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

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3
votes
1answer
226 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
209 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
89 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] ...
5
votes
1answer
482 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 ...
5
votes
1answer
305 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: $$\sum\limits_{q}^{q\in qV}\sum\limits_{q'}^{q'\in q'V}{f(q)g(q')\delta(q-q')}=\sum_{q}^{q\in qV}{f(q)g(q)}.$$ ...
2
votes
1answer
378 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
437 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
1k 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 ...
12
votes
1answer
228 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
1k 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
473 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
211 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
198 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. ...
9
votes
1answer
291 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 ...
14
votes
3answers
1k 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 ...
4
votes
1answer
650 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 ...
1
vote
1answer
196 views
0
votes
1answer
143 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 ...
16
votes
1answer
439 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
5answers
611 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 (...
2
votes
1answer
194 views

Difference between Map[f[#] + g[#] &, {a, b, c}] and Map[f[x]+g[x]&, {a, b, c}]

Map[f[#] + g[#] &, {a, b, c}] vs Map[f[x]+g[x]&, {a, b, c}] My question is: why is the output different? ...
8
votes
1answer
340 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 ...
12
votes
2answers
2k views

How do I work with Root objects?

I want to solve the trigonometric equation : $$(3-\cos 4x )\cdot (\sin x - \cos x ) = 2.$$ I tried Solve[(3 - Cos[4*x])*(Sin[x] - Cos[x]) == 2, x] It returns the ...
4
votes
1answer
807 views

Symbolic integration in the complex plane

Context While answering this question, I defined (symbolic and numerical) path integrations as follows ...
2
votes
0answers
227 views

Numerical-Symbolical Integration (Calculus)

I created a simple numeric-symbolic integration. Here you can use symbolical and numerical techniques at the same time. You can also interpolate numerical integrals. The problem with my function is ...
3
votes
3answers
681 views

Superscript prime symbol

x\[Prime] looks like $x_'$, ugly right? Is there a way to make a symbol with prime to look like $x'$? That's what I'm trying right now: ...
1
vote
1answer
430 views

How to define a derivative/Variation operation in Mathematica from scratch

I am looking for a method in Mathematica 8 to define my own derivative/variation (independent of built-in operations). I do not want to re-define built-in objects since I fear that this could cause ...
1
vote
2answers
235 views

Symbolically associate vectors and their norms

I am wondering how to handle the following situation: I do have vectors of known dimension that I would like to handle symbolically. I suppose I can do something like ...
9
votes
1answer
3k views

Complex number operations: telling Mathematica variables are real

I want to do Conjugate[a + b*I], but when I do that, the solution is Conjugate[a] - I*Conjugate[b]; when for me, a and b are ...
7
votes
2answers
621 views

Symbolic manipulation with unevaluated sums

If I have two expressions with sums in them, like this: $$\begin{align*} b&=\frac{\sum_{i} (x_i - \bar{x})(y_i -\bar{y})}{\sum_{i}(x_i -\bar{x})^2}\\ r&=\frac{\sum_{i} (x_i - \bar{x})(y_i ...
15
votes
1answer
289 views

Polynomial expectations of generic distributions

Summary Polynomial expectations depend only moments and cross moments of a multivariate distribution. I would like to use Expectation to compute polynomial ...
9
votes
1answer
572 views

Managing Exclusions in Plot[]

When I do: ...
2
votes
1answer
251 views

Identifying the sign of an expression in an interval

My expression is the following: $$ \frac{(1-\alpha ) \alpha h^2 (h+2) \mu r}{(h+1) ((1-\alpha ) h+1) (\alpha h+1)}-\left(\frac{\alpha h \mu }{h+1}\right)^{\alpha } \left(\frac{(1-\alpha ) h \mu ...
8
votes
2answers
551 views

Why aren't these additions of integrals and summations equal?

I have the following code: Simplify[Integrate[f[x] + g[x], x] == Integrate[f[x], x] + Integrate[g[x], x]] To test: $$\int{\left(f(x) + ...
7
votes
4answers
1k views

Mathematica gives wrong answer for an integral

When I execute the following, Integrate[ Exp[-w^2 + I w^3], {w, -∞, ∞}] I get (2 E^(2/27) BesselK[1/3, 2/27])/(3 Sqrt[3]) ...
16
votes
1answer
383 views

What does “suitable for symbolic manipulation” in the documentation mean?

This question is related to this other one I posted on Stack Overflow some time ago. There, in a beautiful answer, acl (with some unhumble editing done by me) showed that the derivative of ...
6
votes
1answer
518 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 ...
4
votes
1answer
239 views

Symbolic bit vectors

I'd like to see how addition and xoring bitvectors mix together. To do this, I implemented (a primitive) vec_add and vec_xor: ...
14
votes
2answers
1k views

How to deal with complicated gaussian integrals in Mathematica?

As we know, for most Gaussian integrals, we can get the analytical result. Now I have many Gaussian integrals to treat, which have the following general form, ...
12
votes
1answer
1k views

How does Mathematica integrate?

Basically, this question can be considered to be an extenstion to my other question. What I wanted to do was this integral as homework (it is indefinite BTW so no approximations using Simpson's Rule ...
11
votes
1answer
328 views

How can I eliminate a function in a system of PDEs, Maple-style?

Maple can separate and eliminate a function in a system of PDE equations, with casesplit in the PDEtools package. How to do ...
7
votes
3answers
2k 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. ...
25
votes
1answer
518 views

How to augment the realm of functions Mathematica thinks it knows how to integrate symbolically

My question involves extending the functionality of Integrate over specific integrals in the most generic manner. Specifically, is it possible to "hack into" ...
2
votes
1answer
394 views

Reduce/Solve an equation with symbols in powers

I am trying to solve the following equation with respect to x. eqn = x^z + y == a; But when I do ...
2
votes
2answers
249 views

How to find solutions that yield of root of unity?

I have a polynomial with coefficients that are integer polynomials in another (complex) variable. For example: 1 + (1 - v^2) #1 + (-3 - v^2) #1^2 + #1^3 & I ...
5
votes
1answer
344 views

Finding ranges of a parameter for which a function is always positive

I have a complex function of a single variable expressed in analytical form, which also depends on a parameter. I would like to have Mathematica show me for which values of the parameter the real part ...
2
votes
1answer
156 views

Simplification of a symbolic manipulation involving functions of more than one variable

I am facing the following problem. f[x_,y_] = a[x] u[y] + b[x] v[y] Now I can ask Mathematica to calculate ...
8
votes
2answers
192 views

Representing a value in an output as a self defined variable

I'm trying to find a way to have Mathematica always represent a numerical value as a self defined variable that I define using lhs=rhs. For example, if I execute ...
7
votes
3answers
1k views

Using D to find a symbolic derivative

I need to do the following: Define a function Take the derivative of this function and have a look at the symoblic representation Substitute in some values With the bonus that I want to use the ...
4
votes
1answer
595 views

Does the Im function work with symbolic arguments?

Does the Im function work with symbolic arguments? ...