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

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4
votes
2answers
144 views

HornerForm of polynomials in terms of E^(i x)

I want to know how to get the HornerForm of the following expression in terms of E^(I x): ...
7
votes
1answer
208 views

Limit for Matrix expression

Let's assume that $Q_0$ is $3\times 3$ matrix with $\det Q_0\neq0 $ and $$ Q_{i+1} = \frac{1}{2}\left[ Q_i+(Q_i^{-1})^T \right] $$ I need to find next limit: $\lim _{i \to +\infty}$$Q_i$. In other ...
1
vote
0answers
79 views

Introducing new variables implicitly [duplicate]

I have a calculation expr111 = cs[giso, xiso, 1, 1, 1] that gives the result -((k x)/(2 (1 + 1/4 k (x^2 + y^2 + z^2)))) ...
0
votes
0answers
30 views

Find repeated groups in a long algebraic expression [duplicate]

I have an algebraic output (a solution to a de) similar to, but far longer than: {y->(x+3)^2/sin(7*(x+3))+(x+3)^3/7} I'd like to get Mathematica to notice that the group x+3 appears repeatedly, ...
7
votes
3answers
195 views

Why does Mathematica not seem to know that $i^x$ cannot be equal to $0$?

I am experiencing a curious behaviour of Simplify when handling expressions involving powers of $\mathbf{i}$, such as $\mathbf{i}^x$ where $x$ is unknown. For ...
1
vote
1answer
133 views

Mathematica won't simplify multiplication by zero

I'm getting a huge output, but it appears that almost every term should actually be zero, unless I'm misunderstanding the expression. For example, part of the output reads ...
2
votes
1answer
97 views

Evaluating Abs'[2 x] gives different results than evaluating D[Abs[2 x], x]

I noticed the following difference Assuming[x ∈ Reals, FullSimplify[D[Abs[2 x], x]]] (* 2 Sign[x] *) Assuming[x ∈ Reals, FullSimplify[Abs'[2 x]]] (* Sign[x] *) ...
0
votes
1answer
121 views

Convert expression to C-form and simplifying

I have an expression which is the sum of many terms of the form $$ \frac{0.00000000274341}{(0.000363856+(0.611425+z)^2)^{3/2}} $$ My problem is that I need to include this long expression in a ...
1
vote
1answer
111 views

Assumptions in mathematica when Symplify on Log[Exp[a/b]]

In mathematica 9.0: This: Assuming[b > 0 || b < 0, Simplify[Log[Exp[a/b]]]] yields: a/b However, this: ...
0
votes
1answer
125 views

Simplify expression after substitution

I tried to substitue variable x of one equation with another variable z (z=nx/(nx+m)). See as follow: ...
3
votes
1answer
139 views

FullSimplify yielding different results in mathematica 8 and 9

I have been experiencing some problems running a certain mathematica file in version 9. I've tracked the problem to a particular sum that I perform. Running the same code in version 8 and 9 I get two ...
7
votes
2answers
2k views

Fourier Transform of a Step Function

I'm trying to obtain the form of a sinc function that I know I'm supposed to get in Mathematica. I'm doing this because I intend to do a lot with Fourier transforms (FT) and I'd like to know I'm not ...
0
votes
1answer
144 views

Why does Mathematica find a form for this general sum, but not for some special cases?

Today I found a Sum which Mathematica will simplify for a general parameter value $\nu$, but which will not simplify fully for special cases $\nu = 1, 3, ...$ despite the fact that the general answer ...
2
votes
2answers
123 views

Transform Piecewise[] into sum of indicators

I'm interested in transforming a piecewise defined function into a sum of indicator functions, ultimately with the aim to be better able to integrate them. As an example I would like to transform the ...
12
votes
1answer
250 views

How to enlarge $\it{Mathematica}$'s knowledge about certain functions?

