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

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1
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1answer
82 views

Subtracting Series

When I input the following $$\sum_{n=0}^{m+1}x[n]-\sum_{n=0}^{m}x[n]$$ which in InputForm is: ...
11
votes
2answers
295 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 ...
24
votes
1answer
1k views

Analogue for Maple's dchange - change of variables in differential expressions

Maple owns an interesting function called dchange which can change the variables of differential equations, but there seems to be no such function in Mathematica. ...
5
votes
1answer
81 views

How do I perform exact unit conversions with irrational conversion factors?

Suppose I want to express $3h$ in units of $\hbar$ (where $h$ and $\hbar$ are the Planck constant and reduced Planck constant, respectively). By definition, $h = 2\pi\hbar$, but when I attempt this ...
5
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1answer
241 views

Checking if a symbolic matrix is positive semi-definite

As far as I can tell, there is no way to tell the builtin PositiveSemidefiniteQ about assumptions on symbols. For example, the matrix ...
0
votes
1answer
80 views

Is there a function or option to collect factors under one radical sign?

One of the things that frustrates me most about Mathematica's symbolic manipulations is the fact that output is often presented quite differently than most humans would write it. This is especially ...
1
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1answer
96 views

How can I get symbolic orthonormal eigenvectors for 3 by 3 hermitian matrix?

Using the following syntax, I can obtain the symbolic eigenvalues and eigenvectors of the following Hermitian matrix (a,b,c,d are all real parameters): ...
3
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1answer
144 views

Can Mathematica solve this type of recurrence?

I have the following recursively defined equation: ...
0
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1answer
314 views

How to get the modulus of following complex number

I want to get the modulus of following (1+(x+I*y)/2+(x+I*y)^2/12)/(1-(x+I*y)/2+(x+I*y)^2/12) I use ...
4
votes
2answers
149 views

Well-defined symbolic integral leading to ConditionalExpression

I would like to determine a closed-form expression for the following symbolic integral $$ \int_{-1/2}^{1/2} \!\!\!\! \mathrm{d} x \int_{-1/2}^{1/2} \!\!\!\! \mathrm{d} y \, \frac{1 + b x + c y}{1 + e ...
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0answers
72 views

How do I simplify Interval[{x,x}] to x? [duplicate]

How do I simplify Interval[{x,x}] to x ? Simplify and ...
5
votes
1answer
127 views

Rearrange an algebraic expression so that each variable appears only once

Mathematica gave me a solution to an equation in this form: ans1 = (b c)/(a - a c + b c) $\text{ans1} = \frac{b c}{a - a c + b c}$ From solving the same equation ...
2
votes
1answer
514 views

Working with derivative of conjugate of a complex number

I have a complex function, lets say $g(x)$. I want to take its and its conjugate's derivative. I need the solution of derivative which must be symbolically and computationally efficient. Lets take an ...
3
votes
3answers
131 views

How to Integrate trivial products of DiracDelta

A long while ago I was able to integrate with Mathematica: $$\int_0^1 \delta(1-x)\delta(x) f(x) \,dx = 0$$ using ...
5
votes
1answer
68 views

Simplify complex answer given by DSolve[]

I tried the technique in this question, but that did not work for the solution given by the MWE: DSolve[{f'[t] + f[t]*g[t] == h[t], f[0] == f0}, {f[t]}, t] How ...
2
votes
1answer
104 views

simplifying integrals for multiple exponentials

This is somewhat related to this question, but applied to products of Exp[]. For example, I have a symbolic expression containing terms like $Exp[\int_0^1 f[t]dt](...
0
votes
1answer
86 views

Working with symbolic values in Quantities [duplicate]

I have the following expression: x Quantity[y, ("Milliwatts"*"Seconds"^2)/"Joules"] If I try to convert this to the SI unit, I would expect to get ...
5
votes
1answer
301 views

Slow-down encountered when using NMinimize with a compiled function

I'm minimizing a large function. Evaluating the function is very slow symbolically but using Compile I can get ~100x speed-up on this step. However, despite this, the NMinimize process is only ...
0
votes
1answer
275 views

How to make Mathematica show intermediate steps in integral [duplicate]

