Questions tagged [simplifying-expressions]
Questions on manipulating complicated expressions and making them look simpler using Simplify, FullSimplify and Reduce.
2,162
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Collecting exponentials
Suppose you have expression that is a summation of products of exponentials, how to simplify it by collecting exponentials inside products?
See example what I need:
$$2^{\frac{x}{2}+5}*3^{\frac{1}{2}-...
- 2,615
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0
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66
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3
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3
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1
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How can I simplify the output after integration which is obtained in terms of hypergeometric function in Mathematica?
When I did the integration of the following function, I got the answer in terms of hypergeometric function. But when I did the same integration in MATLAB, a simplified form of expression is coming as ...
1
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0
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36
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Do summation if factor does not depend on index
I have the following sums $$\sum _{j=0}^{n-1} \left(\sum _{c=1}^K \left(\sum _{b=1}^K m[b]^2\right)\right)$$ or $$\sum _{j=0}^{n-1} \left(\sum _{c=1}^K \text{$ n$}[c]\right)$$
where $m[b]$ and $n[c]$ ...
- 115
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2
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Rewriting an expression while using another parameter
I wish to rewrite V and M with the given A. I have provided what the end result is supposed to look like.
Here is V
...
- 111
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53
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Multidimensional FourierCoefficient, how to do / how to get as discrete deltas
I'm trying to turn a pretty nasty differential equation into a spectral form. And while I have done most of the work by hand, I want to check my work with Mathematica.
One step I need is the fourier ...
- 41
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1
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44
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Unable to simplify exponential expression to its simplest form of trigonometric expression by Euler's formula
Applying "FullSimplify" fails to simplify the following expressions:
Input:
...
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2
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answers
51
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Speed up numerical evaluation of extremely large expression
I have a large 4x4 symbolic matrix whose components are scalar functions with arguments (t,r,$\theta$, $\phi$) and various parameters. The LeafCount of the purely ...
- 463
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Leverage swap space on Linux
Maybe this would be better suited on a different stackexchange, but I'll ask it here anyways in case Mathematica has some inbuilt functionality I'm not aware of.
I'm running ...
- 463
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votes
2
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389
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Simplify a simply fraction
I want to simplify a fraction which is (x^2+y^2)/r^2. And the assumption is r^2==x^2+y^2. In this problem, x,y and r are reals and r is not 0. I have tried this:
...
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in xAct, simplify output expression by specfic the form a function with ReplaceAll or Simplify
in xAct, at the beginning I define a function H1(t,r) that depends on two variables using the command DefScalarFunction, then I want to simplify an output ...
- 33
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Simplify of `Mod` in compound logical expression
It's great that
Simplify[Mod[x,2π]==0,Assumptions->{0<=x<2π}]
yields x==0. However even a slightly more complicated ...
- 2,688
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answer
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convert n*Arctan[x] to ArcTan[x]
In the result of solving the equation or the integral often get something like k*ArcTan[x], I prefer the ArcTan[x] form.
For ...
- 4,932
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Scaling a variable multiplied by power series is not giving expected output
I have a power series getting multiplied by a variable, which gets scaled by the small parameter used in the power series. As an example, in the following dummy series:
...
2
votes
2
answers
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The solution for Sinh[] and Cosh[]
I saw this equation a book that has two solution: one Sinh[] and another one is Cosh[] but I can't find them with Mathematica 13?!!
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1
answer
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simplifying DSolve output. Exponentials raised to constant
I see lots of cases where DSolve gives solution that has $e^{c_1}$ in the solution, where $c_1$ is the integration constant.
When solving this by hand, we normally ...
- 109k
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FullSimplify not yielding True for Log[a/b] == Log[a] - Log[b]? [duplicate]
I am not receiving True for Log[a/b]==Log[a]-Log[b]. Is there a way around this problem?
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Why FullSimplify return {} on this solution of ode?
I was calling FullSimplify with timeout on solution of ode. The idea if it timesout, then will try Simplify on same solution ...
- 109k
2
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1
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Can't simplify expression with square roots of square roots
I'm very new to Mathematica, and I've been using it to evaluate some symbolic expressions in my research that are too complicated to do by hand. However, some of them don't simplify when it is obvious ...
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1
answer
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Formal variables no longer simplifying well on new Mathematica version?
I work with a lot of formula manipulation, modular forms etc. For example, the Dedekind eta function comes up a lot, and I'm often interested in the following sort of code:
...
- 1,307
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0
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49
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Integral with triangular functions in exponential and numerator
I am trying to find the solution of an integral with a triangular function in the numerator and in an exponential, but after an hour Mathematica has not given me an answer. I wondered if there is a ...
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3
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Mathematica 13.0 simplifies trigonometric integral wrong
I calculate the following general expression:
...
- 73
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1
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64
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How do I verify an equality no matter the equivalent arrangement of the parts?
I am a new user of Mathematica and have been trying to find a method for verifying equality. The issue that I keep running into is that nothing seems to work for all cases. Let me give you some ...
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2
votes
2
answers
155
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Simplifying expression with particular form of variables
I'm trying to express the expression in terms of ratio (wa/py) and (wb/py). Is there any command or function that could achieve ...
-3
votes
1
answer
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Taking sentences with a spatial factor [closed]
To ask my question precisely, I should say that I have got many terms, among them some have coefficients $M^n$. Some things like :
$$f = f_1(M) + f_2(M) + M f_3(M)+ M^2 f_4(M)+f_5(M)+...$$. I need to ...
