# Questions tagged [simplifying-expressions]

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

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### Implicit assumption in simplifying an equation

So I tried simplify on an equation (see below). ( Laplacian[V[r,\[Theta],\[Phi]],{r,\[Theta],\[Phi]},"Spherical" ] //Simplify) % == 0 %//Simplify Now the weird ...
67 views

### How to force Mathematica to “Together” a fraction under a Log and a Square Root

Consider the following code: Assuming[2 > u > 0 && 2 > x > 0, FullSimplify[Log[x]/Sqrt[4 - x^2] /. x -> 2 Sqrt[(2 - u)/(2 + u)]]] The ...
106 views

### Mathematica doesn't extract Re and Im parts properly

I have a code: ...
119 views

### Renaming one parameter changes the result of Simplify

Surely the following couple of expressions should both output True: ...
706 views

### Are these expressions not equal? Mathematica output is ambiguous

The following plot indicates that the first expression equals the second. But how can I use Mathematica to show that is true: ...
115 views

### Boundary Value Problem and FullSimplify

I'm confused about the output Mathematica is giving me when solving a boundary value problem of the form: ...
64 views

### Simplifying long expressions leads to memory allocation failure

I am currently trying to manipulate a number of expressions into a particular form that will allow me to determine their poles and zeros: ...
80 views

### Simplify differential expressions

One can differentiate a two dimensional vector like this, ClearAll["Global`*"] u[x_, y_] := {f[x, y], g[x, y]} Div[u[x, y], {x, y}] with output ...
132 views

### Can pattern assumptions be made reliable?

It is possible to use patterns in assumptions such as f[_]>0. This does not seem to be explained in the documentation but is for instance pointed out in Is it ...
54 views

### How to automatically transform Abs[Cos[x]]Sec[x] to Sign[Cos[x]]?

Out of some simplification, the term Abs[Cos[x]]Sec[x] appears. How can I make the code automatically transform ...
142 views

### Imaginary part of expression too difficult to calculate

I am trying to calculate the imaginary part of a long expression. It's a long enough expression that Mathematica "hangs" when you run: ...
64 views

### How to force simplify to drop common denominator in inequalities?

Simplify[c>0 && a/c <= b/c] results in c > 0 && a <= b, as hoped. However when ...
77 views

### Solve a complex equation symbolically?

I try to solve this equation symbolically: Solve[A*s - b*Log[Sqrt[(d - e*s)^2 + 1] + d - e*s] - x + b*c == 0, s] (yes: ^2 = cntrl-6) But M. (trial version) is ...
139 views

### Substitution in expressions

As the title suggests, I want in an expression to to some substitutions. For example in the expression $\mathcal{L}^+_0+\mathcal{L}^-_0+\mathcal{L}^+_0+\mathcal{L}^-_0+\mathcal{L}_1$ I want to ...
65 views

### Splitting a general rational polynomial ansatz into powers

EDIT This question is completely wrong and useless. It is mathematically incorrect. I think something like Series is sufficient if you're trying to do something ...
65 views

### Trouble with simplifying trigonometric / hyper-trigonometric functions

Why (correct) expressions like Assuming[p > 0, 2 ArcTan[Sinh[p]] == Pi - 2 ArcTan[Csch[p]] // FullSimplify] Are not correctly evaluated to: True? What is the ...
82 views

### Simplifying nested pure functions

I have several functions: ...
59 views

### How can I reduce my work to get the result automatically?

I want to find the locus of point present of the complex z so that $$|z + 2| + |z - 2| = 18.$$ I tried by hand ...
122 views

### Another example where using FullSimplify gives different result than Simplify

I believe this question is very similar to Result of Series[expression] is different when I simplify the expression, however, due to my lack of Mathematica experience, I am reluctant to call it a bug. ...
68 views

### Eliminating higher order trigonometric terms

I am interested in eliminating higher-order trigonometric terms from a long symbolic expression. Specifically I want to reproduce this simplification that is done (in a tutorial I am working through)...
30 views

### Checking if two expresssions are equal in mathematica fails [closed]

I want to see if two expressions are equal. I have tried all of the methods outlined in this question but none seem to work. I have two expressions, part1 and <...
95 views

### Finding general forms of sums in Mathematica

A general form can be obtained for some sums with binomial coefficients. Mathematica is able to find these general forms for some of the simplest sums. For others the output contains for instance ...
39 views

### Evaluating Fourier coefficients when Exponential terms are present

I am trying an analytical solution for a 3D Laplace equaition, and just wanted to know if I could use the symbolic calculation capabilities of Mathematica to calculate the Fourier coefficients ...
43 views

### Exclude a term in an expression from any computation/simplification, e.g. being multiplied into a list or matrix

My particular problem is to find a way how to manipulate a term so that it is not multiplied into a vector (as being a list or matrix, and potentially being displayed in MatrixForm) for as long as I ...
82 views

### Prevent simplification of trig functions

Mathematica often simplifies trigonometric expressions, for example replacing $\sin(\frac{\pi}{4})$ with $\frac{1}{\sqrt{2}}$, or replacing $\cos(\frac{3\pi}{8})$ with $\sin(\frac{\pi}{8})$. I'd like ...
108 views

### Simplify part of an expression produced by solve

Mathematica outputs an answer using Solve[] but it is not as simplified as it can be. By manually arranging this expression I know that the parts I've highlighted in yellow can actually be simplified ...
63 views