I want to know how Mathematica evaluates this integral: $PV \int _ {0} ^ {i \infty} d \tau \, \frac{e^{-\frac{\tau^2}{2 M^2}}(b^2 - 3 τ^2)^2 (|b^2+\tau^2|-(b^2-\tau^2))}{\tau (\tau^2 - b^2)}$, where ...
0
votes
1answer
60 views

Using Coefficient to pick combinations of parameters in an expression

I have the expression $$ c \partial_{\chi} u = \mu u - \nu v - (u + \beta v)|A|^2 + (\partial_{\chi}^2 u - \alpha \partial_{\chi}^2 v) + \gamma u \\ c \partial_{\chi} v = \mu v + \nu u - (v - \beta u)|...
1
vote
0answers
562 views

Solving Symbolically Equations with Vectors and Matrices [closed]

I want to solve equations with vector variables and vector/matrix parameters symbolically. As a basic example I would like to be able to solve something like $[I-aG]x=b$ where $a,b \in \mathbb{R}^l$ ...
0
votes
0answers
131 views

Alternative to Series

Here is a sample of my code: ...
0
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0answers
288 views

Simplifying terms in a Sum expression

I have a sum in the form of pure function s = Sum[f[k], {k, 0, # - 1}] & of perhaps complicated terms f[k]. The terms <...
10
votes
2answers
534 views

Is there a way to identify a symbolic fraction?

Is there a way to use Head to detect a symbolic fraction? In particular I find, Head[a/b] Head[1/5] Times Rational ...
1
vote
1answer
70 views

Defining a matrix with the symmetry Transpose[A(q)]=A(-q)

I am trying to construct a symbolic matrix with the following property- $$ \left(D_{3\times3}(q)\right)^T = D_{3\times3}(-q) $$ Note that for $q\in \mathbb{R}$, $D(q)$ would be hermitian. So far i ...
4
votes
3answers
185 views

Differential equation with a Heavisidetheta function running for ever

So I'm trying to get the solution of the following differential equation: ...
1
vote
1answer
108 views

Strange timings of integrals involving Hermite's polynomials

I have used Mathematica to calculate tunneling for quantum harmonic oscillator. The code is simple: ...
2
votes
2answers
149 views

Let mathematica combine integral limits

Is there a way to teach mathematica to combine integral limits according to $\int_a^b f dx+\int_b^c f dx=\int_a^cf dx$ to simplify expressions like $\int_0^1 f[t] dt+\int_1^x (1+f[t]) dt$ to $\int_0^t ...
2
votes
1answer
166 views

Symbolic quadratic constrained maximization with non-negativity constraints?

Dear Mathematica users, I attempted to maximize the below quadratic function K, subject to x1+x2<=A, and a series of non-...
1
vote
1answer
43 views

hold specific pattern in symbolic calculation

I encounter some questions when I try to simplify a symbolic expression using Mathematica. For example, I got an intermediate expression ...
19
votes
2answers
361 views

What does f_[whoCalled]^:=f really mean?

I came across the following post by John Doty in this Google Groups discussion: On Friday, January 11, 2013 8:23:16 PM UTC-7, amzoti wrote: It is clear the Mathematica uses Lisp as one ...
4
votes
2answers
399 views

Help at speeding up simplification/nested symbolic integration

I have the following problem: I want to compute an integral of the form $$\int\limits_0^{t_g}\mathrm{d}t_2\int\limits_0^{t_2}\mathrm{d}t_1\left[A(t_1),A(t_2)\right],$$where $\left[B,C\right]=BC-CB$ is ...
3
votes
2answers
146 views

Eigenvectors of large symbolic matrix

I have large symbolic matrix of order 32 x 32 given as ...
2
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0answers
82 views

Integrate with Subscript: does this crash your kernel too?

I encountered some strange behaviour running v10.0.1 on a Mac Pro, while working with Integrate and Subscript. Starting from a ...
3
votes
3answers
132 views

Symbolic integration conditional bug?

