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

learn more… | top users | synonyms (3)

40
votes
4answers
3k 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]) ...
27
votes
3answers
1k 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 ...
12
votes
2answers
10k 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 : ...
40
votes
2answers
1k 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 ...
11
votes
4answers
9k 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 ...
9
votes
2answers
757 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) + ...
58
votes
5answers
2k views

Advice for Mathematica as Mathematician's Aid

I use Mathematica mainly as an aid in symbolic attacks on problems, usually intermediate or harder and often number theoretic. While Reduce, ...
46
votes
2answers
5k views

What is the difference between a few simplification techniques?

I am trying to understand the difference between Refine, Simplify and FullSimplify, and when ...
23
votes
1answer
2k views

A one line proof that one is zero using Mathematica 10

a = (Sqrt[2] + 1) (Sqrt[2] - 1) - 1; {a/a, Simplify[a]/a, b/b == Simplify[b]/b} {1, 0, True} This one line "proof" that ...
11
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 ...
14
votes
2answers
497 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 ...
19
votes
3answers
785 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
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} ...
8
votes
3answers
813 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 ...
2
votes
2answers
2k views

Simplifying expressions with square roots

I would like Mathematica to simplify this expression: $4 \left(16 \sqrt{\left(-1+2 c^2\right)^2}-32 c^2 \sqrt{\left(-1+2 c^2\right)^2}+\sqrt{\left(1-8 c^2+8 c^4\right)^2}\right)^2$ ...
14
votes
1answer
1k 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. ...
9
votes
2answers
4k views

Remove annoying Conjugate

Here is an expression ...
4
votes
2answers
591 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 ...
4
votes
1answer
354 views

Using Hold correctly with Simplify and ComplexityFunction

It seems like Mathematica immediately evaluates the expression Sqrt@I to (-1)^(1/4). I'm trying to use ...
4
votes
1answer
886 views

Reduce an equation by putting a new variable

I have the following equation given: $$ (26-x)\cdot\sqrt{5x-1} -(13x+14)\cdot\sqrt{5-2x} + 12\sqrt{(5x-1)\cdot(5-2x) }= 18x+32. $$ In order to solve it, I want to substitute $t = \sqrt{5x - ...
25
votes
4answers
410 views

FullSimplify wrongly reduces expression to zero

Bug introduced in 9.0 and persisting through 10.4 I get the following output with a fresh Mathematica (ver 10.0.2.0 on Mac) session ...
10
votes
1answer
260 views

How to prevent simplification?

I have a question about the concept of simplification. I want to explain it with an example. When I write $4/8$ in mathematica, output is 1/2. How can I return ...
9
votes
2answers
4k 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 ...
4
votes
2answers
420 views

How can I simplify $\log(512)$ to $9\log(2)$?

Can you explain me about the result of Integrate. ...
3
votes
3answers
450 views

Fullsimplify does not simplify Abs'[1.-a]

I have to simplyfy an expression involving Abs' This works: FullSimplify[Abs'[1 - a], a ∈ Reals] Sign[1 - a] but this ...
17
votes
2answers
1k 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: ...
11
votes
3answers
4k 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 ...
8
votes
4answers
591 views

Counting multiplications (complexity function)

I'm trying to count the number of times multiplication appears in an expression (for the purpose of constructing a ComplexityFunction that would help me simplify a terrible algebraic expression for ...
2
votes
1answer
270 views

Simplify expression to Abs

FullSimplify[Sqrt[1/(a^2 b^2)], Element[{a, b}, Reals]] gives Abs[1/(a b)] How do I simplify the following expression ...
13
votes
3answers
2k 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 ...
8
votes
2answers
917 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 ...
4
votes
2answers
183 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): ...
3
votes
1answer
293 views

Separating exponential terms

Suppose I have a lot of expressions multiplied by factors such as: $$e^{-i\theta[1]-i\theta[2] - i\theta[3]-i\theta[4]-i\theta[5]}$$ I would like to separate this into a product of exponentials of ...
6
votes
3answers
268 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 ...
3
votes
1answer
370 views

What's the correct method to simplify exponentials?

I have a sum of exponentials that I'd like to simplify. The issue is when I use Simplify, Mathematica loves to factor out one exponential factor. See below: $$e^{-i ...
7
votes
4answers
273 views

How do I invoke the default complexity function?

Documentation on ComplexityFunction says: With the default setting ComplexityFunction->Automatic, forms are ranked ...
5
votes
3answers
1k 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
432 views

Simplifying the trace of a matrix expression

I have a long expression involving matrices that I derived using the NCAlgebra package. Can I simplify the trace of the expression? For example, say b is a scalar ...
8
votes
2answers
470 views

How can I get $(r^{1/x})^x$ to simplify to $r$?

Simplify and FullSimplify do not simplify this kind of expression: $(r^\frac{1}{x})^x$. Consider ...
8
votes
4answers
4k views

Checking if two trigonometric expressions are equal

Say I have two trigonometric expressions which are a bit complicated. Is there a quick way to check if they reduce to the same thing (that they are equal) using Mathematica? I was solving this: $y'' ...
4
votes
1answer
779 views

Does the Im function work with symbolic arguments?

Does the Im function work with symbolic arguments? ...
2
votes
1answer
96 views

Arrange equation in normal form

Is there a way, or if not, how could one define a function which takes an equation in any form (for example as given by FullSimplify): $$(A+X_0) x+By=3x$$ and ...
2
votes
1answer
192 views

FullSimplify wont simplify to expression with lower SimplifyCount

I have been trying without success to get FullSimplify to work on some trigonometric expressions. It refuses to convert them to forms that are clearly much ...
21
votes
1answer
435 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 ...
22
votes
1answer
578 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 ...
9
votes
1answer
342 views

Expanding derivatives of hypergeometric functions

Sometimes Mathematica expresses results of integration or summation in terms of symbolic derivatives of Hypergeometric2F1 function, and cannot further simplify ...
13
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 ...
9
votes
2answers
291 views

How to simplify an expression with special functions to zero

The following is a well-known Bessel function identity: $$J_{-n}(z)=(-1)^n J_n(z),\qquad n\in\mathbb Z$$ To check this, I used the following code and the result is as what I expected. ...
5
votes
2answers
2k 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 ...
8
votes
2answers
894 views

a problem about simplifing conjugate

the situation is as follows ...