Questions tagged [simplifying-expressions]

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

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Factorize in a particular way

I was trying to factorise this polynomial expression: TestPolynomial=-p1^2 x1 x2 - p3^2 x1 x3 - p1^2 x2 x3 + 2 p1 p3 x2 x3 - p3^2 x2 x3 into this form, ...
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3 votes
0 answers
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Express polynomials as sum of squares

Well, while SOStools of Matlab can express a polynomials as SOS (Sum Of Squares) by the following theorem: A multivariate polynomial p in n variables and of degree 2d is a sum of squares if and only ...
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  • 131
3 votes
1 answer
95 views

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}-...
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  • 2,615
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0 answers
66 views

It's exactly the same as the original answer by simplification [closed]

I use this ...
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3 votes
3 answers
241 views

Simplify Log monotonicity

Why does: FullSimplify[(n+1)^2>n^2,n>=2] evaluate to True, but: ...
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1 vote
1 answer
103 views

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 ...
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1 vote
0 answers
37 views

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 $n[c]$ ...
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  • 115
1 vote
2 answers
60 views

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 ...
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4 votes
0 answers
53 views

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 ...
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  • 41
0 votes
1 answer
45 views

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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  • 3
2 votes
0 answers
51 views

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 ...
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  • 463
1 vote
0 answers
40 views

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 ...
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  • 463
6 votes
2 answers
389 views

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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0 answers
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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 ...
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1 vote
1 answer
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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 ...
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1 vote
1 answer
116 views

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 ...
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0 votes
0 answers
36 views

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: ...
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2 votes
2 answers
391 views

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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5 votes
1 answer
152 views

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 ...
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1 vote
1 answer
79 views

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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9 votes
0 answers
97 views

Why FullSimplify return {} on this solution of ode?

Update: Same result is generated using 13.1 I was calling FullSimplify with timeout on solution of ode. The idea if it timesout, then will try ...
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  • 109k
2 votes
1 answer
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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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  • 21
2 votes
1 answer
101 views

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: ...
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0 votes
0 answers
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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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  • 131
7 votes
3 answers
1k views

Mathematica 13.0 simplifies trigonometric integral wrong

I calculate the following general expression: ...
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0 votes
1 answer
64 views

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 views

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 ...
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-3 votes
1 answer
70 views

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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  • 91
0 votes
1 answer
63 views

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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  • 465
0 votes
0 answers
61 views

I am unable to plot 3D graph of integral function

I am not able to solve this integral ...
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5 votes
1 answer
124 views

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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  • 1,133
3 votes
1 answer
69 views

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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0 votes
0 answers
42 views

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 ...
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2 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 ...
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  • 4,952
1 vote
4 answers
349 views

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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  • 121
2 votes
1 answer
125 views

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 ...
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1 vote
1 answer
82 views

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
88 views

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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  • 385
2 votes
2 answers
60 views

Collecting terms in an expression using a specific pattern

I have the following expression: ...
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  • 357
2 votes
1 answer
59 views

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 ...
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2 votes
2 answers
91 views

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 ...
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  • 443
1 vote
1 answer
38 views

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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  • 1,663
0 votes
0 answers
89 views

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 votes
0 answers
28 views

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^...
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  • 101
4 votes
3 answers
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 ...
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  • 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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  • 673
1 vote
0 answers
56 views

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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  • 13
0 votes
0 answers
45 views

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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0 votes
0 answers
29 views

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 $v$ ...
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  • 442
0 votes
0 answers
61 views

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 <...
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