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

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3
votes
2answers
261 views
3
votes
2answers
130 views

Mathematica not recognising closed forms as specific values

I have a Mathematica program that outputs a piecewise function, and some parts of the expression are not being recognised as specific numbers when using ...
3
votes
1answer
115 views

Simplify doesn't simplify HypergeometricPFQ with exact arguments

Consider a series: $$\sum_{t=0}^\infty \frac{8^{-11-2t}(22+4t)!}{t!(11+t)!(11+2t)!(32+t)}$$ ...
3
votes
1answer
99 views

Check that a relational expression is true for all complex numbers

How can I use Mathematica to check if a statement like $$\left| \frac{\sqrt{1+2z}-2}{2z-3} \right| \le 1$$ is true for all complex numbers $z$? Also, how can I use Mathematica to check such a ...
3
votes
2answers
220 views

Replacing gamma at half integers by double factorial

It is well-known that for any positive integer $n$ the equality $\Gamma(n+\frac12)=\sqrt\pi\,(2n-1)!!/2^n$ holds, where $!!$ stands for the double factorial. I am using ...
3
votes
3answers
265 views

Mathematica not able to confirm its own solution to differential equation

I type the following into Mathematica: DSolve[q''[x] + 2 x/(x^2 - 1) q'[x] - 4*q[x]/(x^2 - 1) == 0, q[x], x] It gives me the result ...
3
votes
1answer
1k views

Remove annoying Conjugate

Here is an expression ...
3
votes
1answer
37 views

Add rational linear expressions

I want to set work for my 17 year old calculus students and have access to Mathematica 7. I aim to create a worksheet with rational expressions which they will then decompose into partial fractions. ...
3
votes
1answer
142 views

How to simplify to form without imaginary unit

I have an integral that I compute with Mathematica and as a result I get a seemingly complex expression (i.e. the expression contains the imaginary unit, $i$, at some places). However, if I try to ...
3
votes
1answer
426 views

Simplifying an ArcTan expression

The expression $\tan ^{-1}\left(\frac{\sqrt{L^2 \sin ^2(\theta )}}{\sqrt{L^2 \cos ^2(\theta )}}\right)$ can be simplified to $\theta$. After some attempts I got the following to do the job. ...
3
votes
1answer
193 views

Using Hold correctly with Simplify and ComplexityFunction

It seems like Mathematica immediately evaluates the expression Sqrt@I to (-1)^(1/4). I'm trying to use ...
3
votes
1answer
105 views

Do not understand expression returned by FullSimplify

Why Mathematica returns (sec x)^2? (Tan[x]^2 + 1 - Sec[x]^2)/(Sin[x]^2 + Cos[x]^2 - 1) // FullSimplify Sec[x]^2 Because ...
3
votes
0answers
92 views

How to get mathematica to simplify a result

I have the following output $\text{Li}_2\left(3-2 \sqrt{2}\right)-4 \text{Li}_2\left(-1+\sqrt{2}\right)$. This turns out to be equivalent to $\displaystyle\log^2(1+\sqrt{2})-\frac{\pi^2}{4}$. How ...
3
votes
3answers
308 views

Simplifying expression involving total derivatives [closed]

I'm trying to simplify expressions involving partial derivatives of an abstract functions. To obtain the human readable result, I would like to gather terms of total derivatives and hold on ...
3
votes
0answers
147 views

Why doesn't Log[Gamma[]] simplify to LogGamma[] where it could?

I have been playing with various equations involving amount of permutations in relatively large sets. Easiest way to look at these is something like Log[10, bignumber!] . Often expressions, even ...
2
votes
2answers
173 views

Rewriting one expression using a variable representing another expression [duplicate]

I have two expressions: w1 = (a+b)/c^2; w2 = (a^3 + 3 a^2 b + 3 a b^2 + b^3)/c^6; How can I ask Mathematica to try to find an alternative expression for ...
2
votes
2answers
135 views

FullSimplify used with Assuming giving unexpected results

Can someone shed some light on why Assuming[{x ∈ Reals}, x (Sign[x]^2 - 1)] // FullSimplify returns x (-1 + Sign[x]^2) ...
2
votes
2answers
496 views

How do I make Mathematica understand roots of unity?

