Questions tagged [simplifying-expressions]

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

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Converting an equation to the form $ax+by=c$

I have a linear equation that comes as a result of applying orthogonality on a non-homogeneous boundary condition with two unknowns $C_1$ and $C_2$. Can someone help me to express this equation in the ...
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0answers
34 views

Simplifying the final coefficient expression of a PDE solution

I have been trying to solve a boundary value problem analytically which involves a three-dimensional temperature Laplacian over a parallelepiped. In the final step of my solution, using the two non-...
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Calculate density of states for 1D system

The density of states for a 1D system can be written as: $D\left(\omega\right)=\frac{L}{\pi}\frac{1}{d\omega\left(k\right)/dk}$ I have some expressions for $\omega\left(k\right)$: ...
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45 views

Simplifying expressions using elementary properties of integrals

I want to be able to use Simplify (or FullSimplify) to simplify expressions involving, for example, sums of integrals, for ...
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2answers
105 views

Re-writing $f(x, y)$ as $g(x)h(y)$ [duplicate]

Is there a general way of re-writing a function of two variables as a product of two functions, $$f(x, y) = g(x)h(y)$$ Specifically, I’m trying to write an expression, $$f(x, y) = \frac{a y - x}{y - 1}...
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2answers
58 views

How to get rid of imaginary part in cubic root

When I try to solve the following cubic equation for $a$ on mathematica : S=Solve[a^3 - 4 x - 2 a^2 x + 8 x^3 + a (- 6 - 4 x^2) == 0,a]; I get a complex expression ...
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1answer
39 views

Issues arising when using UnitSimplify for getting a dimensionless expression

I am having some difficulties when using UnitSimplify in manipulating expressions for obtaining dimensionless quantities in Mathematica 12.0.0. Here is a minimal ...
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1answer
65 views

Simplify complex expressions

How can I simplify this expression? I tried the functions simplify and FullSimplify. Also the expand function didn't help me. I would like to know about solving such problems in more detail ...
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0answers
63 views

Complete simplification using Simplify or FullSimplify [closed]

I have tried to simplify $\qquad \left(\left(\frac{\left(a^{\frac{a-1}{a}}+a^{\frac{a+1}{a}}\right)^a}{a^{a-1} \left(a^{2/a}+1\right)^{1/a}}\right)^{\frac{a}{a^2-1}}-1\right)^a$ a little with ...
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0answers
39 views

Ordinary differential equation in the real domain

If I have the following equation (y - 1) ^5 == 32 I can select the real solution with Solve[(y - 1) ^5 == 32, x, Reals] Now, I ...
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2answers
57 views

Better way for constant expressions in functions than storing as global variables?

For example, I wrote a function like this: inversions[list_] := Complement[ Subsets[{1, 2, 3, 8, 4, 7, 6, 5}, {2}], Subsets[list, {2}] ] But as you see, ...
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1answer
113 views

Verification of a general solution to d'Alembert equation

I solved a nonlinear differential equation (d'Alembert one) by hand. Mathematica gives the same answer. But I am not able to get Mathematica to verify the solution due to branch cuts. Any one knows of ...
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0answers
107 views

Simplify Vs FullSimplify

I performed an integral and received an extremely long answer. I tried running FullSimplify on the answer, and after 72 hours gave up. Does ...
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1answer
50 views

When does Solve return root objects and when does it not for cubic equations?

Cubic polynomials always have explicit solutions and Mathematica certainly knows about them. But Mathematica will by default show the explicit solution only sometimes. I'm guessing there is something ...
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1answer
43 views

Symplifying expressions with exponentials inside square root

I have an expression $$ \exp (i k x) \sqrt{y^2 \exp (-2 i k x)} $$ When I put this in Mathematica and do FullSimplift, it gives ...
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1answer
68 views

How to Solve this specific inequality

I want to solve this inequality for l. I have tried to use Reduce and Solve and its not worked out. How can I solve this? ...
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1answer
33 views

Collecting items inside parentheses

I have an expression of this type: $$\left( 1+\frac{a+b}{c}\right)^{d} $$ My question is, how can I collect variables inside parentheses? Of course without putting commands inside parentheses.
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3answers
152 views

How to reduce this binary polynomial to the sum of squares in various ways

I can convert this binary polynomial to the sum of the squares of multiple polynomials using the following method: ...
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3answers
213 views

Incorrect Result from DSolve for Diffusion IBVP?

