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

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7
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2answers
2k views

How do I simplify a vector expression?

I am doing vector analysis. I have figured out that the following expression won't be simplified in Mathematica: Simplify[Dot[x, y] - Dot[y, x]] I think the ...
7
votes
2answers
561 views

Simplifying the derivative of $|x|$

Context In[855]:= D[Abs[x], x] /. x -> 1 Out[855]= Derivative[1][Abs][1] In[856]:= D[x, x] /. x -> 1 Out[856]= 1 Question Why is ...
7
votes
3answers
218 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 ...
7
votes
2answers
185 views

Why isn't Simplify doing more simplification of this expression?

When I try this Simplify[(1-a)*(1/(1+x*m))^(1-a)(1+m)^(1-a) + (1-a)*(x*m)^a*((x*m)/(1+x*m))^(1-a)*(1+m)^(1-a)] the output is $$\frac{(1-a) (1+m)^{1-a} ...
7
votes
2answers
254 views

FullSimplify giving unexpected result

When I perform a FullSimplify on the list $$ \left\{-\sqrt{5-2 \sqrt{6}},\sqrt{5-2 \sqrt{6}},-\sqrt{5+2 \sqrt{6}},\sqrt{5+2 \sqrt{6}}\right\} $$ I get $$ ...
7
votes
2answers
203 views

Is there a way to show the details of a numerical computation?

I have recently started using Mathematica as a calculator while teaching (definitely overkill, but I try to use as few tools as possible). I would like my students to be able to trace simple numerical ...
7
votes
2answers
135 views

How do I invoke the default complexity function?

Documentation on ComplexityFunction says: With the default setting ComplexityFunction->Automatic, forms are ranked ...
7
votes
2answers
324 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 ...
7
votes
3answers
236 views

Simplify with Assumptions Sqrt[(expr)^2]

While trying to simplify expressions in the form Sqrt[(expr)^2] when expr>0 I noticed a peculiar behavior that was not ...
7
votes
2answers
169 views

Behavior of Reduce with variables as domain

When using Reduce, I accidentally put a set of variables as the domain. To my surprise, it not only seems that Reduce expects ...
7
votes
3answers
497 views

FullSimplify does not work on this expression with no unknowns

I can't reproduce this simple example from Habrat, 2010 ("Mathematica : a Problem-Centered Approach"). It is supposed to demonstrate the functionality of ...
7
votes
1answer
708 views

Simplify an expression containing NonCommutativeMultiply

How does mathematica evaluate the following expression to zero: ...
7
votes
1answer
154 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
274 views

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

Bug existed in version 7 and is fixed in version 10.0.0 I have a rather ugly Mathematica expression (edit: shown below) that I would like to simplify with a time constraint; simplifying without a ...
7
votes
1answer
295 views

RootSum result manipulation/simplification

Consider the sum sum1 = Sum[ k/( k^7 - 2 k + 3), {k, Infinity}] ...
7
votes
1answer
916 views

Assumptions on unknown functions

I'm trying to do analytic calculations in a quantum mechanic harmonic oscillator basis. Specifically I want to be able to evaluate functions of the many particle density. I define the following ...
7
votes
1answer
227 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 ...
7
votes
1answer
204 views

Why does simplification in Mathematica depend on variable names

Mathematica fails to put the following into an obvious simplest form: ...
7
votes
0answers
256 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
2answers
357 views

Simplify Binomial Function

The following input ...
6
votes
4answers
372 views

Attaching persistent assumptions to symbol definition

Is it possible to attach assumptions to a symbol? This relates to this question. Most of my work involves physical equations, i.e. there are basic assumptions on variables that will always hold true ...
6
votes
2answers
117 views

Partial result of aborted evaluation of FullSimplify

When FullSimplify invoked on a large expression, it can run for hours. If I do not have time to wait, and abort the evaluation, I get no result, although, ...
6
votes
3answers
131 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
3answers
914 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 ...
6
votes
1answer
784 views

Simplify $\cos(n \pi)$ and $\sin(n \pi)$ when n is an integer

I was trying to calculate this integral in Mathematica 9: 2/π Integrate[ Cosh[a x] Cos[n x], {x, 0, π}, Assumptions -> n ∈ Integers] I got as a result : ...
6
votes
1answer
569 views

How to Simplify equations over a Ring with Mathematica?

