Questions tagged [simplifying-expressions]

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

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1answer
78 views

Simplify rules with variable number of arguments

Problem How to simplify the following rules? The rules simplify (single, double, triple ...) summations of Kronecker delta. Replacement should occur if any summation and the Kronecker delta share an ...
1
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1answer
56 views

Make Mathematica apply the same rule exhaustively in simplification

Use Case Mathematica evaluate the partial derivative as: $$\frac{\partial}{\partial A_{abc}}\sum _{j=1}^J \sum _{k=1}^K \log \left(\sum _{l=1}^L A_{jkl} B_{jkl}\right) = \sum _{j=1}^J \sum _{k=1}^K \...
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1answer
61 views

Different solution on trigonometric function in mathematica and wolframalpha using Simplify and FullSimplify [closed]

I have this expresion: -cos(a3) (cos(a2) sin(a1) + cos(a1) sin(a2)) And when I simplify with wolframalpha online, it give me this: ...
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1answer
65 views

Simplify sum of unnatural conditional functions generated by derivative

I try to use Mathematica to evaluate: $$\frac{\partial}{\partial A_{abc}} \sum_{j=1}^{J}\sum_{k=1}^{K}\log\left(\sum_{l=1}^{L}A_{jkl}B_{jkl}\right)$$ I get: $$\sum_{j=1}^J \sum_{k=1}^K \frac{\begin{...
5
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3answers
417 views

Simplify sum of Kronecker delta

The following simplification is correct: $$ \sum_{j=1}^{J}\sum_{k=1}^{K} \delta_{a, j}\delta_{b,k}A_{j,k} = A_{a, b}$$ How to make Mathematica do that? Try: ...
3
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1answer
72 views

Simplify and Sign working only in small expressions

I'm trying to find the sign of some very long expressions, but I don't seem to make it work using Simplify[Sign[...], Assumptions ...]. Here is an example of my problem. I can easily find the sign of ...
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0answers
80 views

Mathematica can't solve system of equations

I'm trying to solve an admittedly gnarly system of equations: ...
1
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0answers
43 views

Expression simplified for explicit int values, but not with FullSimplify/FunctionExpand and Assuming. What formula does Mathematica use?

I have a $_4F_3$ hypergeometric function (Mathematica 11.3) HypergeometricPFQ[{1, 3/2 + n, 1 + 2 m + n, 1 + 2 m + n}, {2 + n, 2 + n, 3/2 + 2 m + n}, z] If I ...
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2answers
49 views

Simplifying with restrictions on the whole expression

Suppose, for the sake of keeping things as simple as possible, that I have the following equation that I wish to simplify in Mathematica: $y = x x$ But suppose further that I also have a restriction,...
0
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1answer
72 views

FullSimplify not simplifying expression containing the form Sin[n] where n is an integer [closed]

I have a function f[n] which give 0 for integer input, but FullSimplify doesn't work for it, why? ...
1
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2answers
211 views

Simplify product of complex numbers

I am trying to take product of a complex number with its conjugate. When I take A*Conjugate[A] // FullSimplify The output is as desired ...
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3answers
88 views

Eliminating radicals from denominator or numerator of an expression

I need to find the limit when r2 tends to r1 of the following expression: ...
5
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0answers
121 views

Integrate under assumptions

I am trying to solve the following integral: $$\int_0^\infty u^{\sigma-1} \exp\left[-c u^\sigma\right] \mathrm{d}u$$ under the assumptions $\sigma \in (0,1)$ and $c>0$. I know the result is $$\...
4
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4answers
303 views

Alternative form of ArcSin[Sin[x]]

Is it possible to get the following result in Mathematica by using only built-in functions: $$\arcsin( \sin(x)) = x $$ if $x \in [-\pi /2 , \pi/2]$ $$\arcsin ( \sin(x)) = \pi - x $$ if $x \in [\pi /...
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1answer
59 views

