Questions tagged [symbolic]

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

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votes
3answers
459 views

Reduce ODE into 1st order

I have an explicit set of differential equations: $ \ddot{x}=f(x,\dot{x})$ I would like to reduce it in the following way: $ \dot{y} = g(y)$ by substitutions as shown here: wikipedia. I have done ...
10
votes
2answers
1k views

Non-commutative algebra (NCAlgebra): How to properly SetCommutingOperators

I am starting to work with non-commutative algebra in Mathematica and had a look at the NCAlgebra package. I installed it and can use its functions. However, what I am struggling with is the ...
10
votes
3answers
553 views

How to implement symbolic Ramanujan's summation in Mathematica?

How to implement Ramanujan's summation in symbolic form in Mathematica? For instance, I want as input the function $f(x)=x$, as output $-1/12$, as input $f(x)=1/x$, as output $\gamma$ (Euler's ...
10
votes
1answer
425 views

Mathematica: computing a difficult integral

I am trying to compute the following integral: Integrate[Exp[Sum[-((cw λ - b[i])^2/(2 σ^2)), {i, 1, n}]], {cw, 0, 1}] And currently Mathematica outputs ...
10
votes
1answer
701 views

Is it possible to find a limit of a sequence given by its recurrence relation?

I need to calculate a limit of a sequence given by its recurrence relation. I tried the following: ...
10
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1answer
170 views

How do I expand StirlingS2[n, 10] in terms of elementary functions?

I know that it is possible to expand StirlingS2[n, 10] in terms of elementary functions of n. I tried ...
10
votes
2answers
646 views

Symbolic Integration along contour: branch cut problem?

Context Following this question on path integrals in the complex plane, having defined again a numerical and symbolic integrator along a path as ...
10
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2answers
639 views

Symbolic tensor simplifications and the identity matrix

How can I get Mathematica to simplify the following expressions, with $Assumptions including Element[n,Integers], n > 0, and <...
10
votes
2answers
423 views

Symbolically prove that two expressions are identical

I encountered this problem when trying to reproduce the result of this paper. (The relevant parts are all included in the preview i.e. the 1st page of the article. This link is just given as ...
10
votes
1answer
157 views

Bug in GeneratingFunction?

Bug introduced in 7.0 and fixed in 9.0.0 According to the documentation GeneratingFunction[a[n],n,x]==Sum[a[n]x^n,{n,0,Infinity}] However, for $a_n=1/(n+2)$ I ...
10
votes
2answers
291 views

Integration of Booles and Gaussians in high dimensions

Context As a follow up of this question, I would like to predict the connectivity of the so-called cosmic web in arbitrary dimensions. The connectivity $\kappa$ is defined as the number of ridges ...
10
votes
1answer
389 views

Wrong limit: Limit[(1 + (-1)^n/n)^n, n -> Infinity]=1 (Mathematica 10.4 and W-Alpha)

Bug introduced in year 2002 (?) and fixed in 11.0 Since $(1-\frac{1}{n})^n\to 1/e$ and $(1+1/n)^n\to e$, the sequence $(1+\frac{(-1)^n}{n})^n$ has no limit as $n\to\infty$, but has limits for odds ...
10
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1answer
1k views

Compute inverse Laplace transform with Integrate

Since inverse Laplace transform is just an integral, while we already have InverseLaplaceTransform built in, can we compute it with ...
10
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1answer
2k views

Symbolic scalar-by-matrix derivative

Let's say I want to calculate the following scalar-by-matrix derivative $$\frac{\partial}{\partial A} \text{tr} \left[(\vec X^T A)^T (\vec X^T A)\right],$$ with $\vec X$ and $A$ being a $n \times 1$ ...
10
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1answer
206 views

How to predict the degree of the first series coefficient?

Given an expression f that is a function of x and a number x0, what is the least integer <...
10
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0answers
300 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 ...
10
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0answers
329 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 ...
9
votes
3answers
739 views

Efficient code for solve this equation

We have $a*b*c=-1$, $\frac{a^2}{c}+\frac{b}{c^2}=1$, $a^2 b+a c^2+b^2 c=t$ What's the value of $a^5 c+a b^5+b c^5$? I tried ...
9
votes
2answers
724 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. ...
9
votes
2answers
762 views

How to solve this system of trigonometric trancendental equations over the reals?

Namely, $$\left\{x^2+2 x \sin (y)+3 \cos (y)=0,\sin ^{-1}\left(\frac{x}{2}+\sin (y)\right)=y-\frac{\pi }{3}\right\}$$ My simple-minded trial ...
9
votes
5answers
5k views

How do I obtain the correct double limit?

The command Limit[(Sin[x^2] + Sin[y^2])/ (x - y) /. x -> 0, y -> 0] (* 0 *) I think that Mathematica finds the iterated limit instead of the double ...
9
votes
3answers
343 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 ...
9
votes
1answer
444 views

Deep learning outperforms in symbolic integration and ODE?

