# Questions tagged [simplifying-expressions]

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

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### Why do Resolve and ForAll fail with trigonometric expressions?

Why Resolve is not able to solve this problem? Similarly Solve and Reduce are not able to do ...
458 views

### Sum of sinusoids at the same frequency but with different amplitudes and phases

Three sinusoids at the same frequency are superimposed: Cos[3.1 - t] + 5 Cos[π/4 + t] + 2 Sin[0.3 + t] How can the resulting oscillation be stated in the following ...
28 views

### Simplify argument of Logs

I have the following expression ...
123 views

### Strange result simplifying higher order BesselJ

Consider the following integral: $$\int_0^1 Z_n^m(r)\ J_m(\rho r) r dr$$. The solution of this should contain a single Bessel function: $$(-1)^{(m-n)/2}\ J_{n+1} (\rho)/\rho$$ (see https://www.osti....
56 views

### Expanding Pochammer symbols/Gamma function for simplifying expressions

TLDR: How to expand gamma functions or Pochammer symbols in an arbitrarily long product? Some context I am trying to find out a closed-form expression for $\langle r^\alpha\rangle$ for the non-...
45 views

### Why can't Mathematica simplify $\left(e^{t/m}(gm)^{1/k}\right)^{-k}$? [duplicate]

It seems Mathematica can't simplify this Simplify[(e^(t/m)*(g*m)^(1/k))^(-k)] The result is I think it should be
1 vote
66 views

### More intuitve way to simplify a simple expression involving two exponential factors

Is there a way to ask Mathematica to simplify expressions it generates, like: $e^{-\frac{A t}{v^3}-\frac{v^2}{2 w^2}} \left(-1+e^{\frac{A t}{v^3}}\right)$ into a more readable form by taking out the ...
1 vote
103 views

### Using Reduce to simplify (not solve) system of equations

I'm dealing with a Mathematica program that generates a set of coupled non-linear equations involving an unknown function and its derivatives with respect to at least one independent variable. My goal ...
1 vote
101 views

### Why does assuming f[_] > 0 does not work while Element[f[_], Reals] does?

Refine works with symbols in either way: Refine[Sqrt[x^2], Element[x, Reals]] (* Abs[x] *) Refine[Sqrt[x^2], x > 0] (* x *) ...
71 views

### PiecewiseExpand fails to address assumptions

PiecewiseExpand seems to ignore more complex assumptions. Here's an example: ...
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### How to factorize $x+y$ in this kind of example?

Consider the following simple polynomial in two variables 5 + 2x + 2y. Suppose I want to simplify it to 5+2(x+y). I have no idea ...
307 views

### How to make ReplaceAll recognize what to be replaced in a situation like this?

I'm a bit confused on how ReplaceAll works. For example ReplaceAll[2x+2y, x+y -> 1] just gives ...
107 views

### Simplify inverse of function

This would be a noob question, but I need help simplifying the inverse of an expression ...
39 views

### How to make MMA distinguish between symbolic coefficients and variables when doing factorization? [closed]

I what to factor a polynomial with complicated symbolic coefficients Factor[p0^2 + k^2 r^2 \[Tau]^2 - 2 k p0 r \[Tau]^2 \[Omega] + p0^2 \[Tau]^2 \[Omega]^2] In ...
56 views

### How to collect specific terms in an equation and set them to new parameters?

I have this equation ...
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### Long outputs manipulation

does anyone know how to get the expressions of this shortened form? when I try to use "show all" my mathematica collapses
37 views

### Simplifying symbolic expression using replacement rules

I am trying to carry out a linear stability analysis of a two PDE system. I start by defining the equations and then define the perturbation along with the replacement rules required. I then use a ...
112 views

### How to force Mathematica to simplify in terms of half angles?

By basic trigonometric identities, the expression $\frac{\sinh(x)}{\sqrt{2}\sqrt{1+\cosh(x)}}$ simplifies to $\sinh(\frac{x}{2})$. But Mathematica seemingly don't perform this simplification. I tried ...
40 views

### RuleDelayed with Simplify?

I have the Rule yRule = y -> Function[{l,m,x},x^(l + 1) Exp[-((2 I m)/x)] Hypergeometric1F1[1 - l, -2 l, (2 I m)/x] ] Is it possible to replace and simplify ...
48 views

