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Questions tagged [symbolic]

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

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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 ...
TSwift's user avatar
  • 121
11 votes
0 answers
350 views

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 ...
Eduardo Serna's user avatar
10 votes
0 answers
320 views

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 ...
yyli's user avatar
  • 111
9 votes
0 answers
186 views

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 ...
user48151's user avatar
9 votes
0 answers
945 views

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 ...
senseiwa's user avatar
  • 515
8 votes
0 answers
277 views

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 ...
bbgodfrey's user avatar
  • 61.8k
7 votes
0 answers
404 views

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.: ...
Ricardo Buring's user avatar
7 votes
0 answers
3k views

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 ...
Stanislav Poslavsky's user avatar
6 votes
0 answers
239 views

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 ...
Gluoncito's user avatar
  • 517
6 votes
0 answers
227 views

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 ...
bbgodfrey's user avatar
  • 61.8k
6 votes
0 answers
1k views

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]] ...
larry's user avatar
  • 735
6 votes
0 answers
170 views

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 ...
Rainer's user avatar
  • 2,931
5 votes
0 answers
135 views

How to write down and check the Karush-Kuhn-Tucker conditions?

This is a simple touchstone for a serious matter. I try to solve with Mathematica 13.3.1 on Windows 10 problem 1278 from "The Kvant". Let real numbers $x_1,x_2,\dots,x_n$ satisfy the ...
user64494's user avatar
  • 27.3k
5 votes
0 answers
83 views

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\...
Vladimir Reshetnikov's user avatar
5 votes
0 answers
141 views

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 ...
dbm's user avatar
  • 1,249
5 votes
0 answers
251 views

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. ...
Quasar Supernova's user avatar
5 votes
0 answers
122 views

TensorContract applied twice

I have a very simple question about TensorContract command: I'm declaring ...
MaPo's user avatar
  • 909
5 votes
0 answers
300 views

Interval Arithmetic with Symbolic Intervals

I've run into a problem with IntervalUnion and IntervalIntersection when dealing with symbolic intervals. The following code ...
Histograms's user avatar
  • 2,276
5 votes
0 answers
138 views

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 ...
Vladimir Reshetnikov's user avatar
5 votes
0 answers
1k views

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 ...
nonlinearism's user avatar
4 votes
0 answers
210 views

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 ...
Kellen Myers's user avatar
  • 2,711
4 votes
0 answers
127 views

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 ...
George Varnavides's user avatar
4 votes
0 answers
44 views

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: ...
Arnaud Carignan-Dugas's user avatar
4 votes
0 answers
129 views

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 ...
CasperYC's user avatar
  • 1,642
4 votes
0 answers
185 views

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 ...
Shafiq Ahmad's user avatar
4 votes
0 answers
228 views

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. (...
William Kennerly's user avatar
4 votes
0 answers
241 views

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 ...
user3658307's user avatar
4 votes
0 answers
96 views

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)...
Conor Cosnett's user avatar
4 votes
0 answers
350 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 ...
Kyle's user avatar
  • 41
4 votes
0 answers
89 views

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....
Seb's user avatar
  • 735
4 votes
0 answers
1k views

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 ...
REX's user avatar
  • 41
4 votes
0 answers
123 views

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] >...
Art's user avatar
  • 183
3 votes
0 answers
156 views

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 $$D_{x,y}f_{ij}(x,y)=\lambda_{i,j} f_{ij}(x,y).$$ ...
user1620696's user avatar
3 votes
0 answers
39 views

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, ...
srossd's user avatar
  • 260
3 votes
0 answers
78 views

Asymptotic expansion for a function containing irrational exponents

I'm trying to find an asymptotic expansion of a function containing irrational exponents in the form of a power series (which also might contain irrational exponents). It works correctly if I request ...
Vladimir Reshetnikov's user avatar
3 votes
0 answers
84 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 ...
Yann's user avatar
  • 31
3 votes
2 answers
224 views

Alternatives to NumericQ that allow symbols to be considered numeric

I am writing a program in which I am using NumericQ. I am trying to allow symbols to also be considered Numeric, so I have been using NumericQ[a]=True for all of ...
Davis Ellis's user avatar
3 votes
0 answers
150 views

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 ...
Physor's user avatar
  • 153
3 votes
0 answers
162 views

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 ...
ayr's user avatar
  • 2,444
3 votes
0 answers
183 views

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 ...
Vladimir Reshetnikov's user avatar
3 votes
0 answers
72 views

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: ...
user129412's user avatar
  • 1,339
3 votes
0 answers
144 views

Convergent infinite sum fails to converge in Sum[...]

It looks like this. ...
xiaohuamao's user avatar
  • 4,728
3 votes
0 answers
341 views

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 ...
Everett You's user avatar
  • 2,297
3 votes
0 answers
206 views

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 ...
masterxilo's user avatar
  • 5,739
3 votes
0 answers
79 views

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 ...
Vladimir Reshetnikov's user avatar
3 votes
0 answers
461 views

Polynomial kernel expansion

I am trying to calculate the polynomial kernel expansion using Mathematica. I have tried the Expand and Simplify functions with ...
JC1's user avatar
  • 131
3 votes
0 answers
184 views

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 ...
user36314's user avatar
3 votes
0 answers
247 views

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 ...
Veteran's user avatar
  • 439
3 votes
0 answers
126 views

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: ...
Vlad's user avatar
  • 39
3 votes
0 answers
413 views

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)...
wonderich's user avatar
  • 923

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