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Simplifying an expression(s) for an equilibrium point?
Trying to use Bob Hanlon's solution from here for the following system doesn't seem to work here, why?
How do I simplify the equilibrium point to this simplified expression?
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61
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I am unable to plot 3D graph of integral function
I am not able to solve this integral
...
5
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1
answer
124
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Factor out common terms from a list of terms
I was looking for an automated way to factor out common terms from a list.
Example (assuming n<1):
...
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votes
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answer
69
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Select with simplification does not work
Given a list, I want to find all elements that have positive imaginary part.
For example, if $y,z\in\mathbb R$ and $a>0$ and the list is $\{ ia+y, -ia+z\}$, then the result should be $\{ia+y\}$.
...
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42
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Simplifying conditional expression
I have an expression of the form
ConditionalExpression[I a + y1, {True, True, True, True}]
as a result of some computation. (The expected answer is just ...
- 923
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votes
1
answer
80
views
Get the correct branch form Solve
I am reproducing the derivation in this article (exploration of a family of circles centered on an ellipse).
I only need the outer curve, the results obtained from Mathematica are more complicated ...
- 4,932
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4
answers
349
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Finding a closed-form solution or a better approximation to a function in Mathematica
I have the following equation:
$$f(L) = \left\lfloor{\frac{1}{4}\sum_{n=1}^{L-1}\left\lfloor n+300\times2^{n/7}\right\rfloor}\right\rfloor$$ where $1\leq L \leq 99$
My goal is to find a closed-form ...
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votes
1
answer
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ReplaceAll with Powers
If I run the following code:
a^2/b^2 /. {a/b -> c}
I'm getting output:
a^2/b^2
How can I obtain ...
- 23
1
vote
1
answer
82
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Solving multivariable trig Identities
I'm trying to solve for a certain set of trig identities in terms of other trig identities. I saw this and this, but in my example, I have two tries:
...
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2
votes
1
answer
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Mathematica is messing around with absolute values and sqrts of complex numbers?
I know that $$\begin{pmatrix}0&Z\\Z^*&0\end{pmatrix} \quad\text{has eigenvalues}\quad \lambda_\pm=\pm|Z|$$
but Mathematica gives me
...
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2
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60
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2
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1
answer
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Simplifying a power of complex exponential quotient
I have an expression of the form $(\frac{-1+e^{i\,N\,\phi}}{-1+e^{i \phi}})^n$.
I want to use mma to hopefully simplify it.
I have tried ComplexExpand[], PowerExpand[] with simplifying assumption in ...
2
votes
2
answers
91
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Implies does not return true for a equation
Check the Edited too, please:
i have a simple equation which i expect to get TRUE from Implies but it just returns the same thing to me. Implies works well for easier examples but I have some more ...
- 443
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How to use System`Private`AssumptionAccess and Assumptions`*?
I see this function is used by some symbols in Assumptions`*, and it HasDownCode and does not ...
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Simplification of long trigonometric expression taking a long time
I have tried to Simplify as well as FullSimplify a long trigonometric expression to get a simplified form of the expression but it takes a very long time almost hours and sometimes it also shows error ...
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0
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28
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How to combine several similar terms in computation of algebra?
As the title shows, how can I combine several similar terms when I try to compute some complex algebra terms. For example, I want the result of $$\frac{1}{6} b_1 \left(-\left(b_2^2 \left(-2 \sqrt{3} e^...
- 101
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votes
3
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138
views
Equalities for trace with symbols
Mathematica does not seem to know basic rules for computation with trace when one uses symbols; e.g.
FullSimplify[Tr[A.B] == Tr[B.A]]
gives as output
...
- 625
3
votes
2
answers
126
views
Replacing an arbitrary function of a variable [closed]
If I do something like
1/Sqrt[x] /. {Sqrt[x] -> a}
it does not lead to an expected result, but can be fixed with
...
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How to simplify and get the results I want?
How to simplify and get the results (3.10) I want?
I want to get the result of (3.9)and (3.10) according to (3.6),(3.7)and(3.8). But the result I got was not (3.10). I don't know where I made a ...
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Integrate requires FullSimplify
I have to solve this integral:
\begin{align}
\int_{-\pi}^{\pi}\int_{-\pi}^{\pi} \text{dMI}(\phi_1, \phi_2)\log\left(4\pi^2\text{dMI}(\phi_1,\phi_2)\right)d\phi_1 d\phi_2
\end{align}
where
$dMI(\phi_1,\...
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Global assumption non zero
I would like to define globally an assumption stating that I have a nonzero real vector $v$.
For now, I put :
$Assumptions = Element[v,Vectors[{100},Reals]]
but $v$ ...
- 442
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61
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FullSimplify crashes kernel
I'm trying to simplify an enormous analytic expression as much as possible. When I use Simplify, I get a half-decent result in about 20 seconds. However when I use <...
- 381
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0
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42
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Simplify does not work for a certain kind of fraction
I have come up with an expression like this:
b = (a^49. + a^50.) * Exp[a^(1./2)] / a^(99./2)
I expect that the large power on the denominator can cancel with that ...
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1
answer
94
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Help with optimization of Reduce/Solve function
I have a set of vectors in $3$D as shown below,
...
- 268