Questions tagged [simplifying-expressions]

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

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1answer
52 views

How to use `TransformationFunctions` to simplify this expression

I see this interesting question here. But I want to simplify it with the help of Simplify function (Maybe the ...
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1answer
97 views

How can I always get the simplest solution from Integrate? [closed]

When I evaluate this. Integrate[1/(x (1 + x^4)^(1/4)), x] // FullSimplify In 11.3 I get ...
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38 views

Canceling factors from numerator and denominator with complex number

I have the following expression: $\text{expr} = i \frac{\sqrt{a-b}}{\sqrt{b-a}}x$. Clearly simplifying expression gives $\text{expr}=x$ by cancelling the numerator and denominator. However, I am not ...
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168 views

`Series` gives wrong result

Bug introduced in 10.0 or earlier and persisting through 12.0. The following code shows that Series gives different results depending on whether one simplifies the ...
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2answers
64 views

Simplify expression with non-commutative products

I am using NCAlgebra but I am open to any solution. I would like to simplify some expressions with many terms (a few dozens) using: the fact that each term is a ...
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40 views

Cancelling power terms in numerator and denominator

.Dear Community. I have the following expression in Mathematica: (1 + x) (x + (w/(A (1 - y)))^(1/y)) (A (1 - y))^(1/y) I would like to simplify it so that terms ...
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1answer
72 views
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1answer
42 views

Factorizing non commutative terms

Is it possible to factor a ** b ** c - a ** b ** d as a ** b ** (c - d) ? I am using ...
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1answer
259 views

How to use Mathematica to simplify this kind of trig sum?

$$ S=\sum_{k=0}^{10}\sin\left(\frac{(2+4k)\pi}{23}\right) =\sum_{k=0}^{10}e^\left(i\frac{(2+4k)\pi}{23}\right) =e^{i\frac{2\pi}{23}}\sum_{k=0}^{10}e^{i\frac{4k\pi}{23}} =e^{iu}\sum_{k=0}^{10}\left(e^{...
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65 views

Simplify expression to Floor

I would like to simplify the expression below to Floor[L/2], for L \[Element] Integers: ...
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3answers
241 views

How to simplify this formula?

$$ \int \frac{1}{\sqrt{1-2 x^3}} \, dx $$ Integrate[1/Sqrt[1 - 2 x^3], x]// FullSimplify The result is very complex. Then I want to differentiate it with the ...
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37 views

Imposing symmetry conditions

I have functions with some symmetry properties, how I have to impose the corresponding conditions within Mathematica, in order to perform all simplifications automatically? ...
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52 views

Determine if a mathematical statement always holds

I know that $\exists a,a\in\mathbb{Z}\land a+1>a$ is always true, and $\forall a,a\in\mathbb{Z}\Rightarrow a+1>a$ is also always true; I try to use function ...
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1answer
65 views

How can I show that the equation holds?

Suppose we have the following data: $ r=\frac{vk}{h^2}$ $u[i,j]$ is a function of two variables with $i,j$ integers. $\frac{u[i,j+1]-u[i,j]}{k}=v\frac{u[i+1,j]-2u[i,j]+u[i-1,j]}{h^2}$ Then I would ...
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1answer
48 views

Simplify without changing the denominator

I have the following expression: ...
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1answer
35 views

Hiding trivial conditions when using Reduce

I use Reduce to find conditions on some parameters such that certain inequalities are fulfilled. An additional condition is that all parameters are positive. The first problem is that I have to ...
2
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1answer
63 views

Simplifying an expression with many Kronecker deltas

I have an expression with lots of Kronecker deltas, with terms like: $\delta_{1,a}v_1+\delta_{2,a}v_2+\delta_{3,a}v_3+\delta_{4,a}v_4$ where $v$ is some four-component vector and the indices $a,b$, ...
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1answer
58 views

Refine Max[#] with assumptions breaks with more elements

Can someone please explain the following phenomenon to me? I am using Refine to evaluate a symbolic Max expression with a ...
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0answers
40 views

How to use Collect function to reverse the transformation

I want to use the collect function to combine (x^3+3 x^2 y+x^2+3 x y^2+2 x y+x+y^3+y^2+1) into ((x + y)^3 + (x + y)^2 + x + 1),...
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Simplify, ComplexityFunction, and expression rearrangement

Context: Mathematica is being used to simplify expressions. These expressions are then exported to be used in a C-family language. Naturally enough, desiderata include execution speed, and avoidance ...
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2answers
125 views

How to simplify Sum's and Product's of arbitrary length?

I would expect Sum[Subscript[x,i], {i, 1, n}] + Sum[-Subscript[x,i], {i, 1, n}] and ...
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0answers
51 views

Simplification of expression under symmetry conditions

How to simplify the following expression: ...
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2answers
85 views

How to reduce this equation to the form of y == k*x + b

I want to reduce this equation to the form of y == kx + b, but I cann't do that using MMA. ...
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1answer
91 views

Does Mathematica know about identity involving ArcSin(Cos(x))? [duplicate]

Given that $0 < x < \pi/2$, it can be shown that $$\arcsin(\cos(x)) = \pi/2-x,$$ however, I was unable to make Mathematica to simplify the LHS into the RHS. I was guessing that, ...
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418 views

Using Reduce over integers produces weird result

Using Reduce to solve $x^2(1+x)=y(3y-1)$, over integers should yield $$(x, y) = (-1,0),(0,0),(1,1),(4,-5),(6,-9)$$ However, when I enter ...
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113 views
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47 views

Simpler closed form for spherical coordinates of points on great circle?