Sum was simplified and I don't know how it was done

I want to compute the sum $\qquad \sum_{i=1}^{n+r}(i+1)n^{i-1}(n+1)^{n+r-i}$ However, when I input the expression ...
2
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1answer
97 views

Simplifying elliptic functions

I am working with (long) elliptic functions, which are rational functions in WeierstrassP and WeierstrassPPrime. As expressed in ...
2
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0answers
56 views

Simplify (or Reduce) a system of inequalities intelligently

I have the following system of inequalities of 4 real variables 3 (a + b) + 4 (d + c) > 0 && 2 (a - d) + 3 (b - c) > 0 The system can be written as ...
8
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2answers
177 views

Issue with Upvalues

I want to introduce two variables (I call them EXt and EXtC, where "C" stands for complex conjugate) which would mimic the behavior of a phase of a complex number. For that, I use the following tags: ...
10
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2answers
826 views

Mathematica can't simplify some logarithmic expressions

When I simplify some logarithmic expressions in Mathematica, it just returns the expression ...
0
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0answers
43 views

How can I simplify expressions correctly?

the final output of my code gives this expression which i call ttt: ...
3
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2answers
115 views

Rewrite $ x\sqrt{1-y^2/x^2} = \text{sgn}(x)\sqrt{x^2-y^2} $

I'm trying to coax Mathematica into rewriting $ x\sqrt{1-y^2/x^2} = \text{sgn}(x)\sqrt{x^2-y^2} $ for $ x $ and $ y $ real. I have tried all combinations of ...
0
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2answers
57 views

Calculate value of expressions based on solution of given linear equations

I have these three equations: 1/X + 1/Y == 1/15; 1/Y + 1/Z == 1/20; 1/Z + 1/X == 1/25; I want to calculate the value of expression: ...
1
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1answer
140 views

Simplifying a Sum of Fractions by Removing Fractions in Denominators

I have a sum of fractions of the form $x1 - \frac{(x2 + x3)}{(x4 + x5)} - \frac{(x6 + \frac{x7}{x13})}{(x8 - x9 - \frac{x10}{(x11 + x12)})}.$ How might I simplify it to remove fractions from the ...
1
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0answers
41 views

How to force the output to be in terms of a specific function?

I have a rectangular function rect[t], which is a window function with values of $ 1 $ in the interval $ (-\frac{1}{2},\frac{1}{2}) $:- ...
0
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1answer
42 views

How to assume lexicographical ordering

Suppose I have functions which depends on the symbols $c[I]$, where $I$ is some subset of $\{1,2,...,n\}$. For example, $$f = c[1] + c[1,2,3] + c[1,2],$$ $$g = c[2] + c[2,1],$$ Code: ...
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0answers
59 views

For Fourier Transform with $ x(t) $, how to obtain result in terms of $ X(f) $?

I have a function $ x(t) $ and I denoted its Fourier transformation as $ X(f) $. I want to get the Fourier transformation of $ x(t)\mathrm e^{2\mathrm i \pi f_0 t} $, and I know the result is $ X(f-...
1
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0answers
40 views

Help Simplifying Expressions [closed]

I have the following set of equations: 1) $\text{$b_1$} \cos (\text{$\beta_1$} u)-\text{$b_1$} \cosh (\text{$\beta_1$} u)-\text{$b2$} \cos (\text{$\beta_1$} \theta y)-\text{$d_2$} \cosh (\text{$\...
1
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0answers
40 views

Simplyfing a quotient of polynomials [closed]

I am trying to simplify some quotient of polynomials. In this case, they are really easy but I will have to deal with way harder expression and I wanna know how to do it in full generality. An example ...
0
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4answers
95 views

help with simplifying function

I am computing the 4th order talyor approximation of this function $$\big(\frac{b}{g-x}\big)^{0.25}$$ The analytic textbook result is: $$b^{0.25} \big(\frac{1}{g^{0.25}}+\frac{0.25 x}{g^{1.25}}+\...
10
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3answers
550 views

Remove Abs from Norms of Vectors

I have the following norm Norm[{a, b*c}] (* Sqrt[Abs[a]^2 + Abs[b c]^2] *) How do I remove the Abs from it? ...
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3answers
83 views

How to force an expression to be shown in terms of a specific function?

