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

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4
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1answer
539 views

Checking if an expression is equal to zero

I have 6 points in $\mathbb R^3$ as follows: ...
4
votes
2answers
123 views

Why doesn't FullSimplify find simpler expression given a set of transformation rules?

I've defined a set of rules, which I want to use with FullSimplify, as follows: ...
4
votes
2answers
327 views

Cleaning up InverseLaplaceTransforms in Mathematica

I am attempting to use Mathematica to model an electrical circuit in the s domain. The circuit contains capacitances and and inductances. I've written a series of equations using Kirchoff's laws to ...
4
votes
2answers
289 views

Calculate information entropy integral in infinite square well problem

In the context of information theory, entropy is a measure of uncertainty of a random variable. In quantum mechanics, the uncertainty principle states that $\Delta x\Delta k \ge 1/2$. The same can be ...
4
votes
2answers
415 views

How to use SuperLog by loading SMLE.m

I am researching a software reliability model that has many parameters that need to be estimated. I want to use a maximum likelihood estimator (MLE) to estimate those parameters. After I searched ...
4
votes
2answers
613 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
148 views

Why are some equal expressions more equal than others?

n1 = 1/3 (2 + (-Sqrt[3] + 2 Sin[(2 π)/9])/(Sqrt[3] Cos[π/9] - Sin[π/9])); n2 = 1/2 + Sin[π/18]/(3 Cos[(2 π)/9] + Sqrt[3] Sin[(2 π)/9]); n3 = 2/3 (1 - Cos[4 π/9]); ...
4
votes
1answer
431 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), ...
4
votes
1answer
43 views

Simplify With Assumptions Not Using Distributive Property Of Dot Product

Given the following expression Assuming[(n | d | t) ∈ Vectors[3, Reals] && n.t == 0, FullSimplify[(n + d).t]] Why does mathematica give me the below ...
4
votes
1answer
97 views

FullSimplify on complex numbers seems inconsistent

FullSimplify[c Conjugate[c]] returns Abs[c]^2 while FullSimplify[2 c Conjugate[c]] ...
4
votes
2answers
219 views

Assumptions with patterns

I want that Mathematica assumes every symbol like Subscript[s,i] to be evaluate as a real and positive number. I have tried ...
4
votes
1answer
972 views

Simplifying an ArcTan expression

The expression $\tan ^{-1}\left(\frac{\sqrt{L^2 \sin ^2(\theta )}}{\sqrt{L^2 \cos ^2(\theta )}}\right)$ can be simplified to $\theta$. After some attempts I got the following to do the job. ...
4
votes
1answer
167 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 ...
4
votes
1answer
226 views

How to make Mathematica express an equation in terms of previously defined functions

I was given a problem for my physics class, and perhaps I have taken it too far, but I wish to finish what I started. I have a function (i warn you that this does not look pretty) ...
4
votes
1answer
141 views

Dealing with 6 VERY large equations. Am I doing this correctly, and can I expect a solution?

I'm new to Mathematica, but so far, everything seems straight forward and intuitive, which is really nice. However, I've come to use this software since I have to show a rather nasty 3x3 matrix is ...
4
votes
3answers
89 views

Automatically split an expression and use TrigFactor to solve the parts

I want to simplify the following expression: 1/2*(Sqrt[3]*Cos[x]*la - Sin[x]*la - lb + Sqrt[3]*Cos[x+y]*lf - Sin[x+y]*lf) I used ...
4
votes
1answer
97 views

Problem with Simplify, Sqrt, and Set: What's going on?

I am having some trouble getting Mathematica to simplify an expression of the form Sqrt[x]*Sqrt[1/x], where x>0. The problem is that x is assigned to some complicated form by the time Mathematica ...
4
votes
1answer
114 views

TensorReduce not simplifying transpose for symmetric matrix?

I know Mathematica is not very good with symbolic manipulation of matrix expressions, but I was surprised to find that it can't reduce the following expression: ...
4
votes
1answer
377 views

How to find the most compact form of an equation

I would like to know whether there is any general approach to obtain the most compact form of an equation with Mathematica. I used to believe that the FullSimplify...
4
votes
1answer
42 views

What do I need to know about simplifying expressions involving Symbolic Tensors?

I want to use Mathematica to show that the inner product of a vector with itself is equal to the square of its norm. This is what I tried: ...
4
votes
1answer
153 views

Collect without grouping terms

The built-in function Collect, when applied to more than one variable, will group expressions by the first variable, as here: ...
4
votes
2answers
317 views

ArcTan[x,y] problems

I need an ArcTan[x,y] function that is continuous in (0,2 π) For the standard ArcTan function: ...
4
votes
2answers
178 views

Remove redundant parameters from equation

I have random expressions like (b1 x + b2 x)/(b3 + b4/b5 x) + Sin[b6 x] where $x$ is a variable and {b1, ..., b6} are parameters to be fitted. This expression is ...
4
votes
1answer
211 views

Mathematica rule to express exponentials as multiplication

I'm sorry if this has been asked before, but it is a very simple question and I would imagine it shouldn't be terribly hard for someone that knows to answer. I'm essentially trying to tell ...
4
votes
2answers
142 views

Can one use Map during Expand?

