic Integration Bug
Bug introduced between 5 and 8 and persisting through 12.0.
I think I may have found a bug, and want to verify is this reproducible in other versions and platforms and not a mistake of mine.
I ...
- 111
9
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0
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179
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Symbolically evaluating gradients/Hessians
I'm taking a machine learning course, which involves taking a lot of analytical gradients and Hessians. It would be ideal if I could perform these calculations in Mathematica. However, I am only aware ...
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9
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849
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Symbolic Weak Form
Usually I write the weak form by hand for my FEM code, but it's a little annoying and mechanic sometimes.
So, I wonder, is there any way to generate the symbolic weak form in Mathematica? For ...
- 515
8
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0
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276
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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 ...
- 60.7k
7
votes
0
answers
401
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Integrating rational functions of several variables over $\mathbb{H}^4$
Let $W$ be a rational function of $8$ variables $a,b,c,d,e,f,g,h$ from this file, e.g.:
...
- 171
7
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3k
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Solve huge symbolic system of linear equations
I have a system of 76 symbolic linear equations (i.e. some coefficients are symbolic) with a sparse coefficient matrix. However, neither Solve[] nor ...
6
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0
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211
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Can I use Mathematica ML capability to translate an image of a formula?
If I am given a pdf image of a mathematical symbolic formula can I translate it into Mathematica syntax using ML?
I tried using Classify, but I can only translate parts of the equation and I don't ...
- 517
6
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226
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DSolve Returns Incorrect Solutions for First-Order ODE
Bug introduced in 10.4 or earlier and persisting through 11.3. Reported to Wolfram Technical Support as CASE:4150361.
Fifty-one DSolve questions on this site are ...
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6
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1k
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Is it possible to simplify an expression in vector form, which involves crossproduct and dot product?
I often need to simplify expressions involving cross product and dot product, for example:
f = Dot[Cross[Cross[p1 - p, e1], Cross[p2 - p, e2]], Cross[p3 - p, e3]]
...
- 695
6
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168
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Operator which can be interpreted as binary and unary
I'm a bit lost with the way how e.g. the + operator is implemented in Mathematica as binary (infix) and unary (prefix) operator depending on the context, since I would like to define a similiar ...
- 2,861
5
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134
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How to highlight internal symmetries while simplifying a symbolic expression?
Context
I would like to have a function which symmetrizes and simplifies a symbolic expression to highlight its internal symmetries.
I believe such a function would be extremely useful for post ...
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5
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79
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How to get an asymptotic of the real-valued branch of the inverse function?
Consider function $f:\mathbb R^+\to\mathbb R^+$, defined as $f(x) = x + x^2\left(1 + \log x\right)$. I need to find an asymptotic approximation of its inverse function $f^{\small(-1)}\!:\mathbb R^+\to\...
- 7,163
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133
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Can I extract symbolic expression of neural network loss function?
Once we create a neural network with NetChain in Mathematica, can we extract the loss function in the symbolic form for Mathematica to play with symbolic manipulations using Mathematica's built-in ...
- 1,229
5
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238
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Integrating a product of three Spherical Harmonics
The following command is returned unevaluated. The answer is well known to be related to Wigner's 3j Symbol which is also a defined function in Mathematica.
...
- 1,648
5
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115
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TensorContract applied twice
I have a very simple question about TensorContract command:
I'm declaring
...
- 909
5
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296
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Interval Arithmetic with Symbolic Intervals
I've run into a problem with IntervalUnion and IntervalIntersection when dealing with symbolic intervals.
The following code ...
- 2,256
5
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0
answers
1k
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Symbolic matrix calculus: What's new in Version 9
I have seen some of the related posts, which ask about doing matrix calculation on tensors unknown dimensions. One of the posts mentioned that version 9 has some capability, but it was concerned about ...
- 151
4
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0
answers
163
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Differentiating with D vs. Derivative
I was tinkering with something and needed a high-order derivative of a function that, when differentiated, needs the product rule (and so, subsequent derivatives - without simplification - become ...
