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

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3
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2answers
289 views
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1answer
141 views

Simplifying expressions using rules that span nonconsecutive terms

Suppose there is some function with the property f[x,y] f[y,x^2] / f[x^3,y] == f[2x,y] How can I simplify an arbitrary expression that contains the lhs of the ...
1
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1answer
90 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 ...
20
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1answer
282 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 ...
6
votes
3answers
419 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
391 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
177 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} ...
6
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1answer
643 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
0answers
213 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
2answers
349 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 ...
3
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1answer
318 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
221 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
143 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 ...
3
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1answer
425 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. ...
4
votes
1answer
592 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 - ...
10
votes
1answer
455 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
168 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
298 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 ...
17
votes
3answers
491 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 ...
3
votes
3answers
371 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
488 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
254 views

RootSum result manipulation/simplification

Consider the sum sum1 = Sum[ k/( k^7 - 2 k + 3), {k, Infinity}] ...
11
votes
2answers
3k 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 : ...
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1answer
363 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
275 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
2answers
470 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) + ...
1
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1answer
201 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 ...
5
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2answers
219 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
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2answers
487 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] *) ...
11
votes
1answer
491 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
1answer
492 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
143 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 ...
35
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 ...
4
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1answer
240 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), ...
2
votes
2answers
450 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
191 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: ...
34
votes
2answers
755 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
384 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
584 views

Simplify an expression containing NonCommutativeMultiply

How does mathematica evaluate the following expression to zero: ...
5
votes
1answer
234 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, ...
6
votes
4answers
324 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 ...
12
votes
2answers
468 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: ...
16
votes
2answers
636 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: ...
10
votes
3answers
2k 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. ...