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

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4
votes
2answers
331 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 ...
4
votes
1answer
766 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 - ...
4
votes
2answers
255 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: ...
4
votes
1answer
689 views

Does the Im function work with symbolic arguments?

Does the Im function work with symbolic arguments? ...
4
votes
2answers
239 views

Why doesn't FullSimplify simplify expressions with DiracDelta?

I want to simplify a complicated expression with some Dirac delta distributions, but FullSimplify does not do what I want. Specifically, I want ...
4
votes
1answer
346 views

Can I check if an expression is positive using assumptions?

I have the following notebook: ...
4
votes
2answers
178 views

Why Refine does not simplify Cos[2*Pi*FractionalPart[1/2*(i + j + k)]] to $(-1)^{i+j+k}$?

I am obtaining in Mathematica: Cos[2*Pi*FractionalPart[1/2*(i + j + k)]] We know that for $i, j, k$ being positive integers this expression after simplification ...
4
votes
1answer
209 views

Can't simplify Abs[a*Cos[x]]^2

Why doesn't FullSimplify[ Abs[a*Cos[x]]^2, Assumptions -> {{a, x} ∈ Reals}] simplify to (a*Cos[x])^2 but this query ...
4
votes
1answer
192 views

Infinite expression encountered when simplifying ArcTan sums although the result is finite

If I attempt to simplify the sum ArcTan[1/x] + ArcTan[x] with ArcTan[ Simplify[ TrigExpand[ Tan[ ArcTan[1/x] + ArcTan[x]]]]] ...
4
votes
1answer
295 views

Simplifying numerical expressions involving special functions

I've encountered the following problem. There is the identity (Legendre's relation) that the special functions EllipticK[x] and ...
4
votes
2answers
109 views

Symmetrise a complicated expression

I am calculating the derivatives of a symmetric function $F(a_1, a_2)$ and got very complicated expressions, which I'd like to write in a symmetric form with respect to $1 \leftrightarrow 2$ (clearly ...
4
votes
1answer
270 views

Mathematica doesn't simplify a simple expression

The question is simple as that. I have: ...
4
votes
1answer
454 views

Checking if an expression is equal to zero

I have 6 points in $\mathbb R^3$ as follows: ...
4
votes
2answers
270 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
319 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
1answer
147 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
357 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
79 views

What options need to be set for Simplify to perform a certain manipulations similar to FullSimplify?

Simplify performs algebraic transformations and is fast, while FullSimplify tries a wide range of transformations involving ...
4
votes
1answer
163 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
130 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
78 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
2answers
182 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
76 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
78 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
251 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 ...
4
votes
1answer
88 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
156 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
134 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
180 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
131 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
139 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
0answers
91 views

Simplest identity that cannot be proved by FullSimplify [on hold]

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
88 views

Better way to compute triple (or higher order) convolution

I have an identity that I want to verify: $$\sum_{i+j+k\ge ...
4
votes
0answers
128 views

How to get mathematica to simplify a result

I have the following output $\text{Li}_2\left(3-2 \sqrt{2}\right)-4 \text{Li}_2\left(-1+\sqrt{2}\right)$. This turns out to be equivalent to $\displaystyle\log^2(1+\sqrt{2})-\frac{\pi^2}{4}$. How ...
4
votes
0answers
93 views

Simplifying expressions involving Divisible

FullSimplify[ Divisible[p^2 - 1, 24] , Element[p, Primes] && p > 3] Should evaluate to True, but I get ...
3
votes
3answers
526 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
2answers
815 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
2answers
304 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
2answers
252 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
214 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 ...
3
votes
2answers
147 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
731 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
95 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
242 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
181 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
110 views

Assumptions within Simplify

I am using the ratio between two error probabilities in various functions. I want Mathematica to display this ratio in the most simple manner. How do I let Mathematica know that, in this case, the ...
3
votes
1answer
764 views

Trace of FullSimplify

I have a symbolic function and I used FullSimplify command to simplify the equation given below. I am calculating it by hand but I couldn't reach the same solution. ...
3
votes
2answers
519 views

Combining and separating sums

How can I combine or separate sums in Mathematica in the way that Together or Expand work for rational expressions? For ...
3
votes
4answers
190 views

Simplify binary expressions

Is it possible for Mathematica to do simplifications for expressions where the variables are binary, such as: a + b = 1 + 2*c => a + b = 1 Here c must be 0 because if it is 1, the RHS is 3 but ...