Questions tagged [simplifying-expressions]

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

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Efficient evaluation of real/imaginary parts of long expressions

I have the following, rather compact, but complex, expression (see below). I simply want the real part of this. Now, when I do the usual, i.e., ...
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1answer
42 views

Mathematica is not simplifying trignometric functions under Abs although I provide assumptions

I am trying to simplify a simple expression, (1/2)*((-Pi)*Abs[Sin[t]] - Pi*Abs[Sin[t - 2*Pi]] - 2*Pi*Abs[Sin[t - Pi]] + 4) i.e $$ \frac{1}{2} (-2 \pi \...
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1answer
68 views

Simplify with Semi-Infinite Interval

I'd like to Simplify an expression using an Interval constraint. This question shows that you need to put the variable in a <...
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68 views

Complex conjugate of real number [duplicate]

I'm trying to take complex conjugate of some terms in a function. I tried this ...
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1answer
197 views

Fastest way to simplify rational functions

I am using Series to approximate function of two variables: Series[f[x,y],{x,0,m}] the function is a complicated sum of ...
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0answers
126 views

Substitution of expressions using Groebner basis

I know this topic came up numerous times (most of the results are detailed in the comments of this link Is there a way to to substitute for symbols, simplify, and back-substitute?). However, I have ...
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1answer
58 views

Simplify equation with two variables

I'm trying to simplify the following equation with respect to r: $-0.192852 + c1^6 (-21743.3 + 81452.7 r^{0.26297} - 379334.0 r^{0.32579} + 730090.0 r^{0.36131} + 18787.9 r^{0.38222} + 448129.0 r^{0....
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2answers
51 views

Clarity of assumptions in PowerExpand

I am trying to simplify a complicated expression which involves $\log$ of sum of $e^{i x_{i}}$ terms, and I found out that using PowerExpand it gets greatly simplified. But I know that PowerExpand ...
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1answer
110 views

How to convert Sine to Cosine?

I have some trigonometric quantities, which may be expressed in either sine or cosine, e.g., ia = Cos[wt], ib = -Sin[π/6 + wt], <...
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1answer
39 views

How to PowerExpand a generic Product?

I have: PowerExpand[Log[Product[f[i], {i, 1, n}]]] // InputForm (* Output: Log[Product[f[i], {i, 1, n}]] *) However, I would expect to get the following as the ...
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49 views

Copying very long expression to LaTeX

I have a long expression (even after using Simplify) which I am trying to copy to LaTeX using the "Copy to LaTeX" command. However, it is too messy for LaTeX to ...
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1answer
31 views

Testing dependent variables

I'm trying to test whether or not I can simplify a function using Mathematica. At first glance it seems there is a dependency of $w$ on $R_0$, but I'm wondering if Mathematica can help me remove this. ...
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1answer
63 views

Using defined function to simplify expression

I have an expression $\sqrt{1-6e^{ik}+e^{2ik}}$ I want to simplify this expression by defining $f(k) \equiv 1-6e^{ik}+e^{2ik}$ So that my output will be $\sqrt{f(k)}$ Thanks
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2answers
101 views

Reduce does not get a result

I try to solve the following inequation. ...
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36 views

Implicit assumption in simplifying an equation

So I tried simplify on an equation (see below). ( Laplacian[V[r,\[Theta],\[Phi]],{r,\[Theta],\[Phi]},"Spherical" ] //Simplify) % == 0 %//Simplify Now the weird ...
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1answer
74 views

How to force Mathematica to “Together” a fraction under a Log and a Square Root

Consider the following code: Assuming[2 > u > 0 && 2 > x > 0, FullSimplify[Log[x]/Sqrt[4 - x^2] /. x -> 2 Sqrt[(2 - u)/(2 + u)]]] The ...
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1answer
107 views

Mathematica doesn't extract Re and Im parts properly

I have a code: ...
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0answers
122 views

Renaming one parameter changes the result of Simplify

Surely the following couple of expressions should both output True: ...
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1answer
717 views

Are these expressions not equal? Mathematica output is ambiguous

The following plot indicates that the first expression equals the second. But how can I use Mathematica to show that is true: ...
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1answer
124 views

Boundary Value Problem and FullSimplify

I'm confused about the output Mathematica is giving me when solving a boundary value problem of the form: ...
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0answers
80 views

Simplifying long expressions leads to memory allocation failure

I am currently trying to manipulate a number of expressions into a particular form that will allow me to determine their poles and zeros: ...
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2answers
110 views

Simplify differential expressions

One can differentiate a two dimensional vector like this, ClearAll["Global`*"] u[x_, y_] := {f[x, y], g[x, y]} Div[u[x, y], {x, y}] with output ...
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2answers
151 views

Can pattern assumptions be made reliable?

It is possible to use patterns in assumptions such as f[_]>0. This does not seem to be explained in the documentation but is for instance pointed out in Is it ...
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0answers
61 views

How to automatically transform Abs[Cos[x]]Sec[x] to Sign[Cos[x]]?

Out of some simplification, the term Abs[Cos[x]]Sec[x] appears. How can I make the code automatically transform ...
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1answer
147 views

Imaginary part of expression too difficult to calculate

I am trying to calculate the imaginary part of a long expression. It's a long enough expression that Mathematica "hangs" when you run: ...
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2answers
78 views

How to force simplify to drop common denominator in inequalities?

Simplify[c>0 && a/c <= b/c] results in c > 0 && a <= b, as hoped. However when ...
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1answer
104 views

Solve a complex equation symbolically?

