For questions about symbolic computation, as opposed to numerical computations.
5
votes
4answers
168 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 ...
1
vote
2answers
135 views
Write a function that returns the logarithmic derivative
How can we write a function that if we input an expression f, it returns the log derivative $\frac{1}{f} \frac{df}{dx}$. We have to use a conditional or pattern test so that the function accepts any ...
7
votes
2answers
98 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.
...
2
votes
0answers
60 views
Reducing exponential inequalities fails
I am quite stumped by this problem :
Reduce[ N^(x-y) <1 && N > 0 , x, Reals]
gives the expected result
...
6
votes
0answers
106 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 ...
2
votes
2answers
78 views
Mass Symbolic Manipulation with Subscripts? (from plaintext Input)
The simplest example of the change being sought is a greek letter, typed in as plaintext nu, and its may be replaced by the symbol, ν:
expr = 3nu*kx*ky+ ...
5
votes
1answer
72 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 ...
1
vote
1answer
100 views
Improve performance for finding Fibonacci number which have divisibility property
In this post, the OP requires finding a Fibonacci number having some divisibility property with Mathematica and Maxima. I tired tried that Mathematica code on Mathematica 9.0 and it's still slow ...
4
votes
2answers
75 views
Problem with adding vector to symbolic function (for NDSolve)
I'm trying to set up a system of differential equations for passing to NDSolve. Note that my initial conditions are vector valued so Mathematica should know that ...
4
votes
3answers
282 views
Why the difference?
When I do the double sum using the sigma notation I get
$$1 + \sum_{n=0}^{\infty}\sum_{k = n}^{\infty} \frac{1}{(k+2)k!}$$
$1 + e - \cosh[1]$
When I do the sums as below, I get the expected ...
-1
votes
3answers
197 views
Sqrt — how to get negative branch?
One of the many attractions of Mathematica is that integers are generally treated as exact symbolic entities, and not just as numbers. I was just playing with Sqrt, and was puzzled by what appeared to ...
1
vote
1answer
73 views
Why is a non-convergent series simplified to zero?
Sum[Sin[n*x]*Sin[n] /. x -> 1, {n, 1, Infinity}] ==
Sum[Sin[n*x]*Sin[n], {n, 1, Infinity}] /. x -> 1
Sum::div: Sum does not converge. >>
...
3
votes
1answer
40 views
Non commutative multiply- expand expression
I began to use Mathematica a few days. My problem is: How to expand expression like $(a+b)*(a+b)$, where this multiplication is non commutative? Mathematica can do this?
1
vote
1answer
68 views
Generating a list of symbolic coefficients [duplicate]
I am trying to do something which I assume should be very simple: I want to generate a list with symbolic coefficients that looks like this:
...
0
votes
2answers
70 views
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
...
0
votes
0answers
18 views
Symbolic Calculations with formal matrices [duplicate]
I want to make calculations with matrices in the form (for lovers of statistical mechanics, is just the first step replica symmetry breaking)
...
2
votes
1answer
96 views
Is it possible to create a compiled function with some symbolic arguments?
I am trying to create a compiled function that takes in several arguments. However, some of the arguments contain symbolic entries and thus I get the following error message when executing the cell ...
2
votes
1answer
55 views
Differentiating with respect to vectors of unspecified length
Given a function defined by
f[x_,y_] := Sum[ x[[i]] (g[y[[i]]] - g[Total[y]] - Log[x[[i]]]), {i, 1, Length[x]}]
I can easily calculate the derivative for a fixed ...
1
vote
1answer
60 views
Only perform a symbolic differentiation once
I want to define a function that involves a differentiation step that Mathematica can do easily, which might be of the form
...
0
votes
1answer
87 views
Alleviating a bottleneck involving a function call with symbolic derivatives
I have a bottleneck problem involving a function call with symbolic derivatives.
I don't have much experience with Mathematica (or any dynamic language) and I'm certain that the way I've set this up ...
9
votes
2answers
200 views
Find closed form expression for series expansion coefficients [duplicate]
Is there a built-in function that will find a general expression for the coefficient of the series expansion of a function?
Series will only give the explicit ...
4
votes
4answers
129 views
Extracting variables from an expression
I'm looking for a way to extract a list of variables from an expression, for example with an input like:
...
7
votes
1answer
239 views
What is the confidence limit on this convergence?
When I run this,
Product[n^MoebiusMu[n],{n,1,Infinity}]
I get $\frac{1}{4 \pi^{2}}$
Over on Math Overflow they are saying it shouldn't happen. So, how do ...
3
votes
3answers
203 views
Efficient code for solve this equation
We have know $a*b*c=-1$, $\frac{a^2}{c}+\frac{b}{c^2}=1$, $a^2 b+a c^2+b^2 c=t$,
What's the value of $a^5 c+a b^5+b c^5$?
I tried
...
4
votes
1answer
94 views
Identical code, different answers?
I'm having some trouble with identical code giving different answers. On a fresh kernel (MM 9.0.0.0, Windows 64-bit), running the same code, copy-paste, gives two different answers:
...
2
votes
1answer
117 views
Variable name string to expression
I'm not sure how to name this problem appropriately. But anyway.
I have, say, three variables (arrays in my case), which I call:
A1, A2, A3
I would like to ...