The result of DSolve for the following IBVP doesn't seem to satisfy the IBVP: \begin{cases} u_{t} - ku_{xx} = 0 &\mbox{} k>0,x>0,t>0 \\ u(0,t)=p(t) &...
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1answer
26 views

Reducing large polynomial expression to product of simplar polynominals

A beginner to Mathematica. I am trying to express a large symbolic polynomial expression as a product of factors of simpler polynomials: For example I was able to factor this expression: ...
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1answer
44 views

Applying the command “expr/.rule”, to find the expansion of Cos[a+b]

how can i find the expansion of Cos[a+b], using the expression g[f[{a,b}]].So i am specified to use one shot replacement to get the expansion by replacing the argument of the expression given. I tried ...
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1answer
49 views

Simplify multiple layers fractions

I have a complicated fraction ...
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1answer
26 views

How do I get from a few sub equations to a final equation?

I have a few start equation like Z1 and Z2 in the S domain. How can I use Mathematica to get the final equation? Including the index numbers?
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1answer
33 views

help on simplification with integrals

V 12.1 How can one help Mathematica obtain zero for the following expression, by telling it that $k$ is really just a constant? $$ k \int_{-\infty }^{\infty } f(x) \, dx-\int_{-\infty }^{\infty } k ...
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3answers
156 views

Inhomogeneous Heat Equation Formula Not Satisfying IVP

From Wikipedia, However, when I plug the formula of $u(x,t)$ into Mathematica 12.1, it doesn't seem to satisfy the PDE (does not give $0$): Here is the code: ...
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0answers
41 views

Extention of Times operation causes bug in Expand?

I have the following code in Mathematica 11.01 : ...
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1answer
105 views

How to express this radical in terms of Golden Ratio?

(1/3)*Sqrt[(1/11)*(-3 - 2*Sqrt[5] + 3*Sqrt[178 + 82*Sqrt[5]])] $$ r=\frac{1}{3} \sqrt{-2 \sqrt{5}+3 \sqrt{82 \sqrt{5}+178} \over 11} $$ I need to express this ...
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1answer
35 views

Cancel out common factors in algebraic expressions that are equal to zero

I have the following original expression: (100 c)/(e y) + (100 b x)/(e y) + (100 a x^2)/(e y) == 0 which, after factoring out the common terms looks like this ...
4
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1answer
53 views

Compare 2 expressions with variables

I want to check if two expressions are equivalent with Mathematica. For example, is $2 x + 4 + 2$ equivalent to $2 (x + 2 + 1)$. I tried the === operator, which I ...
2
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1answer
51 views

Exploit bilinearity of KroneckerProduct symbolic calculations and inconsistence (apparently)

Mathematica 10 recognizes the bilinearity of the trace and the Kronecker product, as well as Tr$\otimes$Tr$(A\otimes B)=$Tr($A$)Tr($B$). But I have issues trying to implement this in symbolic ...
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1answer
24 views

Simplify Difference of Conjugate Pairs

Is it possible to easily simplify the difference of conjugate pairs? In particular, if there's just a single variable, then FullSimplify[a - Conjugate[a]] ...
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1answer
43 views

Simplify Jacobi Polynomials

How can I force Mathematica to use the identities satisfied by Jacobi polynomials $$ (1-\cdot)P_n^{(\alpha+1,\beta)} = \frac{2}{2n+\alpha+\beta+2}\left((n+\alpha+1)P_n^{(\alpha,\beta)}-(n+1)P_{n+1}^{(\...
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1answer
417 views

Why does Mathematica give exact solution 0 for this indeterminate expression?