For example, when we work over a ring, the equation x^3=0 does not imply x^2=0 or x=0, but ...
6
votes
1answer
155 views

How to reduce expressions with complex coefficients in the form of a+0.*I

I'm trying to get an eigenvalue equation in Mathematica, and the result is an expression with coefficients of the form a + 0. I. For example, Is there any clever ...
6
votes
1answer
124 views

Is there a version of Together that doesn't cancel common factors?

I'm running code that produces a long combination of rational functions with free constants that need to be tuned such that the combination vanishes. My current method is to put the combination over ...
6
votes
1answer
247 views

Simplifying a trigonometric sum

I want to caculate Cos[θ] + Cos[2 θ]+ ... + Cos[n θ] Sum[Cos[k θ], {k, 1, n}] ...
6
votes
1answer
803 views

Properly Force Mathematica to Simplify Log Expressions/Rules

I want to be able to expand $\log(x^n e^x) = n \log(x) +x$: FullSimplify[Log[x^n Exp[x]], x > 0 && Element[n, Integers] && n > 1] yields ...
6
votes
1answer
200 views

Simplify with TransformationFunctions, Bug?

I want to use custom transformation functions in Simplify, but mathematica does not seem to use them properly. Consider the following ...
6
votes
1answer
221 views

Forcing Mathematica to use certain simplification rule

I'm trying to force Mathematica to use following transformation function ...
6
votes
1answer
696 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
2answers
182 views

Simplify 2D polyhedral Regions like Interval

I don't think there's a built in "RegionSimplify" for polyhedral Regions and derived akin to how Interval automatically simplifies its argument expression: ...
6
votes
1answer
124 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
147 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
2answers
353 views

Simplify — is this simplest result Mathematica can provide?

I have a question about Simplify: When I do a simplification the returned result is not as simple as I want. When I ask for the Norm of an complex expression, ...
5
votes
3answers
388 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. ...
5
votes
2answers
238 views

Inequality with assumptions not simplifying

Can someone explain to me why the following does not simplify to True (as all constituents are positive)? ...
5
votes
1answer
240 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
2answers
231 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 ...
5
votes
2answers
256 views

on simplifying an expression

After some integration process, I ended up with the following expression: ...
5
votes
2answers
452 views

Replacements/Substitutions in Mathematica

I am a new user of Mathematica and have some questions about the simplifications of calculated expressions. I am unable to attach an image of the session, but my Mathematica commands are: ...
5
votes
2answers
636 views

How to group the powers of one variable?

Consider the following expression: $\sqrt{a x} \sqrt{b x}$ What do I use to make it simplify to: $\sqrt{ab} x$ I tried actually everything (Simplify, FullSimplify, Collect and so on...) and such ...
5
votes
3answers
170 views

Converting expressions to “edges” for use in TreePlot, Graph

This question is similar to this: Nested list to graph. How to "flatten" an arbitrary expression, eg expr = a[b[c, d[e][f], g], h] to a list of key-value pairs ...
5
votes
3answers
534 views

How to prevent Mathematica combining similar terms?

For example, given: x + 2 x y - x y + y I need to put it in this form: x (1 + 2 y) - y (x - 1). But Mathematica will simplify ...
5
votes
2answers
152 views

Simplifying general solutions of differential equations (driven harmonic oscillator)

Solving general differential equations in Mathematica usually leads to somewhat unsightly results. As an example, consider the solution of the driven, damped harmonic oscillator: ...
5
votes
2answers
128 views

FullSimplify inconsistent

I'm having problems using FullSimplify to simplify a differential equation. The expression is simplifying just as I would like when I express a variable ...
5
votes
2answers
920 views

Log of products to sum of logs

I have a log of products: $$\log \left(\prod _{i=1}^n \left( g(a(i,i)) \prod _{k=1}^i f(a(i,k))\right)\right)$$ That I turn into a sum of logs (I know everything involved is nice enough): $$\sum ...
5
votes
1answer
173 views

Simplification of integrals depending on a parameter [duplicate]

Assuming[Element[n, Integers], Integrate[Sin[x]*Sin[n*x],{x,0,Pi}]] returns 0, which is obviously wrong for n=1. ...