3
votes
1answer
135 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
vote
0answers
58 views
Symbolic Integration of Boole [closed]
Why is
Integrate[Boole[x < 1], q]
resulting in
Piecewise[{{x, x <= 1}}, 1]
I'd expect
...
2
votes
3answers
267 views
How to calculate partial derivative of an unknown function
How can I force Mathematica to calculate symbolically the partial derivative of a function u[x,y] with respect to a variable ...
2
votes
3answers
235 views
Symbolic derivative of $n$-term product
I want to determine the relationship that must exist between the $x_i$ and $y_i$ such that
$$
\frac{\partial}{\partial\theta} \prod_{i=1}^n \frac{f(x_i,\theta)}{f(y_i,\theta)} = 0,
$$
where
$$
...
3
votes
1answer
146 views
What properties make this equation difficult to symbolically solve?
I tried to solve the following equation with Mathematica's solve:
Solve[K*(2*Tan[L/2*Sqrt[P/(EI)]]-L*Sqrt[P/(EI)])+4*P*Sqrt[P/(EI)] == 0, P]
It gave the ...
2
votes
1answer
127 views
Can I reduce a matrix inequality such as $\mathbf x^\prime\mathbf A\mathbf x > \mathbf x^\prime\mathbf x$?
I'm new to Mathematica. When I do linear algebra, I wonder if I can have an inequality such as $\mathbf x^\prime\mathbf A\mathbf x > \mathbf x^\prime\mathbf x$, where $\mathbf x$ is a column vector ...
4
votes
0answers
72 views
Using Resolve and ForAll to prove takes a really long time
I've been trying to prove a lemma for my paper using Mathematica... basically that
$$\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] ...
2
votes
1answer
145 views
symbolic integration of a definite integral, how to speed up
I am wondering what are the general tips & hints for speeding up symbolic integration. As far as I understand, it solely depends on the form a function is represented before it is processed by ...
4
votes
1answer
155 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:
$$\sum\limits_{q}^{q\in qV}\sum\limits_{q'}^{q'\in q'V}{f(q)g(q')\delta(q-q')}=\sum_{q}^{q\in qV}{f(q)g(q)}.$$
...
1
vote
1answer
141 views
Nested Sums to multiple sum
I would like to automatically "move nested sums to the left". I mean, just take out of an expression all the summations and go from a nested Sum to a multiple sum. Something like starting with:
...
2
votes
1answer
191 views
How can I solve an exponential inequality in Mathematica?
I would like to solve the equation:
A Exp[m t + s Sqrt[t] x - 1/2 s^2 t] >= K
with respect to x (which is in the exponent) ...
5
votes
4answers
514 views
How to get exact roots of this polynomial?
The equation $$ 64x^7 -112x^5 -8x^4 +56x^3 +8x^2 -7x - 1 = 0 $$
has seven solutions $x = 1$, $x = -\dfrac{1}{2}$ and $x = \cos \dfrac{2n\pi}{11}$, where $n$ runs from $1$ to $5$. With ...
11
votes
1answer
167 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 ...
5
votes
4answers
510 views
How to find the sum all even numbers of this sequence?
I have a sequence $(u_{n})$
$$u_1= 1, \quad u_2 = 2, \quad u_3 = 3, \quad u_{n}= -u_{n-3} + 3u _{n-2} +2 u_{n-1}, \quad \forall n \geqslant 4.$$
I want to list the first $20$ terms of this sequence ...
-1
votes
1answer
174 views
How to efficiently fill in matrix values?
I would like to efficiently fill in or assign values to matrix m:
m={
{a[1,1],a[1,2],a[1,3],a[1,4]},
{a[2,1],a[2,2],a[2,3],a[2,4]},
{a[3,1],a[3,2],a[3,3],a[3,4]},
...
1
vote
1answer
149 views
Symbolic calculation
Is there any software where this kind of symbolic calculation is possible?
s = 0
for i = 1 to m
j = 2 i + a - t
if (j > 0) s = s + a
I want s as a ...
1
vote
1answer
123 views
Functions that operate on symbolic matrices?
I'd like to write functions that operate on symbolic matrices, and do nothing when fed anything else.
...
8
votes
1answer
157 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 ...
11
votes
3answers
537 views
Is learning to use Mathematica useful for pure theoretical research in Mathematics and Computer Science?
I am looking for opinions from Mathematica users about Mathematica itself. After reading the faq, I thought that in some sense I "wish to solve a problem using Mathematica" ... although I understand ...
3
votes
1answer
264 views
Computation of parametric integral
I am trying to compute the integral
Integrate[(g^(u^(g - 1)))/(1 + u^g), {u, 0, t}]
but as an answer I get my input expression. There must be something wrong ...
0
votes
1answer
143 views
0
votes
1answer
115 views
Industrial Level Applications. Recipe for mixed notation of equations set
I am working with large (linear) equations set within Mathematica in numerical notation. For example, set from 4056 eq. is solved for a second, no more. There is no doubt, result is great. But even ...
15
votes
1answer
287 views
Speeding up trigonometric integral
Context
On a possible non trivial toric topology for the Universe (nothing less!).
Problem
I would like to carry out the following integral for $\ell=2,4\cdots 20$.
$$\int _0^{\pi }\int _0^{2 \pi ...
5
votes
4answers
193 views
Prevent Part[] from trying to extract parts of symbolic expressions
If you have a list, e.g.
{1, 2, 3}
then you can extract the $k$th part using Part (...
