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

learn more… | top users | synonyms (3)

5
votes
1answer
143 views
+100

Symbolically prove that two expressions are identical

I encountered this problem when trying to reproduce the result of this paper. I want to prove int == intpaper assuming ...
2
votes
0answers
37 views

Simplifying integer inequalities to equality [on hold]

I try (in Mathematica 10) FullSimplify[l >= l1 + l2, {l <= l1 + l2, Element[l | l1 | l2, Integers]}] But that gives back ...
0
votes
1answer
53 views

Metric Simplify & grouping

I'm changing a basis from one metric to another. When simplifying the result Mathematica doesn't seem to grasp all the possible simplification: ...
0
votes
2answers
74 views

Problem with simplification of $\sqrt{1+\frac{y^2}{x^2}}$

When I evaluate my Mathematica code I get out a term of the following form: $\sqrt{1+\frac{y^2}{x^2}}$. However, I also have $\sqrt{x^2+y^2}$ terms that I would like it to cancel with. For example, ...
0
votes
0answers
43 views

Simplify a complex trigonometric equation resulting from constraint solving

In the solving of mechanical constraints, I often meet complex trigonometric equation that I have to simplify. Here the equation I would like to simplify : Mathematica notebook presenting the ...
0
votes
0answers
26 views

Expectation of summation with symbolic indices

I am working on symbolic computations with mathematica. I faced an issue with taking expectation of a large expression involving summations with symbolic indices. Is it possible to take expectation ...
0
votes
0answers
30 views

How to solve a quadratic inequality containing parameters?

I have the following inequality to solve for $R$ in terms of $\delta$ and $n$, with assumption that $n \geq 3$ and $\delta>0$: $$-2 < 2 -\frac{16n\delta^{2}}{R^{2}\sin^{2}\frac{\pi}{n}} \left(...
2
votes
1answer
228 views

Simplifying square root of exponential

Very simple question: Why doesn't Mathematica simplify this square root expression? Refine[Sqrt[Exp[I p]], p > 0] // FullSimplify It should give ...
0
votes
1answer
27 views

Making multi-linear polynomial change of variables (simplifications) by updating `replacementFunction`

This is an evolution of one of my previous questions; I've got a partial answer to that question and now have a much cleaner question to ask: Question: What changes to ...
6
votes
3answers
215 views

Why doesn't Lambert function (ProductLog) simplify?

I have Simplify[ProductLog[x*Exp[x]]] By the definition of the Lambert function, this should be simply x. But Mathematica outputs this: ...
1
vote
0answers
144 views

Problem of calculating the residue of a expression (to confirm the result from a paper) [duplicate]

I use Mathematica to confirm a result from a paper which is to calculate the residue of a expression at zero. The code and result are given below. Is this residue too complicated for Matheamtia or ...
1
vote
1answer
125 views

Residue failed to reproduce this residue in a paper

This problem is a more clearly state of my original problem which is off topic, so I reconsider my problem carefully based on previous discussions, and gives the following valid code to reproduce my ...
0
votes
0answers
46 views

NCAlgebra: define a scalar variable

I have a linear operator L and a scalar h, and would like to expand L[f + h phi] to ...
3
votes
1answer
73 views

Replacing patterns (determinants) in a rational multivariate function and/or getting `replacementFunction` to work on a multi-linear expression

Given a rational multivariate function known to contain determinants, what is the best way to rewrite the function in terms of the determinants? A simple example: ...
4
votes
1answer
87 views

How to tell Mathematica to avoid simplification of product of exponentials with the same base?

