Questions tagged [simplifying-expressions]

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

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53 views

solving an equation by suggested method [closed]

I have an equation I want to do this issue: T(dV/dT)-V=0 and obtain T that satisfy this relation. How can I do it? we should at first obtain V and then Drivate it. How can?
2
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2answers
81 views

Symbolic properties of Re and Im

I want to define a function f such that f[x] is real whenever x is real. So I define ...
2
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1answer
81 views

Simplifying this expression with Gamma

The Gamma function has the property that $\Gamma(z+1)=\Gamma(z)z$, so this expression: ...
2
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1answer
51 views

How to get the result in terms of a previously defined expression?

Say I have a vector X[n_] := Table[Subscript[x, i], {i, 1, n}] and a matrix of connections: ...
4
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0answers
26 views

How does Simplify deal with contradictions in the assumptions?

Context Sometimes Simplify does generate a warning when the assumptions are self-contradictory. Take this example: ...
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0answers
32 views

Eliminate radicals from a symbolic expression

I get a lot of expressions of the type -(((11 + z) (13 - z + Sqrt[25 - 26 z + z^2]))/( 6 (-11 - z + Sqrt[25 - 26 z + z^2]) (7 - z + Sqrt[25 - 26 z + z^2]))) Which ...
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0answers
44 views

Why doesn't Mathematica ComplexExpand integrals?

Consider this code example: ComplexExpand[Re[Integrate[f[t], {t, a, b}]]] Mathematica gives me the result as ...
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0answers
26 views

Why are these expressions with shifted delta functions not equal?

I have the following equation Exp[a-t]*DiracDelta[t-a] == DiracDelta[t-a] which cannot be evaluated. However, if I plug in 0 for a: ...
0
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1answer
73 views

Why doesn't Mathematica cancel this constant out of the integral?

I have the mathematical expression Integrate[f[r], {r, τ, t}] == a*Integrate[f[r]/a, {r, τ, t}] which is obviously true for all functions ...
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0answers
64 views

What did FullSimplify do to deliver a likely wrong expression?

I recently hit a bug in my code and it eventually turns to be a likely error in the simplification of a formula given by FullSimplify. The code is attached and ...
0
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2answers
55 views

Fraction not simplifying — potential precision error [closed]

I have the following fraction which in principle can be simplified such that the term (constant + $\omega$) cancels on the top and bottom. Mathematica is not doing so and I'm guessing it's an issue ...
3
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2answers
69 views

Trouble verifying a solution to a differential equation

I am reading a physics book which has discussed one approach towards solving the differential equation $$ \frac{d^2 x(t)}{dt^2} = Cx(t) $$ as follows: Using Mathematica to solve the equation. I tried ...
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1answer
35 views

Comparing two equivalent definite integrals

Reading this question on Math.SE, I tried the following Mathematica instructions ...
8
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1answer
108 views

Why does Simplify work diferently for (a+b)/e versus (a+b+c)/e?

I am playing around with Simplify amd assumptions. I noticed that: Simplify[x > (a + b)/e, x < (a + b)/e] ...
2
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1answer
40 views

Finding diagonal $p$ of a cyclic quadrilateral with sides $(a,b,c,d)$

Let the semi-perimeter of each divided triangle be $$(2s_1,2s_2)= (a+b+p, c+d+p);$$ How to find the common diagonal $p?$ Equating common circum-diameter fetches $$ \dfrac{a^2b^2}{c^2d^2}=\dfrac{s_1(...
3
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1answer
38 views

How can I remove vanishing derivatives of hypergeometric functions?

I have a lot of expressions containing derivatives of hypergeometric functions of the sort: $$_2F_1^{(0,0,1,0)} \left(\frac{1}{2} , 1 ; \frac{3}{2} ; 0 \right). \tag{1}$$ The last argument is always $...
5
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0answers
70 views

Simplification depends on the names of variables

I am sure this issue has been discussed here, but it has never been asked whether this behavior is a bug. Therefore my direct question to the community: do you think this behavior is a bug? ...
0
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1answer
61 views

How to remove global constants in front of polynomial expressions?

I have a list of polynomials, many of them are equals up to some constants. For instance I have: ...
3
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1answer
72 views

Simplify Gamma function given integer variables

I want to simplify the following Gamma[1 + d - k] given the constraint that 1 + d - k is a positive integer. I have tried using ...
2
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1answer
61 views

Contradictory results for ODE in Mathematica [closed]

I am Solving the ODE $$x'(t)=A x(t)+w(t)$$ MMA gives a general result as $$x(t)\to e^{A t} \int_1^t e^{-A K[1]} w(K[1]) \, dK[1]+c_1 e^{A t}$$ Now I substitute $w(t)$ by $e^{-t}$, and obtain: $$c_1 e^{...
2
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1answer
63 views

Why is Mathematica telling me that two equal sequences are unequal?