Short version: how to simplify this expression given these conditions? Note that expr[[3]] is equal to 1, although Mathematica won't simplify it as such. ...
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56 views

How to simplify an expression with implicit vector functions and cross product operation?

1.The pattern is set in order to calculate the integral of a derivate of a function (to return original function, first fundamental theorem of calculus) ...
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2answers
78 views

Simplify root inside of root

xxx=(2 Sqrt[1 - 2/(1 + Sqrt[G1])] G1 + 2 Sqrt[((-1 + Sqrt[G1]) G1)/(1 + Sqrt[G1])])/(-1 + 2 G1) I have quite complicated expression. I want to simplify little ...
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103 views

Simplifying polynomial fractions with same `DiracDelta` function in both denominator and numerator

I am trying to simplify an expression with multiple Diracdelta functions in both numerator and denominator. For example, ...
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3answers
140 views

isolating a specific variable to one side in an equation

I am trying to do a simple operation of manipulating an equation of multiple variables (say, $x,y,z$), so that I can get one of the these variables on the LHS and everything else on the RHS. It should ...
13
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0answers
114 views

Reduce[Sin[x]==0,x] splitting odd and even multiples of Pi

as from Title, I'm wondering why Mathematica does not automatically give a single, simple solution for the problem Reduce[Sin[x] == 0, x] for which I obtain the ...
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3answers
62 views
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122 views

Analytical full-width half-maximum of hyperbolic functions composition

I'm trying to find the analytical FWHM of the following function (that I know has a Bell-type envelope): ...
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1answer
109 views

Taking Real, Im, and Abs of polynomial fractions

I want to find out real imaginary and Abs of polynomial fractions composed of real-valued variables. For example, consider we have a polynomial fraction $f=\dfrac{a_1 +b_1 i }{a_2 +b_2 i }$ where $...
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1answer
47 views

Simplifying terms by substitution and/or elimination [closed]

I would like to simplify the output of a calculation. For example, in the output image below, y^3 and y^(5/2) can be simplified ...
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1answer
53 views

Is there a global parameter that limits the number of variables handled by Simplify?

It seems that Simplify is unable to handle (at least some) expressions involving 22 or more variables. Consider the code snippet below: ...
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1answer
143 views

Simplify is not simplifying a compound inequality as expected

The Simplify command is having trouble verifying a compound inequality, even while it correctly handles the two corresponding single inequalities. I'm starting ...
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1answer
106 views

What is the first slot value in this expression?

I would like to know what is the first slot value in the following expression ...
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0answers
35 views

What options should I feed to FullSimplify to make it strongly prefer elementary functions?

I want that FullSimplify strongly preferred all elementary functions as opposed to all non-elementary. Can I do it?
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2answers
389 views

An example from a Mathematica tutorial on integration returns a different answer from the tutorial

This page on "Integrals that Can and Cannot Be Done" suggests that, almost surprisingly, Mathematica can express the following integral in terms of elementary functions: ...
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41 views

details of the simplifying process

I have a complicated expression: ...
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1answer
61 views

How to Reduce conditions of Piecewise function

Edit I had problems with pasting an example to stackoverflow itself so here is the link to PasteBin containing sample code: https://pastebin.com/yi6AyrHy I have fairly big piecewise function which I'...
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0answers
70 views

Find all pattern in expression

Consider this problem: I have a functional $\mathcal{F}$ acting on some function $n(t)$ such that $$ \mathcal{F}[n(t)]=0 $$ $$ \mathcal{F}[n^*(s)n(t)]=\alpha(t,s) $$ $$ \mathcal{F}[n(s)n(t)]=0 $$ ...
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2answers
61 views

how to get rid of the denominator in the squareroot, that appears in the denominator?

Here is an example: $\frac{\nu y_0}{\left(x_0+\frac{1}{2}\right) \sqrt{\nu ^2+\frac{\left(4 x_0^2+4 y_0^2-1\right){}^2}{16 y_0^2}}}$ ...
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2answers
66 views

Simplify Integrate results

I wish to simplify the overlap of two gaussian-type orbitals, primGauOrb = ((2 α)/π)^(3/4)E^(-α (x^2 + y^2 + z^2)); And then integrate it, ...
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2answers
119 views

Simplifying the expression by defining functions

I want to simplify the function below by using FullSimplify: ...
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0answers
62 views

Why is Log[8 E^(3 Log[0.5]) != 0 [closed]

My wife and I have tried to calculate Log[8 E^(3 Log[0.5]) on a TI-Nspire and we got the result -8E-14. We have changed th settings of calculation to Exact and the result was 0 (correct) If I use ...
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1answer
60 views

A single expression that performs substitution and simplifies a trigonometric form [closed]

I'm very new to Mathematica. I searched through the online documentation, but I don't understand why it realizes that $\sin(n\pi)$ for $n\in \mathbb{Z}$ is $0$: ...
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0answers
53 views

Change a single letter changes the result

these two codes give different result. FullSimplify[a-b,Assumptions->a==1+y&&b==1+y-x] this give x ...

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