I'm often troubled with the following task. I need to carry out symbolical computations involving certain special functions. Let me take as an example Barnes gamma-function. It is included in ...
6
votes
1answer
146 views

Forcing Mathematica to use certain simplification rule

I'm trying to force Mathematica to use following transformation function ...
1
vote
1answer
152 views

Simplifying with noncommutative multiplication

I am trying to do some quantum algebra computations in Mathematica. Up to now I was able to make the noncommutative multiplication linear and to factorize powers. However, I still have some issues ...
7
votes
2answers
223 views

How to automatically get rid of trig functions in an expression?

I have a large expression containing many terms like this: Sin[1/2 ArcTan[(2 Log[5])/(Log[5]^2 - 2)]] where a trig function is invoked on a rational multiple ...
8
votes
3answers
1k views

Simplify expressions with Log

How can I get Mathematica to simplify the following expression n Log[a] + m Log[b] - m Log[a + b] - n Log[a + b] into ...
3
votes
2answers
214 views

Simplifying expressions involving Sum

I am trying to use Mathematica to simplify a symbolic expression involving Sum. Particularly, I define a sum via ...
2
votes
1answer
449 views

How to show factorial in expanded form with variables

When evaluating the following (Factorial[n + 1]/Factorial[(n + 1) - (k + 1)]) with Mathematica 9, the result is sent to output as ...
0
votes
0answers
82 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
1answer
194 views

Simplify vector expression - is there something like “Factor” for vectors, dot products etc.?

I am looking for a way to simplify dot products etc. Here is a minimal example: Lets say I have two vectors a and b: Array[a,2] Array[b,2] Now I evaluate their ...
3
votes
2answers
107 views

How to use SuperLog by loading SMLE.m

I am researching a software reliability model that has many parameters that need to be estimated. I want to use a maximum likelihood estimator (MLE) to estimate those parameters. After I searched ...
1
vote
0answers
60 views

How to take the log of an equation? [duplicate]

I am researching a software reliability model that has many parameters that need to be estimated. I want to use a maximum likelihood estimator (MLE) to estimate those parameters, but my model is too ...
1
vote
0answers
29 views

How to achieve the real component of my expression? [duplicate]

How to achieve the real component of my expression? Input: expr = Csc[θ/2] Sin[(n θ)/2] (Cos[1/2 (1 + n) θ] + I Sin[1/2 (1 + n) θ]); Re[expr] ...
1
vote
2answers
119 views

Show Simplified Directives [closed]

Is there a way to force Mathematica to convert an already rendered Graphic to the simplified Directive form of that Graphic. Background: I am currently editing Graphics using Drawing Tools and then ...
6
votes
3answers
119 views

How to simplify my expression to the style of “a+b*I”?

How to simplify my expression to the style of "a+b*I"? Expand[(E^(I θ) (-1 + E^(I n θ)))/(-1 + E^(I θ))] ...
6
votes
1answer
190 views

Simplifying a trigonometric sum

I want to caculate Cos[θ] + Cos[2 θ]+ ... + Cos[n θ] Sum[Cos[k θ], {k, 1, n}] ...
8
votes
2answers
146 views

How to reduce the number of operations needed to evaluate an expression? [duplicate]

For some numerical calculations in C++ I have, for example, this complicated expression to evaluate. Given as Mathematica input, in its original form it is ...
5
votes
2answers
186 views

How to find monotonically increasing intervals of a function

I tried this code, but not working Clear[f]; f[x_] := x^3 - 3 x + 2; ForAll[{x1, x2}, x1 < x2, f[x1] < f[x2]] Reduce[%, {x1, x2}, Reals] I expected the ...
4
votes
1answer
150 views

Can't simplify Abs[a*Cos[x]]^2

Why doesn't FullSimplify[ Abs[a*Cos[x]]^2, Assumptions -> {{a, x} ∈ Reals}] simplify to (a*Cos[x])^2 but this query ...
1
vote
0answers
98 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, ...
5
votes
3answers
252 views