These two sequences are identical: ...
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0answers
39 views

How to read Z == 0. - 0.00162663 W

I am solving a set of three linear equations with four variables and found out the values of X, Y and ...
2
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1answer
51 views

Interpreting an expression

When reducing and simplifying a complex algebraic inequality I get an expression containing Root[-a + b #1^3 &, 1] < β < (a/b) How can I interpret the ...
2
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0answers
36 views

Factor independent term from a summation?

Can I factor $t^2$ from $\frac{1}{t}\sum_{n=1}^{n1}t^2Exp[-a n^2+bn]$ to get $t\sum_{n=1}^{n1}Exp[-a n^2+bn]$ using some command? ...
3
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2answers
116 views

Removal of radicals to form algebraic expression

FullSimplify[( Sqrt[(x + h)^2 + y^2] - a) - e (Sqrt[(x - h)^2 + y^2] - b) == 0] How to remove the radicals to obtain an algebraic expression of fourth order using ...
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0answers
41 views

Finding the domain in which a function is analytic with no imaginary part

I was wondering if it is easy to see if a given expression evaluates to a real number in a given domain? Let e.g. f(x,y,z) be some function depending on three ...
6
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2answers
99 views

Simplifying expression containing Gamma

According to this site this expression involving Gamma is valid: $$\prod_{k=0}^{n-1}\Gamma\left(\dfrac{k+z}{n}\right) = n^{\frac{1}{2}-z}(2\pi)^{\frac{n-1}{2}}\...
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1answer
76 views

How to check if an expression is real in some domain

I was wondering if it is easy to see if a given expression evaluates to a real number in a given domain? Let $f(x,y,z)$ be some function depending on three variables $x,y,z$. I would like to know if $...
0
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1answer
28 views

How to simplify polynomial to get to particular factor?

If I have an expression like this ex = -l + l t - 2 t^2 + T + (l - 2 t) y This can be written as ...
4
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2answers
83 views

Simplifying an expression containing inverse trigonometric functions

I somehow know that when simplifying the expression $$ \frac{2}{3} \left(2 \sqrt{3 B^2+4 J^2} \cos \left(\frac{1}{3} \cos ^{-1}\left(-\frac{J \left(9 B^2+8 J^2\right)}{\sqrt{\left(3 B^2+4 J^2\right)^3}...
2
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3answers
80 views

How to solve these complex equations for plot?

I am trying to Plot this code but it is not showing any plot. I want a bistable type plot between "NL" and "P0" and there are six equations and six unknowns. The code is given ...
0
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1answer
36 views

Need help understanding the results of the unit function

I want to get Limit of the following function at $T\to 0$. $$ Eig=\frac{8 (\eta +J \sinh (2 \beta \eta ) \sinh (2 \beta J)+\eta \cosh (2 \beta \eta ) \cosh (2 \beta J))}{\eta Z^2} $$ where $Z=2 (...
1
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0answers
29 views

DSolve couldnot give correct solution or full simplify couldnot simplify correctly [closed]

I am using Mathematica 12.1.1 and solved the second order differential equation: DSolve[y''[x] - 3 y'[x] + 2 y[x] == 2 x^2 + 2 x*e^x, y[x], x] ... and it gave a ...
4
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2answers
100 views

Expression involving square roots not simplifying

I have a relatively simple expression here that is not simplifying: $$ \frac{2 s_0 \left(\sqrt{\gamma ^5 s_0}+\sqrt{\gamma ^9 s_0}\right)+\sqrt{\gamma ^3 s_0}+2 \sqrt{\gamma ^7 s_0}+\sqrt{\gamma ^{...
2
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1answer
80 views

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 ...
4
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1answer
131 views

Simplifying the final coefficient expression of the solution to a Laplacian

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-...
0
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0answers
32 views

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 $\omega\left(k\right)$: ...
2
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0answers
49 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 ...
4
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2answers
110 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}...
1
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2answers
62 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 ...
1
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1answer
46 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 ...
2
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1answer
66 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 ...
1
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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 ...
3
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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, ...
4
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1answer
119 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 ...
1
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0answers
115 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 ...
3
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1answer
51 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 ...
0
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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 ...
0
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1answer
79 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? ...
1
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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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