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

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40
votes
2answers
3k views

What is the difference between a few simplification techniques?

I am trying to understand the difference between Refine, Simplify and FullSimplify, and when ...
35
votes
2answers
831 views

Why does Simplify ignore an assumption?

Here is the example: Simplify[x + y, x + y == a] Simplify[x + y, x + y == 5] Mathematica 9 output: x+y 5 I expect the ...
34
votes
4answers
2k views

Can I simplify an expression into form which uses my own definitions?

This seems like a simple thing to do, but I couldn't find anything relevant from Mathematica documentation. So suppose I have an expression: a*b/(a + a*Cos[a/b]) ...
34
votes
2answers
990 views

Is it possible to make Mathematica reformulate an expression in a more numerically stable way?

I'm writing a numerical optimization, and I'm having a problem with an expression of the form $$ e^{-t} (1+\mathrm{erf}(t)) $$ The overall shape of the function looks correct, but when $t$ is small, ...
27
votes
1answer
3k 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 ...
25
votes
3answers
874 views

Common subexpression from two expressions

I am working with some unpleasantly tedious polynomials, which need to be manipulated in various ways (integrate with respect to some variable, differentiate with respect to another). Since these ...
24
votes
1answer
513 views

A better simplification function

I am creating this question and posting an answer to it as a help for those who have problems with Mathematica simplification oddities that appear in other questions on the site. First of all, there ...
21
votes
4answers
881 views

An apparently “simple” limit?

Let $c$ and $h$ be real values. I was using Mathematica to compute the limit $(h \rightarrow \infty)$ of the following expression: $$ \frac{\left(h^2 +c^2 h^2 + \sqrt{4 h^2+\left(h^2+c^2 ...
20
votes
1answer
367 views

How can I see which transformations Simplify attempts?

The documentation for Simplify[expr] says that it performs a sequence of algebraic and other transformations on expr, and returns the simplest form it finds. How can I see which transformations it ...
20
votes
1answer
520 views

Transform Root objects into Trigonometric expressions

Consider the Root objects roots = Table[Root[-1 + 27 #1^2 - 162 #1^4 + 243 #1^6 &, i],{i,1,6}] These can be expressed in terms trigonometric functions as ...
18
votes
3answers
658 views

How can I completely ban usage of some functions in output and mandate use of others?

For example, I hate that Mathematica uses Pochhammer symbol in outputs and prefer all the expressions in Gamma function. How can ...
16
votes
2answers
893 views

Why doesn't FullSimplify drop the Re function from an expression known to be real?

For some reason Mathematica does not properly simplify this expression: ...
15
votes
1answer
190 views

How to instruct FullSimplify to assume that PossibleZeroQ returns correct result?

Sometimes I have a really huge expression that cannot be significantly simplified by FullSimplify. I would like to, so to speak, "simplify with faith" using ...
14
votes
3answers
3k 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} ...
14
votes
3answers
279 views

Why does Mathematica simplify $x/x\to1$?

If I enter x/x, I get 1. Such behavior leads to this: Simplify[D[Sqrt[x^2], x, x]] 0 ...
14
votes
1answer
345 views

How to enlarge 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 ...
14
votes
1answer
226 views

What's wrong with Simplify and FullSimplify?

I have a quite complex list of equations and inequalities I combine to a boundary condition for my cost function. After investigation of two days I found the bug (I really name it a bug!). One of my ...
13
votes
4answers
717 views

FullSimplify Over Reals Automatically

Frequently, Mathematica will produce some expression in a complicated form, with a number of unset variables. For me, it is rare that I would be interested in solutions that are generalized to both ...
13
votes
2answers
266 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}= ...
12
votes
2answers
7k views

How to specify assumptions before evaluation?

If I request mathematica evaluate an integral for me, I'll often get a more general ConditionalExpression than I want. Example : ...
12
votes
1answer
1k views

Simplify Sin[x]/x to Sinc[x]

I have an expression in the form of $\tt \frac{Sin[x]}{x}$ that I would like to simplify to the form of Sinc[x]. I've tried the ...
12
votes
2answers
581 views

Surprises simplifying simple polynomials

I came across some somewhat surprising behavior of Simplify today, on something very simple. Let's take two cubic polynomials that we know have the same value: ...
12
votes
2answers
339 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 ...
12
votes
1answer
195 views

Unable to evaluate reasonable max expression

Consider the following statement: Max[0, Sqrt[1 - Cos[4 \[Theta]]]] You'll find that Mathematica won't evaluate this, because it doesn't know the range of ...
12
votes
4answers
2k views
12
votes
2answers
790 views

Simplify assumes Boolean 1 and 0 in logical expressions

Per this chat discussion and this previous question where I encountered the strange behaviour: ...
12
votes
0answers
137 views

Why does this happen with FullSimplify? [duplicate]

It is stated at the Wolfram Documentation Center (FullSimplify/Possible Issues) that: Why and when this could happen? How to avoid it? Any patterns? Edit: As pointed out in the comments, this ...
11
votes
2answers
433 views

How to deduce a generator formula for a polynomial sequence?

