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

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0
votes
1answer
194 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
167 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
188 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
170 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
287 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
245 views

Forcing Mathematica to use certain simplification rule

I'm trying to force Mathematica to use following transformation function ...
1
vote
1answer
247 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
401 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 ...
9
votes
3answers
2k 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
261 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
565 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
117 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 ...
1
vote
1answer
270 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 ...
4
votes
2answers
210 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
61 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
132 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
133 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
299 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
185 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
274 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
184 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
143 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
462 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. ...
1
vote
0answers
140 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
709 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 $\frac{1+n x^{m-1}}{(1+x)}$ ? ...
2
votes
0answers
58 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 ...
1
vote
1answer
422 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
164 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 ...
2
votes
1answer
216 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
148 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 ...
6
votes
3answers
983 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
804 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
288 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
277 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 ...
11
votes
4answers
2k views

How do I simplify expressions with square roots?

I want $\left\{\frac{1}{1+\sqrt{2}-\sqrt{3}},\sqrt{5-2 \sqrt{6}},\sqrt{4+\sqrt{15}}\right\}$ to be simplified to $\left\{\frac{1}{4} \left(2+\sqrt{2}+\sqrt{6}\right), \sqrt{3}-\sqrt{2}, \frac{1}{2} ...
1
vote
2answers
919 views

Simplifying expressions with square roots

I would like Mathematica to simplify this expression: $4 \left(16 \sqrt{\left(-1+2 c^2\right)^2}-32 c^2 \sqrt{\left(-1+2 c^2\right)^2}+\sqrt{\left(1-8 c^2+8 c^4\right)^2}\right)^2$ ...
3
votes
2answers
690 views

Eliminate doesn't work in Mathematica

Hello Mathematica users, I have problems trying to eliminate variable $Q(x,y)$ froma PDE, but Mathematica output is just True. The problem is that I already found ...
1
vote
1answer
172 views

How can I eliminate $x_1$ from my two ODEs?

How can I get Mathematica to eliminate $x_1$ in the equations in the first box to achieve the equation in the second box? My code: ...
3
votes
1answer
565 views

Simplifying an ArcTan expression

The expression $\tan ^{-1}\left(\frac{\sqrt{L^2 \sin ^2(\theta )}}{\sqrt{L^2 \cos ^2(\theta )}}\right)$ can be simplified to $\theta$. After some attempts I got the following to do the job. ...
0
votes
1answer
293 views

Simplify equations using list of rules

I have a set of equations that I want to simplify using a list of rules: ...
0
votes
2answers
113 views

How can I transform a quadratic into an factored equation?

How can I transform a quadratic polynomial in x and y into an equation of the form $(x-a)^2+(y-b)^2=c$? f = -9 x + (3 x^2)/4 + (3 y^2)/4; Completing the Square ...
0
votes
3answers
207 views

Conjugate and simplify

I want to get a cosine from taking the real part of a complex exponential: $cos(x) = Re(exp(i x))$. What I do in Mathematica is ...
2
votes
2answers
192 views

Simplifying expression to evaluate limit as $y\rightarrow 0$

I often end up with a function that contains the term $1/(1 + x^2/y^2)$, and I need to evaluate this in the limit $y\rightarrow 0$. By hand, I can rewrite this as $y^2/(y^2 + x^2)$, but how can I tell ...
1
vote
0answers
81 views

How can I get Mathematica to simplify my square root expression? [duplicate]

$$\sqrt{r^2 e^{4 \gamma (r)-4 \psi (r)}}$$ If I set var = r^2*E^(4 \[Gamma][r] - 4 \[Psi][r]) Simplify[Sqrt[var], var > 0] I just get $$\left| r\right| ...
1
vote
2answers
190 views

Set all instances of Exp[-x_] to zero?

To simplify a huge expression efficiently, which involves a variable in a bunch of exponential functions going to infinity, I have tried to substitute ...
11
votes
1answer
186 views

What are the default TransformationFunctions used in Simplify and FullSimplify?

If I do Simplify[(c^3 - s^3)^2 - (s^3 + c^3)^2, TransformationFunctions -> Automatic] (i.e. a verbose version of default behaviour), what transformation ...