There has been a similar question, but it doesn't solve my problem. I have this input: var = Exp[a] Exp[b] And the output is ...
0
votes
0answers
56 views

How do I interpret an certain expression? [closed]

I used Simplify to simplify some long expression and received pretty long simplified form. A part of the output (in Standard Form) is the following: ...
1
vote
2answers
107 views

Factor out imaginary unit of root of obviously negative term

Suppose I have the term $t=\sqrt{-a^2-b^2}$, where $a,b\in\mathbb R$. Of course, we know that it holds $$ t = \mathbb i \sqrt{a^2+b^2} $$ which is (in my opinion) more convenient. How can I get ...
1
vote
1answer
84 views

A simplification of a complex expression

I use mathematica to confirm a result from a paper ("...
0
votes
0answers
36 views

Evaluating a function after simplifying to avoid infinite expressions

My Poly[j_, s_] function simplifies to a polynomial for all j. So I defined a PolySim[j_, s_] = Simplify[Poly[j,s]] function. However, if I try to evaluate PolySim[j,0], since this is PolySim[j,0] = ...
3
votes
0answers
80 views

Bringing rational functions to canonical form

I have a complicated expression, which among other things has stuff like functions of rational functions: expr = f[x/(-x^2 + y)] + f[-(x/(x^2 - y))] (* + ...*) ...
0
votes
0answers
66 views

Avoiding divide by zero to simplify an expression enough to solve

I have a very complicated expression that I'm trying to set to zero and solve. I simplify by substituting in variables, but Mathematica isn't fully simplifying it -- my guess is because it thinks it ...
3
votes
0answers
78 views

Why isn't Mathematica listening to my assumptions?

I'm trying to simplify the expression ωplus := 1/2 c (I f V + Sqrt[4 k^2 - f (f + 8 I k) V^2]) so that I can get it in the form $a+i b$. I am using the global ...
1
vote
1answer
64 views

Need help on simplifying the integral of a square root of a polynomial

I have the following expression a = 4 Cos[af / 2]^2; b = 1 - 5 Cos[af / 2]^2; c = Cos[af / 2]^2; s = Sqrt[a*x^4 + b*x^2 + c] and I need the integration of $s$ in ...
3
votes
1answer
82 views

Factor a polynomial Root into Roots of smallest possible degree

Suppose I have a polynomial Root representing an algebraic number. I want to represent it (if possible) as a product of several polynomial ...
0
votes
2answers
32 views

Simplifying polynomials with conditions on variables

I'm working with polynomials of 5 variables $a,b,p,q,r$ which have a condition $a+b=p+q+r$. I'd like to minimize the number of variables in the answer. However, FullSimplify can't handle even simple ...
2
votes
1answer
74 views

Weird behavior of `HypergeometricPFQ`

Consider the following function: fun = HypergeometricPFQ[{1, x1-y1, 1-x1-y1-2u}, {x2-y1, 3-x2-y1-2u}, 1]; Let us try and evaluate this function on the following ...
8
votes
1answer
516 views

RootSum result manipulation/simplification

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

Simplifying expressions containing unit of zero magnitude

I have obtained the following form as a part of a computation: k (Quantity[0, "Kilohertz"]) + Quantity[1/500, "Kilohertz"] This is typeset as Here, ...
0
votes
0answers
4 views

Simplifying using identies [migrated]

Simplify tanxcos^2x/(sinx-sin^3x) I tried to turn all terms into sin and cos and i got secx as the answer. Then I tried to changed the cos^2x into 1-sin^2x and ended up with tanx/cosx. Why am i ...
2
votes
2answers
311 views

Simplify results further

I have an extremely long result in polynomial form following some matrix operations. However, given the symmetry of the problem, I can safely say that the solution will reduce much further than is ...
0
votes
0answers
33 views

Mathematica can't simplify disguised expression [duplicate]

When I simplify the following quartic polynomial with a linear constraint; Simplify[x y z a + x y z b , a + b + c == 0] // Expand I get what to me seems like the ...
2
votes
1answer
82 views

Way to simplify an inequality with many variables

my problem is the following: I have three inequalities in five variables $x,u,a,b,c\in \mathbb{R},x>0 $: ...
8
votes
1answer
105 views

Adding irrelevant assumptions changes the result of Simplify

I've run into this problem a number of times. A typical example is Simplify[Sign[k], {0 < A, 0 < B, A*Exp[2*y] < k, y > 1}] which evaluates to $1$, ...
1
vote
0answers
39 views

`QPochhammer` function simplification?