- 2,681
4
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0
answers
44
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How does Simplify deal with contradictions in the assumptions?
Context
Sometimes Simplify does generate a warning when the assumptions are self-contradictory.
Take this example:
...
4
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0
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129
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Evaluate $\int_0^1 \frac{\log \left( 1+x^{2+\sqrt{3}}\right)}{1+x}\mathrm dx$
Saw this post and noted that it was posted back in 2013. Just tried V11.3 and got no analytic solution.
Just wondering if there is a way for Mathematica to give the desired result?
Machine VS Human
...
- 1,550
4
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0
answers
184
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How to find an exact solution to this ODE?
I am trying to find an exact solution to this differential equation,
ode = f'''[x] + f[x]*f''[x] - f'[x]^2 == 0
For which, I already know the exact solution ...
- 41
4
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227
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What real symmetric matrices of this type can Mathematica find symbolic eigenvalues for?
I'm working on a problem calculating symbolic eigenvalues of matrices that always have a very simple form: they are real and symmetric and usually sparse. They have two distinct symbolic parameters. (...
- 361
4
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227
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Symbolic second variation (quadratic form matrix)
Mathematica has a calculus of variations package that can compute the first variational derivative symbolically, rather nicely.
Does anyone know if there is a way to compute the quadratic form matrix ...
- 235
4
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0
answers
96
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Create an adequate 'training set' to train a ClassifierFunction which performs the role of the built-in `SubsetQ`
I am trying to "grow" my own SubsetQ function using Machine Learning methods. My cSubsetQ when given two lists (listA and listB)...
- 7,349
4
votes
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answers
319
views
Symbolically Minimizing a Max function
I'm having a tough time with seemingly simple symbolic Minimization/Maximization in Mathematica. I would like to use the Maximize function to work on some unknown random variables and so use min/max ...
- 41
4
votes
0
answers
87
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Derive logistic choice probabilities symbolically
More generally, I am interested in learning what the current limitations of Mathematica are when using it for doing pure mathematics. A recent blog post by Stephen Wolfram (see: http://blog....
- 735
4
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136
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Does it help to do any preprocessing before `FindSequenceFunction`?
I am always amazed how smart FindSequenceFunction can be in discovering general term formula for a sequence of rational numbers. The documentation says it can work ...
- 7,163
4
votes
0
answers
1k
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Analytically solve the eigenvalue problem with infinite dimensions by Mathematica?
If I am given a symbolic expression of all the matrix elements in an infinite-dimensional space, e.g., the Hamiltonian of a quantum mechanical system, is it possible to get the symbolic expression for ...
- 41
4
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121
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Using Resolve and ForAll to prove takes a really long time
I've been trying to prove a lemma for my paper using Mathematica... basically that
$$\forall \{n, d_i, d_j\} \in \mathbb{Z},\ n \ge d_i > d_j \ge 2$$
it's true that
$$V[1, n, d_i-1, d_j-1] >...
- 183
3
votes
0
answers
123
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How to find a power series expansion of a function obeying a certain PDE?
Let us suppose that I have some differential operator $D_{x,y}$ acting on functions of two variables $(x,y)$. I want to solve one eigenvalue equation
$$D_{x,y}f_{ij}(x,y)=\lambda_{i,j} f_{ij}(x,y).$$
...
- 481
3
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0
answers
38
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Why is TensorContract[x, {}] not always x?
If I use TensorTranspose on an undefined symbol, nothing happens unless the permutation is the identity. For instance, ...
- 228
3
votes
0
answers
79
views
Can I solve a differential equation with the (ir)regular Coulomb wavefunctions?
When I evaluate
DSolve[w''[ρ]] + (1 - (2 η)/ρ) w[ρ] == 0, w[ρ], ρ]
Mathematica returns me a solution in terms of the Hypergeometric1F1 and HypergeometricU ...