There comes a new paper on arXiv (arXiv 1912.01412, Deep Learning for Symbolic Mathematics by Guillaume Lample, François Charton) claiming that a deep learning model outperforms Mathematica a lot in ...
9
votes
1answer
1k views

Symbolic linear algebra

I would like to know how I can ask Mathematica to expand (and simplify) such an expression : $$ (\alpha A + \beta B)^\top (\alpha A + \beta B) $$ where $\alpha,\beta$ are two real numbers and $A,B$ ...
9
votes
1answer
477 views

${\frac {\partial^{2} u}{\partial {x}^{2}}} +{\frac {\partial ^{2} u}{\partial {y}^{2}}} =0$ with one boundary at infinity

Is there a trick to make Mathematica solve $${\frac {\partial^{2} u}{\partial {x}^{2}}} +{\frac {\partial ^{2} u}{\partial {y}^{2}}} =0$$ with one boundary condition at $\infty$? Boundary ...
9
votes
2answers
142 views

How to stop DSolve from solving equations [duplicate]

I'm tring to solve this ODE, DSolve[y'[x] == Sqrt[1 + (x/y[x])^2] - x/y[x], y[x], {x}]. Mathematica gives this as the result: I don't want Mathematica to solve the ...
9
votes
2answers
174 views

Closed form of product of Gamma function

Mathematica recognizes this closed form \begin{align} \prod_{k=1}^{n-1}\sin(\pi k/n) &= 2^{1-n}\,n \end{align} just fine: but fails on this one despite that this expression also has a known ...
9
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2answers
695 views

InverseFourierTransform of simple function takes forever

i'm quite new to Mathematica. I'm trying to do something along the lines of: ...
9
votes
2answers
634 views

Analytic solution to Orr-Sommerfeld-Squire equations for a special case

Hello everybody in Mathematica SE. Although my question is related to flow stability analysis, this should be a general application of MMA to solve a system of ODEs. Thank you for your suggestion! ...
9
votes
3answers
262 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 ...
9
votes
1answer
237 views

When to use GenerateConditions -> True

Many functions, usuallly those involving integration, take a GenerateConditions option which often defaults to False, or at ...
9
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3answers
4k views

Algorithm for parts integration

Sorry if this is a duplicate, I've searched how to do this to no avail. What I'd like to do is a function that integrates by parts $n$ times, i.e $$ \int u(x) v(x) dx = u \left(\textstyle{\int}v\...
9
votes
2answers
212 views

How can I make FourierCoefficient et al. handle the zero-order term correctly?

Say that I would like to use Mathematica to step through one of the most famous solutions to the Basel Problem, using Parseval's Identity, $$ \sum_{n = -\infty}^\infty \left|c_n\right|^2 = \frac{1}{2\...
9
votes
1answer
827 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 ...
9
votes
2answers
4k views

Noncommutative multiply- expand expression

I began to use Mathematica a few days ago. My problem is: how do I expand expressions like $(a+b)\ast(a+b)$, where the multiplication is noncommutative? Can Mathematica do this?
9
votes
2answers
913 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 ...
9
votes
1answer
619 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 ...
9
votes
2answers
2k views

Coordinate free differential forms package

I am looking for a package in Mathematica which can handle differential forms in a coordinate free manner. I am aware of several packages which do differential forms, but it seems that for all of them ...
9
votes
1answer
138 views

Nice use case for symbolic tensors?

I come from before the times of symbolic tensors in Mathematica, and am used to working with concrete tensors and custom commands to contract them using Transpose, Dot, etc. I recently realized that ...
9
votes
2answers
440 views

Why is ToRadicals[] not able to handle all cases? Is there a workaround?

The documentation for the function ToRadicals says: ♦ There are some cases in which expressions involving radicals can in principle be given, but ...
9
votes
1answer
490 views

Verifying and deriving basic (block) matrix identities

How can I use the new symbolic matrix/tensor capabilities to verify matrix identities, such as (1) or (2) Even better, how can I ask Mathematica to derive expressions for X, Y, Z, and U like ...
9
votes
1answer
270 views

Comparing exact expressions for equality — is it really OK if I get wrong answer?

Bug introduced in 7.0 or earlier and fixed in 10.2.0 I found an unexpected behavior (that I think of as a bug) in evaluation of the equality operator applied to mathematical functions with exact ...
9
votes
2answers
1k views

Bug in Integrate for Mathematica

Bug introduced in 8.0.0 and fixed in 9.0.0 Consider the following: ...
9
votes
1answer
123 views

DSolve fails with four variables

How is that DSolve has no trouble solving this: DSolve[{ D[G[x1,x2,x3],x1]==0, D[G[x1,x2,x3],x2]==0, D[G[x1,x2,x3],x3]==0 },G[x1,x2,x3],{x1,x2,x3}] but it fails ...
9
votes
0answers
138 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 ...
9
votes
0answers
553 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 ...
9
votes
0answers
143 views

When and why are Assuming and Assumptions not equivalent? [duplicate]

In this question there's an example of an integral where using Assuming and Assumptions give different results: ...
8
votes
2answers
447 views

Can I get rid of the noise in my differential equation solution?

I am solving a differential equation: ...
8
votes
3answers
446 views

Series expansion wrong

I had to work with some series expansions lately, and at some point I realised that something was becoming inconsistent at some point. It seems that applying Factor ...
8
votes
3answers
6k views

How to solve an overdetermined system in Mathematica

I would like to understand the reasons and find a way to avoid such behaviour of the Solve function in Mathematica 8. ...

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