Consider the function which in Mathematica is denoted as QPochhammer[a,q,n], and its infinite product cousine: which in Mathematica reads ...
3
votes
4answers
416 views

Mathematica not able to confirm its own solution to differential equation

I type the following into Mathematica: DSolve[q''[x] + 2 x/(x^2 - 1) q'[x] - 4*q[x]/(x^2 - 1) == 0, q[x], x] It gives me the result ...
1
vote
2answers
125 views

Simplifying ArcTan[Cos[u], Sin[u]]

I am trying to evaluate the following expression in Mathematica: $$ \bigg| \frac{\left(1-z^{-2}\right)^n}{\left(1-z^{-1}\right) \left(2-z^{-n}-z^{-1}\right)} \bigg|^2 $$ Here $z$ is the complex ...
0
votes
0answers
29 views

Finding results using qualifiers?

I have set of recursive function definitions and assumptions $\forall n.t1(n+1)=t1(n)-Y*S(n)$ $\forall n.t2(n+1)=t2(n)+S(n)$ and assumption $\forall n.n<K\rightarrow L1=L2*t2(n)+t1(n)$ I want ...
0
votes
1answer
53 views

Not simplify an easy equation with “Simplify”

I've a problem with the function Simplify. I've this equations x^2 + 2 x + 1 == 0 and 4 x^2 == 0. If I use Simplify, it returns <...
40
votes
4answers
3k 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]) ...
1
vote
1answer
52 views

FullSimplify fail with general assumption

Assume I want to simplify this: -a^(-1) ** b^(-1) + (b ** a)^(-1) given assumption: $\frac{1}{b\_\text{**}a\_}=\frac{1}{a\_}\text{**}\frac{1}{b\_}$ Then it ...
10
votes
1answer
267 views

How to prevent simplification?

I have a question about the concept of simplification. I want to explain it with an example. When I write $4/8$ in mathematica, output is 1/2. How can I return ...
3
votes
3answers
129 views

How to obtain this expression in terms of real functions

I know that this expression (2 (ArcCot[E^(-((I ϕ)/2)) r] + ArcCot[E^((I ϕ)/2) r]))/π is real, because is the sum of a real series, in particular: ...
3
votes
3answers
440 views

Simplify big numbers in a second order equation

How can I simplify big exponents like $10^{39}$ in the solution of a second order equation: ...
0
votes
0answers
53 views

Handling Inequality with condition

I have verifying inequality using Mathematica using Simplify command For Example I want to check whether inequality a<f ...
0
votes
1answer
34 views

Complex number simplifications

My Mathematica notebook is not simplifying some expressions which do look trivial. I mean that one of my outputs contains: ...
0
votes
1answer
36 views

Option for Simplify command in mathematica

What does Simplify[%[[1]], %[[2]]] mean in following code? I mean [[1]] and [[2]] exactly what does refer to? ...
1
vote
2answers
79 views

Double sum in mathematica

It may look like a stupid question, but I was really confused by how double sums works in mathematica: After simplification, the function actually has nothing to do with n2? Also, when I manually ...
2
votes
0answers
75 views

Complicated implicit plotting - can it be tackled?

I'm quite new to Mathematica and have already spent tons of time on problems of this type, browsing through tutorials and topics here. I'm now coming to conclusion that it cannot be done and am about ...
0
votes
1answer
53 views

Simplify assuming $x$ is small [closed]

I would like to assume that $x$ is small so that values of the order $x^2$ (and higher orders) are negligible. For example, I would like Mathematica to return $1-2m$ when I ask it to simplify $(1-x)^...