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

learn more… | top users | synonyms (3)

10
votes
1answer
123 views

Use of some functions of the Developer Utility Package, such as BesselSimplify

The Developer Utilities Package contains several functions that look interesting: BesselSimplify GammaSimplify ...
10
votes
1answer
332 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
1k views

Simplifying trig expressions containing Sqrt or Abs

The following Maple code can simplify abs(sin(x)) into -sin(x) given the condition ...
9
votes
2answers
752 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
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 ...
9
votes
2answers
4k views

Remove annoying Conjugate

Here is an expression ...
9
votes
2answers
609 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
1k views

Simplify an expression containing NonCommutativeMultiply

How does mathematica evaluate the following expression to zero: ...
9
votes
1answer
334 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 ...
9
votes
1answer
113 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
861 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
1answer
82 views

Problem with simplification KroneckerDelta

Bug introduced in 8.0 or earlier and fixed in 9.0 I have: ...
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'' ...
8
votes
4answers
577 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 ...
8
votes
2answers
466 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
3answers
662 views

Sum over binary digits of integer

This might seem like a simple enough question but Mathematica seems to simplify inadequately here: How would you sum over the digits of an arbitrary binary number? I already tried this: ...
8
votes
4answers
398 views

How to make Mathematica simplify $\cos[(i + j + k)\pi]$ to $(-1)^{i+j+k}$?

We know that: $$ \cos\left[(i+j+k)\pi\right] = (-1)^{i+j+k} $$ for $i, j, k$ being positive integers. In Mathematica I've tried: ...
8
votes
2answers
811 views

How can I get Mathematica to simplify $\Vert\{1,\sin(t),\cos(t)\}\Vert_2$ to $\sqrt{2}$?

Context Norm[{1, Sin[t], Cos[t]}] Norm[{1, Sin[t], Cos[t]}] // Simplify (* Sqrt[1 + Abs[Cos[t]]^2 + Abs[Sin[t]]^2] Sqrt[1 + Abs[Cos[t]]^2 + Abs[Sin[t]]^2] *) ...
8
votes
2answers
288 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. ...
8
votes
2answers
895 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 ...
8
votes
3answers
399 views

Getting rid of 0. in middle of expression [duplicate]

Say I have the following expression: 0.355329 + 0.355329 Cos[0.445723 u + (0. + 0.445723 I) v] How can I simplify it so that the expression is simplified to ...
8
votes
2answers
282 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 ...
8
votes
2answers
339 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 $$ ...
8
votes
2answers
131 views

Collect/Factor a fraction

Is there a way to tell Mathematica to factor things only containing a specific combination of a fraction, example: $$\tag{1}f = \frac{a+m\cdot a+b+n\cdot b+c+k\cdot c+d+e}{ab}$$ Is there a way to ...
8
votes
3answers
799 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 ...
8
votes
1answer
2k 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 ...
8
votes
2answers
874 views

a problem about simplifing conjugate

the situation is as follows ...
8
votes
1answer
96 views

evaluation of the sum of KroneckerDelta

I need help. I need to know why the next code doesn't simplify in Mathematica 10 but it does in Mathematica 8. I need some similar in version 10. What can I do? ...
8
votes
1answer
581 views

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

Bug introduced in 7.0 or earlier and fixed in 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 time ...
8
votes
1answer
973 views

Why doesn't FullSimplify get rid of the common factor in this expression?

FullSimplify does not get rid of the z factor in the following expression: ...
8
votes
1answer
478 views

RootSum result manipulation/simplification

Consider the sum sum1 = Sum[ k/( k^7 - 2 k + 3), {k, Infinity}] ...
8
votes
1answer
1k 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 ...
8
votes
1answer
259 views

Why does simplification in Mathematica depend on variable names

Mathematica fails to put the following into an obvious simplest form: ...
8
votes
0answers
385 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 ...
7
votes
5answers
1k 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 $\frac{1+n x^{m-1}}{(1+x)}$ ? ...
7
votes
4answers
271 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
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 ...
7
votes
3answers
258 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
216 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
211 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
4answers
537 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 ...
7
votes
3answers
620 views

Problems using hand-made transformation functions

I experience difficulties when using custom transformation rules. Below I give two concrete problems. I am interested in fixing each of them and in understanding what is wrong with my attitude to the ...
7
votes
2answers
707 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
6k views

Mathematica not simplifying square root expressions even with assumptions

I have the following expression: expr=(Sqrt[2]r Sqrt[(4+r^2) (2+r (r+Sqrt[4+r^2]))])/(4+r (r+Sqrt[4+r^2])) Then ...
7
votes
1answer
107 views

Rationalizing a numerator

My goal was to remove the radical from the numerator of the function: $$f(x)=\frac{\sqrt{x^2+9}-3}{x^2}$$ I first entered my function. ...
7
votes
3answers
341 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
1answer
871 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 ...
7
votes
1answer
214 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
2answers
105 views

Simplify expression to Integer

I have the following function: f[n_]:=(n-1) E Gamma[n,1]; I know that this expression always evaluates to an Integer, but Mathematica doesn't always output the ...
7
votes
1answer
145 views

Why don't 1. (0. + a) or (0. + 1. a) simplify?

I'm handling some mixed-numeric-analytic expressions, and I feel I'm missing some subtleties of how Mathematica handles simplification of such expressions. In particular, I was initially puzzled by ...