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

learn more… | top users | synonyms (3)

1
vote
1answer
93 views

Expansion of Expression

I am trying to expand out expressions that have several terms similar to E[-lH] Sinh[l (H - h)] The Expand command just gives ...
6
votes
2answers
336 views

Simplify Binomial Function

The following input ...
20
votes
1answer
307 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 ...
7
votes
3answers
457 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: ...
5
votes
2answers
435 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: ...
7
votes
2answers
183 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
0answers
247 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 ...
3
votes
1answer
334 views

How to implement Condition programmatically?

I am writing my own symbolic functions with custom symbolic properties. So often I wish to introduce some automatic simplifications or evaluations, which return the same head as it's argument. This ...
1
vote
0answers
232 views

Can mathematica simplify an expression setting simplified answer equal to zero?

Basically I want to reduce something like: Subscript[P, 4] - Subscript[P, 5] == Subscript[R, 4, 5]* Subscript[i, 4, 5] when only one of them is known (...
3
votes
0answers
147 views

Why doesn't Log[Gamma[]] simplify to LogGamma[] where it could?

I have been playing with various equations involving amount of permutations in relatively large sets. Easiest way to look at these is something like Log[10, bignumber!] . Often expressions, even ...
12
votes
4answers
1k views
3
votes
1answer
500 views

Don't simplify an expression

I have an expression that I want Mathematica to fully expand without any simplification afterwards. I want the output to look like the following example. ...
7
votes
2answers
372 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 ...
10
votes
1answer
549 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 ...
12
votes
1answer
173 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 ...
1
vote
2answers
351 views

Replacing variable in an equation with an Interpolating function polynomial and plotting residual

I was trying to plot the residual for the solution of my PDE. However, I was unsure about a couple of things. I imported the data and created an Interpolation polynomial with ...
4
votes
1answer
645 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 - ...
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 ...
3
votes
3answers
415 views

How to simplify the following trigonometry expression such that the number of used characters is minimal?

How to simplify the following trigonometry expression such that the number of used characters is minimal? (13*Cos[t] - 5*Cos[2*t] - 2*Cos[3*t] - Cos[4*t])/4 The ...
5
votes
2answers
595 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 ...
7
votes
1answer
279 views

RootSum result manipulation/simplification

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

simplifying equations [closed]

I have a question that seems easy but I can't solve it. I have an equation like: eqgama = -8.33208*10^56 g1 + 8.18264*10^56 g1^2 == -1.42093*10^56 I use the ...
3
votes
1answer
290 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 ...
8
votes
2answers
518 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) + ...
8
votes
4answers
5k 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 ...
1
vote
1answer
214 views

Inequality of reciprocal functions

Simplify[1/(1/a + 1/b)] { (a b)/(a + b) } That doesn't look right. The given function has an infinite term for a = 0 and one ...
7
votes
2answers
551 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
2answers
565 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] *) ...
5
votes
2answers
233 views

Inequality with assumptions not simplifying

Can someone explain to me why the following does not simplify to True (as all constituents are positive)? ...
3
votes
2answers
261 views
7
votes
4answers
2k 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'' ...
6
votes
1answer
546 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
153 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 ...
4
votes
1answer
266 views

Checking if an Expression Falls within a Range

Is there a simple way in Mathematica to check under what conditions an expression (involving multiple variables) falls within a given range? For example, say I had a real-valued function f(x,y,z), ...
3
votes
2answers
606 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 ...
2
votes
2answers
508 views

How do I make Mathematica understand roots of unity?

Try the following: z = Exp[2 \[Pi] I / 5] Z = { { z, 1 }, { 0, 1/z } } Simplify[MatrixPower[Z, 5]] //MatrixForm Of course, this should return a 2 x 2 identity ...
4
votes
2answers
207 views

How to expand all portions of an expression?

Consider a toy expression: expr = Sin[x (a + b)]/(y (z + c)) I would like to expand all parentheses to get something like: ...
7
votes
1answer
863 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 ...
34
votes
2answers
831 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, ...
9
votes
2answers
451 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, ...
7
votes
1answer
669 views

Simplify an expression containing NonCommutativeMultiply

How does mathematica evaluate the following expression to zero: ...
11
votes
1answer
573 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 ...
6
votes
4answers
357 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 ...
4
votes
1answer
538 views

Does the Im function work with symbolic arguments?

Does the Im function work with symbolic arguments? ...
12
votes
2answers
501 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: ...
37
votes
2answers
2k views

What is the difference between a few simplification techniques?

I am trying to understand the difference between Refine, Simplify and FullSimplify, and when ...
17
votes
3answers
535 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 ...
6
votes
1answer
683 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 ...
16
votes
2answers
693 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: ...
25
votes
4answers
1k 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]) ...