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 ...
azerbajdzan's user avatar
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6 votes
3 answers
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 ...
saturnscalypso's user avatar
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Simplify argument of Logs

I have the following expression ...
BabaYaga's user avatar
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5 votes
1 answer
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....
AstronomyGeek's user avatar
2 votes
0 answers
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-...
Sanjana's user avatar
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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
Y. zeng's user avatar
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1 vote
1 answer
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 ...
kotozna's user avatar
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1 vote
1 answer
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 ...
José Ferreira's user avatar
1 vote
3 answers
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 *) ...
JS S's user avatar
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1 answer
71 views

PiecewiseExpand fails to address assumptions

PiecewiseExpand seems to ignore more complex assumptions. Here's an example: ...
user46831's user avatar
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3 answers
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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 ...
user1620696's user avatar
4 votes
5 answers
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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 ...
user1620696's user avatar
2 votes
2 answers
107 views

Simplify inverse of function

This would be a noob question, but I need help simplifying the inverse of an expression ...
Zain Ahmad's user avatar
0 votes
1 answer
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 ...
Haiqin Tang's user avatar
0 votes
1 answer
56 views

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

I have this equation ...
Dr. phy's user avatar
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2 votes
2 answers
63 views

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
TTT's user avatar
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0 answers
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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 ...
Mjoseph's user avatar
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4 votes
1 answer
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 ...
Sanjana's user avatar
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0 answers
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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 ...
Nitaa a's user avatar
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0 answers
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 ...
mathemania's user avatar
2 votes
2 answers
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?
ThomasAcc's user avatar
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0 answers
64 views

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

One simple example as following ...
eason's user avatar
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2 answers
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 ...
Nitaa a's user avatar
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0 votes
1 answer
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 ...
sai's user avatar
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2 votes
2 answers
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) ...
sai's user avatar
  • 121
8 votes
3 answers
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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? <...
Luca's user avatar
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1 answer
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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 ...
larry's user avatar
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2 votes
1 answer
163 views

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

I have an interval overlap test like this: ...
kirma's user avatar
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1 vote
2 answers
156 views

Converting expression to quadratic formula

I want to manipulate and represent the following expression in a more presentable way. ...
Dotman's user avatar
  • 424
0 votes
1 answer
60 views

Simplifying to remove all imaginary numbers

I have a purely real function (spec[w], where Im[spec[w]]=0), found through ...
Davis Last's user avatar
1 vote
0 answers
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 ...
AG1123's user avatar
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1 answer
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: ...
AspiringMat's user avatar
1 vote
0 answers
71 views

Strange behaviour of Simplify

MMA version 13.3 Can somebody explain the following behavior: Here Simplify works as expected: x1 e[1] + x2 e[1] // Simplify (x1 + x2) e[1] However, here ...
Daniel Huber's user avatar
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0 votes
1 answer
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: ...
csn899's user avatar
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1 vote
2 answers
206 views

Simplifying products of DiracDelta

I want to simplify expressions containing DiracDelta products. For example I want to simplify the expression $$\delta(z-2)\delta(k-5)\delta(t-z-k-9)$$ to give the answer $$\delta(z-2)\delta(k-5)\delta(...
Mohamed Mostafa's user avatar
4 votes
0 answers
110 views

Is there a way to get expressions to output in terms of Log2 instead of Log? [duplicate]

I'm in computer science, pretty much every logarithm I ever encounter is base 2. Normally, Mathematica wants to convert every logarithm to the natural log Log, so ...
Pavel's user avatar
  • 183
0 votes
1 answer
96 views

Get a linear second order differential equation

This question may seems naive, but I still learn calculus: The following equation is a second-order differential equation, since it contains a derivative $h''$, but is it a linear differential ...
Dr. phy's user avatar
  • 213
0 votes
0 answers
58 views

Why would /. Expand rather than replace an expression?

I'm using /., Simplify, FullSimplify, etc. to simplify complicated solutions to a system of differential equations. Part of this is replacing certain expressions by Greek letters, e.g., ...
Alan's user avatar
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0 votes
1 answer
58 views

Can I get Factor or another command to pull out common factors that appear only in subexpressions of very complicated expressions?

This follows a comment I posted earlier, to which I received several responses but which was then closed. I have used Simplify and FullSimplify with Assumptions to reduce down some very complicated ...
Alan's user avatar
  • 11
1 vote
0 answers
78 views

Series expansion message with special functions

I am trying to expand the following expression in alp,eps. Since the expression involves Hypergeometric2F1, I am using HypExp. <...
BabaYaga's user avatar
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1 vote
0 answers
57 views

How do I efficiently define rules for non-commutative algebras, (like differential forms)?

Defining rules seems to be quite troublesome, because whatever rule I make has to have the exact syntax ordering of the expression I want to modify. For example, take this differential form ...
ions me's user avatar
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1 vote
2 answers
64 views

Conjugate symbol

Is there a way to make mathematica display Conjugate[z] as z* or something like that? It gets very verbose when there are multiple conjugates in an expression, it becomes hard to read.
Gappy Hilmore's user avatar
0 votes
0 answers
60 views

Don't understand reasons for error messages when trying to get elements of matrix

I am trying to simplify the seemingly very complicated inverse of a 4x4 matrix. "Simplify" resulted in something only somewhat less complicated. So yesterday I started simplifying the ...
Alan's user avatar
  • 11
1 vote
1 answer
152 views

How can I get the determinant of an 8x8 matrix in a particular form?

I would like to get the determinant of a 8x8 matrix with symbolic representation to a particular form. When I used determinant and fullsimply to answer was too long and did not match the form I was ...
Angad Singh's user avatar
1 vote
0 answers
64 views

Simplify a summation formula with known identity

I can calculate the formula: $$\sum\limits_{i,j=0}^{m-1}\lfloor \frac{i\ n_1 +j\ n_2}{m}\rfloor$$ with Hermite identity: $$\sum\limits_{j=0}^{m-1}\lfloor\frac{j\ n}{m}+x\rfloor=\lfloor m x\rfloor+\...
Stringer Fan's user avatar
0 votes
1 answer
43 views

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 ...
QubitTy's user avatar
  • 107
1 vote
0 answers
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: ...
scriptfoo's user avatar
  • 201
1 vote
0 answers
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 ...
scriptfoo's user avatar
  • 201
0 votes
0 answers
41 views

Bessel function identity fails to simplify, but only sometimes

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 ...
Aaron's user avatar
  • 153
1 vote
2 answers
51 views

Using existing conditions to simplify a certain part of polynomial

Here, I want to simplify the polynomial P1 ...
InFei's user avatar
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