Can one Map a simplifying function to the summands of an Expand before fully expanding the expression in question first? ...
4
votes
1answer
148 views

How can I prevent a polynomial from being simplified?

I'm having a problem with polynomials. Let's say I have a polynomial "2x^2 - 5x + 6 - 3x^2" .. How can I check that this expression is not simplified ? Additionally, I would like to locate the ...
4
votes
1answer
84 views

Simplify Class invariant $G(25)$

How to simplify $$\frac{\sqrt[3]{\vartheta _3\left(0,e^{-5 \pi }\right)}}{\sqrt[12]{2} \sqrt[6]{\vartheta _2\left(0,e^{-5 \pi }\right) \vartheta _4\left(0,e^{-5 \pi }\right)}}$$ This is a ...
4
votes
1answer
50 views

Reliable testing of identities (example: modular functions)

Take, for illustration, the following function (bonus points for anyone who identifies where it comes from!), defined on the upper half plane: ...
4
votes
0answers
69 views

strange FullSimplify result, why zero? [duplicate]

This came up looking at this How to speed up calculation of this equation (FindRoot). Is there some sense to why FullSimplify gives zero here? ...
4
votes
0answers
91 views

Simple arithmetic with Irrationals fails [closed]

While solving a simple puzzle that asked for a few calculations in plane geometry, I ended up with this expression: $-\frac{55}{2}+\frac{\sqrt{27233}}{2}+\frac{1}{2}(55-\sqrt{27233})$ Or, in ...
4
votes
0answers
107 views

Simplest identity that cannot be proved by FullSimplify [closed]

Apparently, FullSimplify is not able to prove all true identities, but usually it does pretty well when it comes to elementary functions. I'd like to know what are ...
4
votes
0answers
102 views

Simplifying expressions involving Divisible

FullSimplify[ Divisible[p^2 - 1, 24] , Element[p, Primes] && p > 3] Should evaluate to True, but I get ...
4
votes
0answers
183 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
votes
3answers
473 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 ...
3
votes
3answers
566 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 ...
3
votes
3answers
160 views

How to evaluate $-i e^{\frac{i k}{2}} \sqrt{-e^{-i k}} = 1$?

In my calculation, there exist some expressions like $-i e^{\frac{i k}{2}} \sqrt{-e^{-i k}}$, which are not simplified to be $1$, and makes further calculations rather complicated. I tried to ...
3
votes
2answers
789 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 ...
3
votes
2answers
993 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 ...
3
votes
4answers
672 views

Join all square root expressions?

Sometimes I observe Mathematica produce expressions exactly like the following after a simplification step: $$\frac{a+\sqrt{-(1-b)}\sqrt{\frac{1}{b-1}}}{\sqrt{c}\sqrt{\frac{1}{c}}}$$ Now, any ...
3
votes
2answers
257 views

Mathematica does not understand (R^3)^(1/3) is the same as R [closed]

In the output from a calculation in mathematica stands a/((R^3*c)^(1/3)), with c and a ...
3
votes
1answer
224 views

Is this a bug in FunctionDomain (V.10)?

I used FunctionDomain[1/(x^3 + 1), x, Complexes] and got 1 + x^3 != 0 Is this a bug in FunctionDomain (V.10)? Can I receive $x \neq -1$, $x \neq \dfrac{1-...
3
votes
3answers
233 views

How can I make Mathematica trigger the simplification of ArcCos[a]+ArcCos[b]?

According to this Wikipedia subsection my guess is that I should be able to convince Mathematica to return zero when doing ...
3
votes
2answers
184 views

Replace expression, but only “outside” of a function [duplicate]

I have a horrid expression, which is basically a sum of exponents with coefficients. Here's a taste: What I want to do is to replace ks with another expression, ...
3
votes
1answer
986 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. ...
3
votes
1answer
144 views

FullSimplify does not distribute Abs over multiplication

FullSimplify[Abs[x]^2, x \[Element] Reals] reasonably returns x^2, but the barely-more-complicated expression ...
3
votes
1answer
151 views

Equality of Reciprocal with Negative Exponent

I want MMA to tell me if two, rather large, expressions are equal. My minimum working example follows. I want MMA to tell me that the following is true:$$x^n = \left(\frac{1}{x}\right)^{-n}$$ I have ...
3
votes
2answers
256 views

What would be the inverse function for the following condition?

I tried the problem but i couldn't take above condition in question in terms of f(x)
3
votes
1answer
198 views

FullSimplify yielding different results in mathematica 8 and 9

I have been experiencing some problems running a certain mathematica file in version 9. I've tracked the problem to a particular sum that I perform. Running the same code in version 8 and 9 I get two ...
3
votes
2answers
189 views

How can I get Mathematica to simplify this i * sqrt expression

In[11]:= FullSimplify[I Sqrt[-1 + w^2], Element[w, Reals], Assumptions -> 0 <= w <= 1] Out[11]= I Sqrt[-1 + w^2] Is it possible to have Mathematica ...