### Substitution inside an expression [duplicate]

I'm trying to get mathematica to replace an expression with a reduced form. I wanted to replace $(k/w)$ with $h$ in a particular expression, and I've tried something like: ...
37 views

### Simultaneous equations help [closed]

I have the following: ...
52 views

### Simplifying Algebraic Expression With Substitution

Is there a way I can make an algebraic substitution in a matrix? I tried using Simplify[P_rhs _ 51, (c44hat*rhohat)^.5 == zeta] Where P_rhs_51 is a 4x4 matrix. ...
44 views

### Simplifying expression with square root of square roots

I have the following expression FullSimplify[ Sqrt[1 + (-1 + a) (-1 + b) + 2 Sqrt[(-1 + a) (-1 + b)]] - Sqrt[ 2 + a (-1 + b) - 2 Sqrt[(-1 + a) (-1 + b)] - b]] ...
60 views

### Complex Infinity of Hypergeometric+Gamma function

I am solving some integral which gives an hypergeometric function+gamma function . The point is that my values of n (see the code below) are integers, so ...
64 views

### Simplifying expressions with square roots of squares

I have a large number of expressions that are of the form, f(a,b)+Sqrt[g(a,b)^2] I understand I can use simplify and make an assumption to get either of the two ...
73 views

### How to apply a continious substitution reduction of (-1 + 3 phi - 2 phi^3 - 6 phi^4 - 20 phi^6 + 6 phi^7 + 3 phi^8 + phi^9)//.{phi^3->1-phi^2}

I have the answer to $(-1 + 3 phi - 2 phi^3 - 6 phi^4 - 20 phi^6 + 6 phi^7 + 3 phi^8 + phi^9)/.{phi^3->1-phi^2}$, that is not the problem. I am looking for a method that continues to apply this ...
162 views

### Force a sum to be simplified

I want to force this sum to be simplified to 1 Sum[Cos[(Pi*l*(2*m + 1))/(n + 1)], {l, 0, n}] Only DiscretePlot3D gives the correct result showing all point to 1
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### Manipulating expressions containing complex exponentials and double integrals

Given that I have Integrate[Integrate[Exp[I w (x-u+v)]f[u, v] , u], v] $\int\left( \int e^{iw(x-u+v)} f[u, v] du\right) dv$ First, I want to first extract ...
180 views

### Simplify $\tan^{-1}(\cot(a))$ to $\frac{\pi }{2}-a$ assuming $0<a<\frac{\pi }{2}$

I know Mathematica is not omnipotent, but still can't help feeling surprised when I encountered this example, and I think it's worth starting a question for it. The example is, ...
105 views

### Forcing FullSimplify to use user defined functions

Is it possible to simplify the expression using user-defined functions? For example if I define: m[l_, x_] := Sum[x^i/i, {i, 1, l - 1}] I would like ...
83 views

### How to calculate $(X^tX)^{-1}X^tY$? [duplicate]

This is MatrixForm[ {{1., 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 1.5, 1.5, 1.5, 2, 2, 2.2, 2.4, 2.5, 2.5, 2.8, 2.8, 3, 3, 3.2, 3.3}}] $X^t$ ...
341 views

### How to find the sum with Mathematica?

That hard problem was invented by V. P. Beshkarev (Russia) in 1971: Sum[Tan[(4*j - 3)*Pi/180], {j, 1, 45}] // FullSimplify The result should be 45, but the ...
47 views

### Simplify a Boole function

I have a very long polynomial expression (which we can call here $f(x,y,z,\zeta)$). The coefficient have this object appearing a lot: ...
55 views

### Simplifying does not give $(1/a)^x - a^{-x} =0$ [closed]

I am trying to simplify a complicated expression by replacing a^{-x} to (1/a)^{x}. I got the expression by hand and try to use simplify function to recheck whether it works. But a^{-x} is not canceled ...
58 views

### Simplify out terms that are large

I have something of the form $$\frac{(A*G+C)(B*G)}{(G^2+junk4)(G + junk3)}$$ I know G is very large, so my largest term will look like: $\frac{ABG^3}{G^4} = \frac{AB}{G}$ And my second largest ...
315 views

### Why is expression not evaluated completely? [closed]

I have a simple sum of complex numbers. In my example their sum is zero. sum = Total[{1 , E^(2*I/3*Pi) , E^((4*I)/3*Pi)}] Print[sum] Try it online! When ...
144 views

### How to make Mathematica recognize $(-1)^{1/3}$ as $-1$? [duplicate]

I am doing some calculations that end up popping out a lot of $-1$s to various fractional powers, and Mathematica doesn't seem to want to set them to $-1$. Is there an easy way to do this?
59 views

### Simplifying complex-valued entries in a matrix

I have a matrix where some entries are complex or roots of unity. For example, (-1)^(2/9) - (-1)^(5/9) + (-1)^(8/9) is one such entry and it is equal to 0. ...
34 views

### How to simplify my integrand to make the function Integrate[] work?

To calculate a physical field, I need to integrate a complicated expression, with Sin and Cos and some 3/2 power. But when I run the Integrate function, it seems running forever. So what could I do to ...
82 views

### Algebraic substitution for polynomial simplification

Consider a polynomial $p(x,y)$ and we want to simplify $p(x,y_0)$ where $y_0$ is a root of some other polynomial $q(y)$. In Maple I would use something like: ...
128 views

### Simplifying polynomials [closed]

I have noticed a strange behaviour in Mathematica regarding simplifying polynomial expressions. Take the following polynomials pol1=3-8s+4s^2 pol2=(2s-1)(2s-3) ...