Removing Abs from Abs[a + Exp[I*c]b]^2

Title says it all. Mathematica produces sometimes expressions of the form Abs[a + Exp[I*c]b]^2 where all three quantities a, b and c are positive real numbers. ...
0
votes
0answers
90 views

Simplifying tedious expression

I have the following output in Mathematica I'd like to simplify, but using Simplify[] and FullSimplify[] got me nowhere. ...
1
vote
1answer
111 views

Collect and simplify both the coefficents and the matched patterns

(This is a far tighter version of a previous question I asked) The problem with Collect is that while Collect[exp, pattern, Simplify] will simplify the ...
1
vote
0answers
93 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 ...
7
votes
5answers
427 views

How to cancel a common term from numerator and denominator?

What mathematica commands are needed to simplify $\frac{x+n x^m}{x(1+x)}$ to $\frac{1+n x^{m-1}}{(1+x)}$ ? ...
5
votes
0answers
88 views

Moles/Liters doesn't get simplified to Molar even though Molar*Liters gets simplified to Moles

Why can't Mathematica 9 simplify mol/L to M, when it can simplify M*L to mol? ...
2
votes
0answers
57 views

Simplifying a quadratic [duplicate]

I have a general query about simplifying expressions in Mathematica, which I will illustrate using quadratics. If I tell Mathematica to simplify $a x^2 + b x + c$ then ...
0
votes
1answer
333 views

How to simplify Sqrt[1/x] Sqrt[x]?

In my expression, there appear terms of the form A^(B Sqrt[1/C] Sqrt[C]). Mathematica doesn't realize that this is just simply ...
7
votes
1answer
135 views

Why does Mathematica not simplify the Gudermannian function?

The Gudermannian function is built into Mathematica, but does not reduce to simpler terms in some simple cases. In particular, the Gudermannian is an odd function of real arguments but Mathematica ...
7
votes
1answer
180 views

Why does Simplify with TimeConstraint return Removed[$$Failure]?

I have a rather ugly Mathematica expression (edit: shown below) that I would like to simplify with a time constraint; simplifying without a time constraint or memory constraint does not return as long ...
2
votes
1answer
169 views

How to select TransformationFunctions based on Assumptions made when using Simplify?

I am re-writing the question using a very simple example so not to confuse matters with the another question being asked where I used the example from there. In general, how to add logic to switch ...
2
votes
1answer
100 views

How to use TransformationFunctions on a compound expression?

I was trying to answer this question but having hard time with the correct way to write the transformation rule. Trying to write a rule to transform ...
5
votes
3answers
705 views

Combining Cos[ ] terms

A function that is the sum of two Cosine terms of the same frequency x[t_] := a1 Cos[w0 t + b1] + a2 Cos[w0 t + b2]; can be simplified to a single ...
4
votes
4answers
571 views

Simplifying a trigonometric expression

I'm sure this has been addressed before, but I can't find it! I want Mathematica to simplify Sqrt[1 - Sin[π/6 - θ]^2] to ...
3
votes
2answers
199 views

Replacing gamma at half integers by double factorial

It is well-known that for any positive integer $n$ the equality $\Gamma(n+\frac12)=\sqrt\pi\,(2n-1)!!/2^n$ holds, where $!!$ stands for the double factorial. I am using ...
0
votes
1answer
163 views

Pull Constants outside of integrals

I would like Mathematica to pull constants outside of an integral: e.g., $\int_0^t f[t] g[s] dt \to g[s] \int_0^t f[t] dt$ This has previously been discussed at replacement rule to pull independent ...
0
votes
0answers
100 views

Simplify function with normalized vector

I made a very simple case: testF[x_, y_, z_] = x^2 + y^2 + z^2 Simplify[testF[x, y, z]] If {x, y, z} is normalized, the simplified result should just be 1. How ...