- 31
3
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0
answers
115
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2D Poisson equation with Piecewise RHS - symbolic solution?
I'm trying to solve the following 2D Poisson equation symbolically:
$$
-\nabla^2 u(x,y) =
\begin{cases}
1-\text{sech}\left(\frac{w}{2 d}\right) \cosh \left(\frac{x}{d}\right)
& -w/2 \leq ...
- 4,325
3
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135
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How can I simplify a symbolic tensor expression?
My question is about simplifying tensor expressions. If I have
$(a+b)\otimes (c+d)$
The function TensorExpand gives
$a\otimes c + a\otimes d + b\otimes c + b\otimes ...
- 153
3
votes
0
answers
152
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Convolution using the Laplace integral transform of certain functions
I am trying to convolve two functions:
$f(t) = e^{- t}$
$g(t) = e^{-(e^{-t})^2}$
$(f*g)(t) = \int_{0}^{t} f(t-\tau)g(\tau) d\tau = \int_{0}^{t} e^{-(t-\tau)} e^{-(e^{-\tau})^2} d\tau$
Using the ...
- 2,374
3
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164
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Computations with OptimizedExpressions without completely expanding them
I have to manipulate huge expressions that are rational functions of many (∼30) variables with integer coefficients. Storing them just as a ratio of two polynomials would be impractical. But they can ...
- 7,163
3
votes
0
answers
72
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Problem solving first order ODE's with DSolve
The issue I am facing is the following. I am trying to solve a system of two coupled first order ODE's with DSolve:
...
- 1,329
3
votes
0
answers
136
views
3
votes
0
answers
337
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How to detect discontinuous point in a symbolic function?
Mathematica Plot function can detect exclusion points automatically. How was that realized? How can I generalize that to included discontinuity of ...
- 2,257
3
votes
0
answers
199
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SymbolicC/SymbolicCUDAFunction generating C/C++ parser?
I wish to do some program transformation and analysis.
Is there any package that generates SymbolicC expressions from C code?
In a sense I'm looking for the ...
- 5,689
3
votes
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77
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Unexpected imaginary term in the asymptotic expansion of DawsonF
FullSimplify[Series[2 DawsonF[x], {x, ∞, 8}]]
(* -I Exp[-x^2] √π + (1/x + 1/(2 x^3) + 3/(4 x^5) + 15/(8 x^7) + O[1/x]^9) *)
What is the reason the term ...
- 7,163
3
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450
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Polynomial kernel expansion
I am trying to calculate the polynomial kernel expansion using Mathematica. I have tried the Expand and Simplify functions with ...
- 131
3
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0
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182
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Simplifying between set theory and logical connectives
I'm trying to find out how to switch between set notation and logic, but am having difficulty. For instance, I know that the following two expressions are equivalent
...
- 31
3
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0
answers
245
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Fourier transformation of HeavisideTheta functions
I want to find 2D-Fourier transformation of the function given below
f = HeavisideTheta[y1]*HeavisideTheta[y2 - y1]
For the purpose, I use built-in function in ...
- 429
3
votes
0
answers
126
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What is so special about variable s$?
I found a nice bug in Mathematica 9.0.1.0. Could anyone check to reproduce it?
Create a file temp.txt with one line:
...
- 39
3
votes
0
answers
400
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Do a gauge transformation for a Chern-Simons theory?
Suppose we have the following Lagrangian density:
$$
L=\epsilon^{\mu\nu\rho}\big(\sum_a A^a_{\mu}(x) \partial_\nu A^a_{\rho}(x)-\sum_{a,b,c}\frac{1}{3} f^{bca} A^a_{\mu}(x) A^b_{\nu}(x) A^c_{\rho}(x)...
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113
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How to combine DifferenceRoot objects for odd and even-indexed terms
I'm trying to analyze a certain infinite sequence $S$, indexed by positive integers starting from $1$. It can be split into two subsequences:
$S^{odd}$ by removing all even-indexed elements and ...
- 7,163
3
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100
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