Questions on manipulating complicated expressions and making them look simpler using Simplify, FullSimplify and Reduce.

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3
votes
1answer
89 views

How to enforce mathematica to analytically evaluate roots?

I am interested in simplifying expressions involving HeavisideTheta. A simple example could be: HeavisideTheta[1 + x - x^2 + x^3] The best I can achieve is with ...
1
vote
1answer
119 views

Simplify results further

I have an extremely long result in polynomial form following some matrix operations. However, given the symmetry of the problem, I can safely say that the solution will reduce much further than is ...
21
votes
0answers
2k views

Simplify matrix algebra

I'm trying to simplify some matrix linear algebra, for example, simplify $$\big(a1\times(A1\cdot A2)\big)\cdot\Big(a2\times A3\cdot A4+(a3\times A5)\cdot(a4\times A6)\Big)^{T}$$ where lower case ...
9
votes
0answers
224 views

Simplify and Sqrt, inconsistent behavior?

I have encountered some problems when using Simplify with expressions containing a square root and isolated a following test case ...
8
votes
0answers
95 views

Why is this evaluation halved when adding units?

Why does this strange behavior occur when dealing with units and quantities? ...
7
votes
0answers
285 views

Faster simplification of linear combinations of some specific functions

After some profiling I've found that my program spends most of its time in the simplification step. The program uses my simplification function many times (over different data). My calculation is not ...
6
votes
0answers
169 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 ...
5
votes
0answers
86 views

Faster way to perform SameQ[Reduce[…], Reduce[…]]

I'm have some expressions that I need to confirm the equality of. SameQ[Reduce[...], Reduce[...]] works like a charm for the more simple expressions, however when ...
4
votes
0answers
109 views

How to get mathematica to simplify a result

I have the following output $\text{Li}_2\left(3-2 \sqrt{2}\right)-4 \text{Li}_2\left(-1+\sqrt{2}\right)$. This turns out to be equivalent to $\displaystyle\log^2(1+\sqrt{2})-\frac{\pi^2}{4}$. How ...
4
votes
0answers
83 views

Transform an expression to remove the singularity

I have the expression Sin[c x]/c. Clearly it is undefined at $c=0$, but that is merely a removable singularity, since $$\frac{\sin(cx)}c=x\frac{\sin(cx)}{cx}= ...
4
votes
0answers
89 views

Simplifying expressions involving Divisible

FullSimplify[ Divisible[p^2 - 1, 24] , Element[p, Primes] && p > 3] Should evaluate to True, but I get ...
3
votes
0answers
96 views

Why does Mathematica show 4095/4096 terms in TrigExpand?

Clear[x, n]; expr = Cos[x]^(n - 2) (1 - Cos[x]^2 + Sin[x]); r=TrigExpand[expr] Where do those 4095/4096 comes from? It is correct, but it seems very strange ...
3
votes
0answers
152 views

Why doesn't Log[Gamma[]] simplify to LogGamma[] where it could?

I have been playing with various equations involving amount of permutations in relatively large sets. Easiest way to look at these is something like Log[10, bignumber!] . Often expressions, even ...
2
votes
0answers
37 views

Extract common factor from vector or matrix

I can't believe this hasn't been asked before but I can't find anything. Is there a way to convince Simplify or FullSimplify to ...
2
votes
0answers
52 views

Better way to compute triple (or higher order) convolution

I have an identity that I want to verify. $$\sum_{i+j+k\ge ...
2
votes
0answers
192 views

Problems with Simultaneous Equation Solving

Let me first explain what I am doing and then I will explain the problem that I can't figure out. I am basically trying to solve 2 equations for 2 unknowns (a1 and ...
1
vote
0answers
56 views

Apart for complex roots?

Let p[x] be a polynomial in x and consider the partial fraction decomposition of 1/p[x]. ...
1
vote
0answers
40 views

Building a ComplexityFunction based on the size of the expression output

I am experimenting with the ComplexityFunction of Simplify and came up with this one: ComplexityFunction->Function[e,Rasterize[HoldForm[e],"BoundingBox"][[1]]] ...
1
vote
0answers
76 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 ...
1
vote
0answers
40 views

Simplifying an inequality inside an answer by parts

I have the following piece of code where I'm evaluating a probability of a variable v being greater than some threshold under a Uniform distribution. ...
1
vote
0answers
26 views

Derive logistic choice probabilities symbolically

More generally, I am interested in learning what the current limitations of Mathematica are when using it for doing pure mathematics. A recent blog post by Stephen Wolfram (see: ...
1
vote
0answers
39 views

Finding simpler implied formulas while preserving contradiction

I have two Presburger formulas A and B such that A∧B≡False. From these I need to find "simpler" formula A′ (as simple as I can make it) such that A→A′ and A′∧B≡False. Is there any simple way to ...
1
vote
0answers
68 views

How to simplify expressions

I read several similar posts but I have not found a solution yet. However, I think that my problem should be quite easy. So here we are. Relations ...
1
vote
0answers
150 views

How to prevent simplification of hypergeometric functions resulting from integrations?

Definite integrals from 0 to Infinity over a product of two hypergeometric (including exponential, trigonometric, hyperbolic, ...
1
vote
0answers
145 views

Is there a way to speed up Simplify and/or PolynomialReduce Modulus-> 2?