Try the following: z = Exp[2 \[Pi] I / 5] Z = { { z, 1 }, { 0, 1/z } } Simplify[MatrixPower[Z, 5]] //MatrixForm Of course, this should return a 2 x 2 identity ...
2
votes
4answers
288 views

Join all square root expressions?

Sometimes I observe Mathematica produce expressions exactly like the following after a simplification step: $$\frac{a+\sqrt{-(1-b)}\sqrt{\frac{1}{b-1}}}{\sqrt{c}\sqrt{\frac{1}{c}}}$$ Now, any ...
2
votes
2answers
169 views

Simplifying expression to evaluate limit as $y\rightarrow 0$

I often end up with a function that contains the term $1/(1 + x^2/y^2)$, and I need to evaluate this in the limit $y\rightarrow 0$. By hand, I can rewrite this as $y^2/(y^2 + x^2)$, but how can I tell ...
2
votes
1answer
292 views

Trace of FullSimplify

I have a symbolic function and I used FullSimplify command to simplify the equation given below. I am calculating it by hand but I couldn't reach the same solution. ...
2
votes
2answers
105 views

Puzzling behavior produced by Exists

I need to simplify a set of solutions of a system, say for example: ...
2
votes
3answers
154 views

Simplify system functions

Consider the code defining two constants: a=Cos[t] b=Sin[t] Suppose that we have another value in terms of Cos[t] and ...
2
votes
3answers
278 views

Problem with simplifying Sinc function

$Assumptions = x ∈ Reals && y ∈ Reals && a ∈ Reals && b ∈ Reals; These work: ...
2
votes
1answer
161 views

Simplify expression to Abs

FullSimplify[Sqrt[1/(a^2 b^2)], Element[{a, b}, Reals]] gives Abs[1/(a b)] How do I simplify the following expression ...
2
votes
2answers
81 views

Is it possible to simplify a trigonometric expression only in terms of $\cos (u)$ OR $\sin (u)$?

I want to expand the following expression into powers of $\cos(u)$ only: a1 + a2 Cos[2 u] + a3 Cos[4 u] + a4 Cos[6 u] The answer that I want (and which I found ...
2
votes
1answer
104 views

Evaluating Abs'[2 x] gives different results than evaluating D[Abs[2 x], x]

I noticed the following difference Assuming[x ∈ Reals, FullSimplify[D[Abs[2 x], x]]] (* 2 Sign[x] *) Assuming[x ∈ Reals, FullSimplify[Abs'[2 x]]] (* Sign[x] *) ...
2
votes
2answers
89 views

Choosing a branch of the square root when performing a series expansion

I have the following problem. Consider expression f=Sqrt[(x-2y)^2] There is an obvious ambiguity in the definition of f ...
2
votes
2answers
87 views

Why Doesn't Mathematica Simplify Combinations of Quotients? (Integer Division)

I stumbled across this as part of a more complicated formula but it can be shown very simply: ...
2
votes
2answers
187 views

Calculate information entropy integral in infinite square well problem

In the context of information theory, entropy is a measure of uncertainty of a random variable. In quantum mechanics, the uncertainty principle states that $\Delta x\Delta k \ge 1/2$. The same can be ...
2
votes
2answers
138 views

Transform Piecewise[] into sum of indicators

I'm interested in transforming a piecewise defined function into a sum of indicator functions, ultimately with the aim to be better able to integrate them. As an example I would like to transform the ...
2
votes
1answer
72 views

Taylor expansion of function of vectors—simplifying the output

I've got a real-valued function of several vectors $f(u,v,w)$ formed by taking scalar products of linear combinations of the vectors, I want to Taylor expand around small $v$ by writing $$f(u,\delta ...
2
votes
1answer
79 views

Truncate High order terms

Suppose I want to compute this : Series[Sin[1/f], {f, Infinity, 10}] but finally I prefer Sin[1/f] up to the fourth order in ...
2
votes
4answers
120 views