I have this function: $\frac{(1-\cos (\theta )) $ and I want to know its value for $x=\pi$, $\theta=0$ and $n\in\mathbb{N}$. It is clear that both numerator and denominator are zero, so the result ...
2
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3answers
112 views

Turning numbers embedded in deeply nested lists into strings [closed]

This must have a simple answer, but I cannot think of it. I want to take the numbers in a list such as: {1,{2,{{3,4},{5,6}},7,8} into strings. ToString will turn the whole list into a string. ...
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2answers
33 views

How do you simplify a boolean expression (!A B)+(B !C)+(BC)+(A !B !C)? [closed]

How would you simplify the following boolean expression (!A B)+(B !C)+(BC)+(A !B !C)? I factorised B and managed to get B(!A+!C+C)+(A !B !C) = B+(A !B !C), but I do not know where I should go next. ...
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3answers
86 views

Finding the value of an expression [closed]

Here is an expression that can be easily shown to equate 2 by analysis. $$\sqrt[3]{7+\sqrt{50}}+\sqrt[3]{7-\sqrt{50}}$$ But no matter what i try Mathematica always shows a complex result:2.62132 + 0....
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1answer
78 views

Is there a way to force Mathematica to collect terms in a more readable way?

I've got the following result from an operation in Mathematica: ...
4
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1answer
56 views

How do I extract just a part of an expression?

I have the result of an operation: ((t0M^2 + t1M^2)*xC/(2*t0M^2) What is the best way to get just the $\frac{t0^2+t1^2}{2\space t0^2}$ from this expression? This ...
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1answer
45 views

Simplifying complex expresion (without ComplexExpand or User defined rules) [closed]

Many times, I've struggled with simplifying complex expressions, such as this extraordinarily simple expression, and Mathematica wont do it: ...
1
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1answer
69 views

How do I define if two variables are equal to each other

Let's say I have the function x + y = z and I know that x = y. How can I define this in Mathematica? I tried using ...
4
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1answer
88 views

A pattern replacement to force Mathematica to replace inexact 0 multiplication by zero

Hi Consider the following expression which contains multiplication by inexact 0 ...
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0answers
63 views

Why doesn't Mathematica simplify? [closed]

Consider the following: Simplify[Integrate[x^(a), {x, x1, x2}], x1 > 0 && x2 > 0 && a > 0] Mathematica doesn't simplify this for me. I ...
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0answers
55 views

How to deal with complex equations in Solve method?

I am trying to deal with complex equations to solve them and use them in the plot. I want to know why these equations are not being solved. ...
1
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1answer
42 views

Is there any way to prioritize Gamma function?

In Mathematica, if you type Gamma[1, 0, -a] It automatically simplifies to 1 - E^a. I wonder though if there is a way to stop ...
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0answers
42 views

Force Solve to respect unit system

I give Solve quantities in FPS and it returns resulting quantities in SI, necessitating that I add an entire section to my workflow where I pick apart the solution ...
3
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1answer
106 views

Simplifying algebraically

Is there a way to derive an simplified expression from other equations. Or create an alternate form such that the main equation takes other equations and manipulates the main function. Here is what I ...
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0answers
27 views

Computations with OptimizedExpressions without completely expanding them

I have to manipulate huge expressions that are rational functions of many (∼30) variables with integer coefficients. Storing them just as a ratio of two polynomials would be impractical. But they can ...
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0answers
34 views

Group parameters that only occur together [duplicate]

I have a long and complex univariate expression with many parameters, $ f(x; a, b, c, d, ...) $. I would like to group those parameters which only ever occur together. Here is a very simple example ...
1
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1answer
29 views

Simplify expression with abstract matrices

After defining a commutator function Commutator[X_, Y_] := X.Y - Y.X; I would like to be able to simplify abstract matrix algebra expressions such as ...
4
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1answer
62 views

How to Force the PolyGamma[0, x] function or the HarmonicNumber[ x ] function

I'm crunching some infinite summations, and sometimes Mathematica generates results that have the PolyGamma[0, x] function (which is the Digamma) and sometimes the <...

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