I'm trying to simplify a series of equations with at most 64 input terms. As the number of terms involved in the equations increase, the runtime seems to grow exponentially. Does anyone know of ways ...
1
vote
0answers
243 views

Can mathematica simplify an expression setting simplified answer equal to zero?

Basically I want to reduce something like: Subscript[P, 4] - Subscript[P, 5] == Subscript[R, 4, 5]* Subscript[i, 4, 5] when only one of them is known (...
0
votes
0answers
50 views

Computation doesn't Finish

I'm trying to solve some problem by the following code: ...
0
votes
0answers
58 views

Symbolic Tensor Algebra

I need to perform basic tensor algebra in order to double check some very complicated simplification. It's nothing fancy, it just has so many factors by the end that it's hard to tell if an error has ...
0
votes
0answers
65 views

Trying to Simplify an Expression

I'm trying to simplify an expression: ...
0
votes
0answers
32 views

Using assumptions when calling Simplify from Collect

I am quite new to Mathematica, so please be patient ;) I have a very long equation that I have to sort for powers of a variable called e and that I want to ...
0
votes
0answers
39 views

How to control factor gathering in Simplify

To make my results more readable, I need to make MMA gather terms differently. In this example, Simplify gathers terms by common z[]: ...
0
votes
0answers
49 views

Handling Accuracy and Simplifying

I have the following problem. I have a system of non-linear equations that I log-linearize around a certain point, let's call it point A, using a function that I ...
0
votes
0answers
25 views

Expanding Function Based on Congruence Classes

I'm trying to get Mathematica to expand $\quad \quad \beta_n=\sum_{r=0}^{n}\frac{\alpha_r}{(q^4;q^4)_{n-r}(q^4;q^4)_{n+r}},$ where $\alpha_r$ is an integer valued sequence that is given by ...
0
votes
0answers
37 views

Simplification of a complex-valued expression with purely real components

(I'm including all the information here, as I'm not sure how much of it is necessary to solve the problem. For a tl;dr skip to the bottom) I've been working on a problem involving calculating ...
0
votes
0answers
43 views

Custom simplification of symbolic definite integral with regards to bounds

I would like to rewrite symbolic definite integrals such that the bounds are always positive. For example : $\int_{-\infty}^\infty f(x) \mathrm{d} x \rightarrow \int_0^\infty \left[ f(x) + f(-x) ...
0
votes
0answers
52 views

What is taking so long in this simplification?

I killed this after 48 hours, it did not seem to be getting anywhere. In the best of all possible worlds it would spit out n!. If I put the summation in a function it does compute factorials ...
0
votes
0answers
30 views

Assumptions for simplifying a long equation

I'm having trouble combining assumptions with the execution of Simplify in a long equation. The idea is to separate imaginary and real parts of a complex equation. ...
0
votes
0answers
44 views

Simplification of (Co)sine of a sum

I have a huge expression with (Co)Sine of a sum like Cos[[Theta] - 2 [Phi]] (after using \Simplify). I wanted to know if it exists a function which forces Mathematica to express the result in terms of ...
0
votes
0answers
48 views

Symbolic manipulation of the moments of an unknown distribution

I'm curious as to whether it's possible to get Mathematica to simplify/manipulate/expand basic expectations, conditional expectations, sums of random variables, etc. A simple example might be: ...
0
votes
0answers
45 views

Can you tell (Full)Simplify to introduce a case distinction?

I got this term¹ as a partial result $\qquad\displaystyle T = -1 + (-1)^{\frac{1}{3} \cdot (1 - 2 n)} - (-1)^{\frac{2}{3} - \frac{4 n}{3}}$ which Mathematica refuses to (full)simplify further, even ...
0
votes
0answers
73 views

How to make Mathematica Simplify?

Let us define r1 = 1;r2 = 2; and ...
0
votes
0answers
69 views

Preventing numeric constants from being pulled out of square roots

If I input Sqrt[2 g], Mathematica automatically pulls out the 2 and returns Sqrt[2] Sqrt[g]. ...
0
votes
0answers
80 views

Recognizing a generalized function as zero

Consider the following expression: HeavisideTheta[x]HeavisideTheta[-x] Mathematica will not simplify it further. But $\Theta(x)\Theta(-x)$ is zero if considered ...
0
votes
0answers
109 views

Gradient from Vectors type

I'm working with Vectors type in Mathematica 9. For this purpose I use the following command: ...
0
votes
0answers
131 views

Alternate method of conjugation using replaceall

Mathematica really struggles to simplify complex conjugates of complicated expressions - even given assumptions for every symbol in the expression being real. Often times I've found that I can ...
0
votes
0answers
209 views

Solving for equilibrium distribution (symbolic) by matrix multiplication

I have a huge transition matrix (81x81). The matrix is too huge to paste here, so I store it in this notebook. (There are constraints on the symbols: $0<p_b<1$ and $0<p_g<1$. If further ...
0
votes
0answers
119 views

How to simplify really complicated symbolic expression?

I have an expression that contains Sinh[x], Cosh[x] and Sin[g], and I want to simplify it ...
0
votes
0answers
145 views

Any way to fully expand an expression of two operators?

I am looking for a way to expand a complicate expression like the follow (A o B + C o (DxE))*(D o (ExF) - ExA + A) Here o and x are the operator. I want to ...