Consider a polynomial sequence $\{p_n\}$ generated by some (simple) rule: $$ \begin{array}{l} p_1(x)=x \\ p_2(x)=2 x-x^2 \\ p_3(x)= x^3-3 x^2+3 x \\ p_4(x)=-x^4+4 x^3-6 x^2+4 x \\ p_5(x)= x^5-5 ...
11
votes
1answer
720 views

What is the proper way to verify that two expressions are equivalent?

First of all, it appears to me that $$\left|\frac{1}{x} + x^2\right| \Leftrightarrow \frac{|1 + x^3|}{|x|}$$ is true. I don't know why, but my attempt to verify it in Mathematica failed. ...
11
votes
1answer
167 views

Using Simplify on a consistent system returns False

Bug introduced in 8.0 and persisting through 10.2 or later It's late, but am I missing something here? Why should two independent equations, which together are consistent, ...
11
votes
1answer
228 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 ...
11
votes
1answer
778 views

How to get FullSimplify to fully simplify my expression with custom complexity function?

To simplify based on the visual complexity of an expression (i.e. the complexity of the function as displayed in the notebook instead of the internal form, which in some cases may be substantially ...
10
votes
3answers
3k 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 ...
10
votes
2answers
615 views

Shaping/simplifying equations in a certain way

A problem I am occasionally facing is to simplify an equation not to it's shortest form but to a form that is simple by other means. Often, this is grouping the term according to certain functions, ...
10
votes
4answers
7k views

Factoring polynomials to factors involving complex coefficients

I've run into some problems using Factor on polynomials with complex coefficient factors. Reading the documentation it looks like it only factors over the ...
10
votes
3answers
1k 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 ...
10
votes
1answer
311 views

Mathematica 10 unable to Simplify[Cos[2 ArcCos[A]]]

Mathematica 10 evaluates Simplify[Cos[2 ArcCos[A]]] as Cos[2 ArcCos[A]], instead of the desired ...
10
votes
1answer
255 views

How to simplify -a*z+a*z to 0 where “a” is an expression

Consider the following: a = 1+(x+y+z+u)^10000 (* Out[57]= 1+(u+x+y+z)^10000 *) e = -a*z+a*z (* Out[59]= z (-1-(u+x+y+z)^10000)+z (1+(u+x+y+z)^10000) *) How can ...
10
votes
1answer
769 views

Is my expression too complicated for FullSimplify or am I doing something wrong?

I have a messily defined function $v(h, w)$ with $h, w \in \mathbb{R}$ and with a removable singularity at $h=1/2$, and I am trying to prove some of its properties using Mathematica. In particular I ...
10
votes
3answers
3k views

Strategies for simplifying complicated expressions

I have a very complicated expression involving trigonometric functions, complex numbers etc. You may find it here as it is too long to be pasted here. You may also find a screenshot of it here. ...
10
votes
1answer
132 views

FullSimplify wrongly reduces expression to zero

I get the following output with a fresh Mathematica (ver 10.0.2.0 on Mac) session ...
10
votes
1answer
267 views

Cancellation of common terms

Can someone explain why the term A in case 2 does not get canceled out when case 1 does? I use "9.0 for Microsoft Windows (64-bit) (January 25, 2013)" ...
10
votes
3answers
964 views

Simplifying trig expressions containing Sqrt or Abs

The following Maple code can simplify abs(sin(x)) into -sin(x) given the condition ...
10
votes
0answers
266 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 ...
9
votes
2answers
662 views

Why aren't these additions of integrals and summations equal?

I have the following code: Simplify[Integrate[f[x] + g[x], x] == Integrate[f[x], x] + Integrate[g[x], x]] To test: $$\int{\left(f(x) + ...
9
votes
3answers
1k views

Why does Simplify[b-a] give -a+b and not b-a?

Simplify[b - a] results in -a + b. I prefer b - a, which is a bit simpler (3 symbols instead ...
9
votes
2answers
572 views

Memory leak issues

I am working with noncommuting objects and basically I am using Mathematica to sort large expressions by normal ordering and simplifying them. To this end, I first create an object called ...
9
votes
1answer
97 views

FullSimplify Produces Result that Includes Hold

Bug fixed in 10.2.0 In the course of developing a solution to Question 79183, I solved the equation ...
9
votes
1answer
672 views

how to simplify large expression with lots of special functions in it (BesselY, Hypergeometric, MeijerG etc…)

I saw this DE in Maple forum. When solving it using Mathematica 9.01, even though the result was correct (both solutions gave the same numerical answer for some random values), Mathematica's answer ...
9
votes
0answers
119 views

Why is this evaluation halved when adding units?

Why does this strange behavior occur when dealing with units and quantities? ...