How do I prevent exponents from being expanded when displaying text

I have a power of 2 in a list, and I want it to show as $2^{31}$ (2 with exponent 31), not 2147483648. I've tried this: ...
2
votes
1answer
472 views

How to show factorial in expanded form with variables

When evaluating the following (Factorial[n + 1]/Factorial[(n + 1) - (k + 1)]) with Mathematica 9, the result is sent to output as ...
2
votes
2answers
416 views

How to expand a general expression in cross and dot product in Mathematica

I am looking for a way to simply the general expression in cross product and dot product with general vectors. I got a help in How do I simplify a vector expression? but soon I find that it doesn't ...
2
votes
1answer
322 views

Nested Sums to multiple sum

I would like to automatically "move nested sums to the left". I mean, just take out of an expression all the summations and go from a nested Sum to a multiple sum. Something like starting with: ...
2
votes
2answers
265 views

FullSimplify inconsistency

I'm pulling my hair out with this one. I have two complex functions f and g, ρ is real. ...
2
votes
4answers
92 views

Cancelling units in two-argument ArcTan

Consider ArcTan[3, -3] (* out: *) -Pi/4 ArcTan[3 a Sin[t/2], -3 a Sin[t/2]] (* out: *) ArcTan[3 a Sin[t/2], -3 a Sin[t/2]] However, we can fix the ...
2
votes
1answer
109 views

Simplify equations with pattern assumptions

When simplifying an expression using Simplify[expr, assumptions], the assumptions has to be explicit. Is it possible to simplify an expression with pattern ...
2
votes
1answer
133 views

Why FullSimplify doesn't work here?

Since the emphasis of this question is on finding a workaround, I decided to post this question with an emphasis on the explanation of the behavior of Mathematica. The Bessel function satisfies the ...
2
votes
1answer
188 views

How to select TransformationFunctions based on Assumptions made when using Simplify?

I am re-writing the question using a very simple example so not to confuse matters with the another question being asked where I used the example from there. In general, how to add logic to switch ...
2
votes
1answer
109 views

How to use TransformationFunctions on a compound expression?

I was trying to answer this question but having hard time with the correct way to write the transformation rule. Trying to write a rule to transform ...
2
votes
2answers
188 views

Expanding Matrix Expressions

I want Mathematica to recognize that A.(-B.C)+A.B.C = 0 Yet FullSimplify and the like leaves the expression as it is. How do I get around this?
2
votes
2answers
152 views

Substitution to write out powers of expressions

I am looking for a substitution command which will write out powers of expressions like this: $$\frac{a ~b^3~ c}{d~ e^{3/2}~ f^2}\to \frac{a ~b~b~b~ c}{d~ e^{1/2}~ e^{1/2}~ e^{1/2}~ f~f}$$ ...
2
votes
1answer
162 views

How can I get Mathematica to simplify my expression?

4.`*^-12 Sqrt[3.0254210421890627`*^22 - 6.25`*^22 T6^2] The above expression is equal to Sqrt[0.48406736675024997` - T6^2] ...
2
votes
1answer
70 views

Simplify rearranges equations?

I've been using Simplify/FullSimplify to simplify some nasty equations, and by and large it does well but sometimes it rearranges equations in an unhelpful way. ...
2
votes
1answer
79 views

Simplify using functional equations

Is it possible to simplify assuming a functional equation, for examlpe to use that one function, g, is the invers of another, f. Simplify[g[f[x]], g[f[x_]] == x] ...
2
votes
2answers
107 views

Simplification with assumptions

I'm trying to make Mathematica do some simplifications for me. I have the expression ((1 + s[1]) (-1 + s[2]) )/(-1 + s[1] s[2]) and want to simplify this with ...
2
votes
2answers
152 views

Pulling out common terms when simplifying complicated equations

I have a complicated expression where common terms are apparent but Simplify[] and FullSimplify[] don't appear able, even with plenty of assumptions added, to reduce down to a simpler form with common ...