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

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6
votes
1answer
196 views

Telling mathematica to output * instead of space for multiplication, so I can copy as plain text

I am trying to get some symbolic expressions in Mathematica which I would like to paste into my C/MATLAB codes. This can be accomplished nicely by selecting the expression and right-clicking to ...
6
votes
1answer
237 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 ...
6
votes
2answers
185 views

How to implement a formal expectation operator over an unknown distribution?

I need to do some simplification of an expression involving averages over a stochastic variable (in order to verify a long analytical calculation). The easiest way to do that, I figured, were if I ...
6
votes
2answers
104 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 ...
6
votes
1answer
643 views

Why does this sum not simplify properly?

I was trying to get Mathematica to simplify some moderately ugly sums and I ran into some pretty weird behaviour, which I tracked down to the following example. I'm working with ...
6
votes
1answer
124 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 $n \times 1$ ...
6
votes
1answer
114 views

Is it possible to disable assumptions used by FullSimplify for zero testing [closed]

Sometimes when I invoke FullSimplify on a large expression, I get a series of messages like this: ...
6
votes
0answers
112 views

Using FunctionExpand to evaluate symbolic derivatives

Some symbolic derivatives of certain special function are not expanded automatically, but FunctionExpand often helps to get a derivative-free closed form ...
6
votes
0answers
272 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 ...
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 ...
5
votes
1answer
234 views

Validating simplifications analytically

I have a rather complex expression which I would like to simplify and check my work along the way (Mathematica does not simplify very basic things and it is frustrating me). In the following example, ...
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 ...
5
votes
1answer
191 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 $A,B$ ...
5
votes
1answer
253 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 ...
5
votes
1answer
328 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
4answers
399 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 (...
5
votes
1answer
509 views

Wallis Formula and Pippenger Product---How do we get symbolic output?

The Wallis Formula computes $\frac{\pi}{2}$ OEIS and the Pippenger Product computes $\frac{e}{2}$ OEIS. Here is a combined formula: ...
5
votes
2answers
125 views

Equality and Quantifiers

I am new to Mathematica and to Math. I do not study math in English, so please bear with me as I try to state my questions.. This is what I am trying to "solve": $$∃!x : A(x) ⇔ ∃x : ¬A(x)$$ In ...
5
votes
1answer
76 views

Why is NHoldFirst not propagated to symbolic derivatives?

I encountered a nasty problem that N cannot evaluate expressions containing a symbolic Derivative of a multi-parameter function ...
5
votes
2answers
157 views

How to check an algebraic number for membership in a list

I need to check an algebraic number for membership in a list of algebraic numbers. The numbers can be expressed in different forms (combinations of radicals, Root ...
5
votes
1answer
445 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 ...
5
votes
1answer
62 views

How to bail out from a non-applicable transformation function?

I provide a custom function in TransformationFunctions options of FullSimplify that can do a transformation only for some values ...
5
votes
1answer
169 views

VariationalD giving the wrong solution?

EDIT: As pointed out in the comments, VariationalD gives a variational derivative (which I don't want), not a derivative with respect to a function (i.e. ...
5
votes
1answer
247 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: $$\sum\limits_{q}^{q\in qV}\sum\limits_{q'}^{q'\in q'V}{f(q)g(q')\delta(q-q')}=\sum_{q}^{q\in qV}{f(q)g(q)}.$$ ...
5
votes
2answers
329 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 ...
5
votes
0answers
59 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: ...
4
votes
3answers
360 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 ...
4
votes
4answers
798 views

Mathematica gives wrong answer for integral

When I execute the following, Integrate[Exp[-w^2 + I w^3], {w, -\[Infinity], \[Infinity]}] I get ...
4
votes
1answer
485 views

Does the Im function work with symbolic arguments?

Does the Im function work with symbolic arguments? ...
4
votes
1answer
229 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: ...
4
votes
2answers
168 views

Why the inequality does not take into account the domain?

I have this inequality: Reduce[(4000-1000k)/(k-4) < 0] and the answer is k ∈ Reals I would expect ...
4
votes
1answer
127 views

Volume within parameter space

Imagine a parameter space with variable 0<p<1, 0<e1<1/2 and 0<e2<1/2. ...
4
votes
1answer
627 views

Symbolic integration in the complex plane

Context While answering this question, I defined (symbolic and numerical) path integrations as follows ...
4
votes
2answers
202 views

How do I evaluate a symbolic integral involving Hermite polynomials?

I want to test a difficult integral : Integral on all reals of some complicated function involving the Hermitian polynomials, exponentials, squares, factorials, and being general considering any ...
4
votes
1answer
122 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: ...
4
votes
1answer
489 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 ...
4
votes
3answers
189 views

Running out of variables

I am running symbolic calculations with Mathematica. Simplification of algebraic expressions is an important part of them as very often final results can be simplified considerably. Typically my ...
4
votes
1answer
172 views

How to extract a possible closed form from WolframAlpha[] output

To find a possible closed form of a number, I can use the function WolframAlpha["6.38905609893065", IncludePods -> "PossibleClosedForm"] It returns a result ...
4
votes
2answers
175 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
1answer
162 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 ...
4
votes
1answer
204 views

How to check if a given expression is an “explicit algebraic number”?

The documentation for PossibleZeroQ says: With the setting Method...
4
votes
2answers
213 views

Problems with Symbolic summation over unknown values

I'm having some real trouble with Mathematica wrongly evaluating various symbolic sums at the moment. I have this function: $$h_{ij}(x) = ...
4
votes
0answers
391 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 ...
4
votes
0answers
83 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] ...
3
votes
1answer
396 views

How do I solve $1 - (1 - (A x)^2)^\frac{3}{2} - B(1 - \cos(x))= 0$?

Consider the equation $$ 1 - (1 - (A x)^2)^\frac{3}{2} - B(1 - \cos(x)) = 0 $$ where $A,B \in \mathbb{R}$ are constants. What is the analytic solution?
3
votes
2answers
230 views

Can Mathematica identify formulae or sequences of numbers?

Can Mathematica suggest what a formula means? For example if I input $$\sum_{i=0}^n i$$ can it infer that this is a sum of integer values from $0$ to $n$? Or if I enter $0,1,1,2,3,5,8,13$, can ...
3
votes
1answer
202 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 ...
3
votes
1answer
518 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. ...
3
votes
2answers
113 views

How to define the irrational domain or any other arbitrary domain?

I have found no way to define the domain of Irrational numbers. I can easily define a test to see if a number is irrational by defining: ...