I have an integral inte1 as below: ...
2
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3answers
94 views

How can I find the rules I need to simplify my expression?

In a previous post, I simplified the following equation f = (P ((2 - ϵ) Log[1 - ϵ] + (2 + ϵ) Log[1 + ϵ])) / ((-1 + ϵ) Log[1 - ϵ] - (1 + ϵ) Log[1 + ϵ]) $\...
1
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2answers
78 views

FullSimplify of equation that contains Log has no effect (and I think it should)

The following equation, f = (P ((2 - ϵ) Log[1 - ϵ] + (2 + ϵ) Log[1 + ϵ])) / ((-1 + ϵ) Log[1 - ϵ] - (1 + ϵ) Log[1 + ϵ]) when fully simplified as ...
1
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1answer
47 views

Eliminating Gamma from result of integration

I think the following integration result can be shown without Gamma. Can anyone explain Why Mathematica Uses Gamma. How to ...
0
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0answers
100 views

FullSimplify of Dirac Delta Function failed

I have t1 and t2 whose difference should be 0. But ...
5
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1answer
54 views

Simplify behavior: assumption as Interval versus assumption as bounds

I am using MMA V11.2 under Linux I am surprised by this: ...
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0answers
30 views

Preferences for simplifying

I often (always?) find that Mathematica prefers to express $(a-1)^2$ as $(-1+a)^2$, thus "wasting" a character. Moreover, for me, the expression $(a-1)^2$ is more attractive since it doesn't have the ...
8
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2answers
93 views

Finding sub-expressions that simplify larger formula

If I use FullSimplify on a large formula it will consequently return a much smaller expression. However, suppose I notice the simplified expression can benefit from ...
8
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2answers
207 views

How to simplify this huge expression to get a known smaller expression?

I have the following massive expression ...
0
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1answer
68 views

Incorrect results in trig table

I have a table given by Table[ Evaluate[ Sum[(Sin[(2 π j x)/(r + 1)])/(r + 1), {j, 0, r}]], {r, 1, 25}, {x, 0, 25}] /. Indeterminate -> 0 The ...
6
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2answers
100 views

Simplifying boolean algebra without using certain operations

when I use Simplify or FullSimplify in Mathematica it often simplifies it using all the existing boolean operations. For example,...
3
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1answer
66 views

Determining the absence of Truth value of an inequality given assumptions

I have a set of assumptions, say, $x > 0$ and $y > 0$. So I specified the $Assumptions = x > 0 && y > 0 Now the inequality $x - y/2 > 0$ ...
5
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2answers
96 views
1
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2answers
142 views

Why Mathematica does nothing with the expression Gamma[2 z]? [closed]

Could someone tell me why Mathematica just returns the input with this expression: Gamma[2z] Gamma[2 z] ? I expected this result: $Γ(2z)=\frac{2^{2z-1}Γ(z)Γ(...
0
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1answer
50 views

Simplifying a solution of an equation

I have a linear system, this way: ...
1
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1answer
45 views

Make a term appear in my solution

There is a solution for a linear system: ...
0
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2answers
275 views

Is $\frac{\log \left(\frac{1}{a}-1\right)+\log \left(-\frac{a}{a-1}\right)}{\log (10)} = 0$? [closed]

I have the following function, which for all values of $a$ is exceedlingly close to 0: (Log[-1 + 1/a] + Log[-(a/(-1 + a))])/Log[10] However, it does not ...
4
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2answers
188 views

Recursively turn expression into nested list

I've been trying to write a simple function that turns an expression into a nested list. So for example, a+2b+3c becomes {a,{2,b},{3,c}}. This is what I wrote: ...
1
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1answer
62 views

Modify the function `Simplify`

When I use Simplify with equations, the function simplifies both sides of the equation, for example: ...