I try to solve this equation symbolically: Solve[A*s - b*Log[Sqrt[(d - e*s)^2 + 1] + d - e*s] - x + b*c == 0, s] (yes: ^2 = cntrl-6) But M. (trial version) is ...
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3answers
147 views

Substitution in expressions

As the title suggests, I want in an expression to to some substitutions. For example in the expression $\mathcal{L}^+_0+\mathcal{L}^-_0+\mathcal{L}^+_0+\mathcal{L}^-_0+\mathcal{L}_1$ I want to ...
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1answer
78 views

Splitting a general rational polynomial ansatz into powers

EDIT This question is completely wrong and useless. It is mathematically incorrect. I think something like Series is sufficient if you're trying to do something ...
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1answer
68 views

Trouble with simplifying trigonometric / hyper-trigonometric functions

Why (correct) expressions like Assuming[p > 0, 2 ArcTan[Sinh[p]] == Pi - 2 ArcTan[Csch[p]] // FullSimplify] Are not correctly evaluated to: True? What is the ...
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1answer
104 views

Simplifying nested pure functions

I have several functions: ...
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3answers
62 views

How can I reduce my work to get the result automatically?

I want to find the locus of point present of the complex z so that $$|z + 2| + |z - 2| = 18. $$ I tried by hand ...
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0answers
123 views

Another example where using FullSimplify gives different result than Simplify

I believe this question is very similar to Result of Series[expression] is different when I simplify the expression, however, due to my lack of Mathematica experience, I am reluctant to call it a bug. ...
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71 views

Eliminating higher order trigonometric terms

I am interested in eliminating higher-order trigonometric terms from a long symbolic expression. Specifically I want to reproduce this simplification that is done (in a tutorial I am working through)...
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1answer
31 views

Checking if two expresssions are equal in mathematica fails [closed]

I want to see if two expressions are equal. I have tried all of the methods outlined in this question but none seem to work. I have two expressions, part1 and <...
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0answers
102 views

Finding general forms of sums in Mathematica

A general form can be obtained for some sums with binomial coefficients. Mathematica is able to find these general forms for some of the simplest sums. For others the output contains for instance ...
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1answer
47 views

Exclude a term in an expression from any computation/simplification, e.g. being multiplied into a list or matrix

My particular problem is to find a way how to manipulate a term so that it is not multiplied into a vector (as being a list or matrix, and potentially being displayed in MatrixForm) for as long as I ...
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1answer
127 views

Prevent simplification of trig functions

Mathematica often simplifies trigonometric expressions, for example replacing $\sin(\frac{\pi}{4})$ with $\frac{1}{\sqrt{2}}$, or replacing $\cos(\frac{3\pi}{8})$ with $\sin(\frac{\pi}{8})$. I'd like ...
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2answers
206 views

Simplify part of an expression produced by solve

Mathematica outputs an answer using Solve[] but it is not as simplified as it can be. By manually arranging this expression I know that the parts I've highlighted in yellow can actually be simplified ...
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1answer
72 views

Substitution inside an expression [duplicate]

I'm trying to get mathematica to replace an expression with a reduced form. I wanted to replace $(k/w)$ with $h$ in a particular expression, and I've tried something like: ...
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1answer
37 views

Simultaneous equations help [closed]

I have the following: ...
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2answers
54 views

Simplifying Algebraic Expression With Substitution

Is there a way I can make an algebraic substitution in a matrix? I tried using Simplify[P_rhs _ 51, (c44hat*rhohat)^.5 == zeta] Where P_rhs_51 is a 4x4 matrix. ...
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1answer
53 views

Simplifying expression with square root of square roots

I have the following expression FullSimplify[ Sqrt[1 + (-1 + a) (-1 + b) + 2 Sqrt[(-1 + a) (-1 + b)]] - Sqrt[ 2 + a (-1 + b) - 2 Sqrt[(-1 + a) (-1 + b)] - b]] ...
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1answer
92 views

Complex Infinity of Hypergeometric+Gamma function

I am solving some integral which gives an hypergeometric function+gamma function . The point is that my values of n (see the code below) are integers, so ...
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1answer
74 views

Simplifying expressions with square roots of squares

I have a large number of expressions that are of the form, f(a,b)+Sqrt[g(a,b)^2] I understand I can use simplify and make an assumption to get either of the two ...
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3answers
88 views

How to apply a continious substitution reduction of (-1 + 3 phi - 2 phi^3 - 6 phi^4 - 20 phi^6 + 6 phi^7 + 3 phi^8 + phi^9)//.{phi^3->1-phi^2}

I have the answer to (-1 + 3 phi - 2 phi^3 - 6 phi^4 - 20 phi^6 + 6 phi^7 + 3 phi^8 + phi^9)/.{phi^3->1- phi^2} that is not the problem. I am looking for a ...
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3answers
166 views

Force a sum to be simplified

I want to force this sum to be simplified to 1 Sum[Cos[(Pi*l*(2*m + 1))/(n + 1)], {l, 0, n}] Only DiscretePlot3D gives the correct result showing all point to 1
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4answers
203 views

Simplify $\tan^{-1}(\cot(a))$ to $\frac{\pi }{2}-a$ assuming $0<a<\frac{\pi }{2}$

I know Mathematica is not omnipotent, but still can't help feeling surprised when I encountered this example, and I think it's worth starting a question for it. The example is, ...
4
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1answer
126 views

Forcing FullSimplify to use user defined functions

Is it possible to simplify the expression using user-defined functions? For example if I define: m[l_, x_] := Sum[x^i/i, {i, 1, l - 1}] I would like ...
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2answers
85 views

How to calculate $(X^tX)^{-1}X^tY$? [duplicate]

This is MatrixForm[ {{1., 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 1.5, 1.5, 1.5, 2, 2, 2.2, 2.4, 2.5, 2.5, 2.8, 2.8, 3, 3, 3.2, 3.3}}] $X^t$ ...

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