I just ran across this: Assuming[x > 0, Integrate[1/t^2, {t, 1, x}]] gives the output ...
2
votes
1answer
90 views

How to define the symbolic expression $V = \frac{1}{N} \sum_{i=1}^N ( y_i(g) - z_i)^2$ in Mathematica?

I want to define this expression symbolically: $V = \frac{1}{N} \sum_{i=1}^N ( y_i(g) - z_i)^2$ in which $\{y_i(g)\}_{i=1}^N$ is to be understood as a symbolic sequence that depends on a vector $g$. ...
0
votes
1answer
73 views

Taking function output as shown, and processing it regardless of its history

I am making some symbolical calculations for my quantum chemistry class. I am supposed to build a wave function composed of multiple other functions, each of which is also composite of some lower ...
1
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0answers
113 views

Summing the probability distribution to 1 to convince myself

I have worked out a probability distribution and want to check its sum which is necessarily 1. First we write $$ r \triangleq \frac{(2 \lambda + \mu)^2}{2(\mu + \lambda)^2}, \quad s \triangleq \...
7
votes
0answers
151 views

How does Mathematica resolve symbolic systems of inequalities? [closed]

Before getting into my question, let me provide some context: I recently started using Mathematica to automatically perform stability analyses that I previously did by hand. A major part of the ...
5
votes
3answers
303 views

Comparison of Dispatch objects ureliable in Mathematica 10

In 2008 I wrote a group theory package. I've recently started using it again, and I found that one (at least) of my functions is broken in Mathematica 10. The problem is complicated to describe, but ...
1
vote
2answers
490 views

DSolve bvlim error due to Boundary condition at infinity

I am solving an Ode using Mathematica that has boundary condition at infinity which is why Mathematica is showing error message. Please help to tackle this problem. ...
3
votes
1answer
131 views

How to get a more compact form of this probability calculation?

Inspired by the probability calculation here, I am trying to solve a little general one: $$\mathbb{P} (\sum_{i=1}^{m-1} A_i + \sum_{i=1}^{m} S_i < L < \sum_{i=1}^{m} A_i + \sum_{i=1}^{m+1} S_i)$...
1
vote
2answers
90 views

Symbolic integration of a indexed product term?

I am trying to perform the symbolic integration of the following expression $$\int \prod_{i=1}^n p(x_i | z) p(z) dz$$ where $$p(x_i|z) = \frac{exp(\frac{-(x-z)^2}{2\sigma_i^2})}{\sqrt{2 \pi \sigma_i^2}...
0
votes
2answers
155 views

Symbolic matrice or vectors in Mathematica?

Suppose I would like to define an expression, containing and array or matrix of symbolic elements. Like this ...
6
votes
1answer
379 views

How to solve this probability symbolically or numerically?

I am trying to calculate the following probability $$\mathbb{P} \big(\sum_{i=1}^{m} (A_i + S_i) \le L < \sum_{i=1}^{m+1} (A_i + S_i) \big)$$ where, $$A_i \sim \exp(\lambda), \quad S_i \sim \exp(...
14
votes
2answers
363 views

How to do algebra on summations of variable expressions?

Is there any easy, general way to handle algebra on variable Sums? For examples, Gaussian Mixtures or Fourier Series: ...
1
vote
0answers
149 views

Symbolic Nullspace computation in parallel

I am trying to determine the nullspace of a large symbolic matrix. The single core evolution seems to take too long. I tried Parallelize[] on the commands ...
1
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0answers
133 views

Symbolic and numeric calculations (and plots) simultanuosly [closed]

I use Mathematica to do a bunch of symbolic calculations (integrals, ...). This is good because I found that sometimes, if I plug in numeric values, Mathematica takes much longer. However, sometimes ...
21
votes
2answers
327 views

Backslide of Limit

A friend of mine showed me this example: Limit[Sum[Sin[Pi*k/n]/(n + 1/k), {k, 1, n}], n -> Infinity] This sample calculates well in v8.0.4: but not in ...
4
votes
2answers
178 views

Remove redundant parameters from equation

I have random expressions like (b1 x + b2 x)/(b3 + b4/b5 x) + Sin[b6 x] where $x$ is a variable and {b1, ..., b6} are parameters to be fitted. This expression is ...