### Limit giving indeterminate result

I have a function $r_h(v)$ given by, $$r_h (v) = \left(\frac{m_0}{2 g} e^{-g v_f} \left(-1+e^{-g(v - v_f)} \right) \right)^{1/5}$$ where $m_0$ and $g$ are just numbers. I want to take the limits of ...
282 views

### How to simplify logical expression?

I would like to simplify (a == c && c != 0) || (a == 0 && c == 0) to a == c How can I do that?
64 views

### Assuming Refine does not work for all If[] expression part

One simple example as following ...
69 views

### How Not to Simplify Exponential of Log?

I have the expression Power[x,I y] Both $x,y$ are real. Now I want to write this expression in term of Exponential of Logarithm. The expression can be rewritten as ...
46 views

### Evaluation gives different results before and after simplifying expression

I am trying to evaluate $h(z)=\frac{f(z)}{g(z)}$ at points $z$ close to 0. Here I have taken an example value of $z=\texttt{z1}=10^{-7}$ for demonstration. I notice that evaluating the fraction before ...
85 views

### How to prevent evaluation without simplification?

I am trying to compute a sequence of terms, which have a form similar to $g(z)$ at different points $z$. For $z$ close to 0, I have observed that the terms are evaluated as 0/0 (indeterminate form) ...
3k views

### Why doesn't Mathematica recognise two integrals as equal?

The following expression $$\int_{0}^{t} f(t_0) \,dt_0 - \int_{0}^{t} f(t_1) \,dt_1 = 0$$ is zero because it is just a change of integration variable. Why doesn't Mathematica give zero in this case? <...
56 views

### Is it possible to get rid of the square root in the solutions of the following symbolic quadratic equation?

I have a quadratic equation, which I want to solve, but don't want the square root to appear within the solutions. I tried converting the discriminant into a quadratic form but failed, not sure if ...
163 views

### Is there a built-in expression transformation which can perform this simplification?

I have an interval overlap test like this: ...
1 vote
156 views

### Converting expression to quadratic formula

I want to manipulate and represent the following expression in a more presentable way. ...
60 views

### Simplifying to remove all imaginary numbers

I have a purely real function (spec[w], where Im[spec[w]]=0), found through ...
1 vote
86 views

### Attempt to find a solution (out of potentially many) to a system of equations with FindInstance runs forever or crashes

I have a system of equations that in principle should have a solution (I would think not a unique one), which I want to solve. I am not interested in all solutions; I just want to locate one, assuming ...
1 vote
143 views

### Simplifying expressions with directional derivative

Suppose I have a function $f(x, y)$ which is differentiable everywhere (but not explicit). When I run a code snippet like: ...
1 vote
71 views

### Strange behaviour of Simplify

MMA version 13.3 Can somebody explain the following behavior: Here Simplify works as expected: x1 e + x2 e // Simplify (x1 + x2) e However, here ...
72 views

### Simplifying fraction containing Abs

The original formula looks like this: Abs[(b x0^2)/(2 a) - (a y0^2)/(2 b)]/Sqrt[x0^2 + y0^2] How to get: ...
1 vote
206 views

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### How to group terms with the same exponential factor together after Expand?

ET[t] := E1*Exp[-I*w1*t] + E2*Exp[-I*w2*t] + E3*Exp[-I*w3*t] + E1*Exp[I*w1*t] + E2*Exp[I*w2*t] + E3*Exp[I*w3*t]; THGExp[t] = ET[t]*ET[t]*ET[t]//Expand; I ...
1 vote
53 views

### Alternative to simplification speed-up by replacing an integer with its "non-exact" counterpart

This is a safe setting which assured that all of the equations I want to simplify are actually fully simplified: ...
1 vote
52 views

### Adjustment of AssumptionsMaxNonlinearVariables which avoids both blocking and partial solutions

I write an application which calls Mathematica via API. However, as it turns out, I would need to manually tune ...
For Bessel functions of positive integer order, it is known that $(J_{i-1}(\alpha_{i,n}))^2 = (J_{i+1}(\alpha_{i,n}))^2$ where $\alpha_{i,n}$ is the $n$th zero of $J_{i}(r)$. Indeed, Mathematica knows ...