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

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2
votes
3answers
163 views

Simplify a composition of functions

How do I make Mathematica simplify, for example, (1-#&)@*(1-#&) into #&? ...
2
votes
2answers
70 views

Trouble simplifying using Replace

I have the following expression: w.a.b.r+w.c.d.r I want to get: w.(a.b+c.d).r So far I used ReplaceRepeated: ...
2
votes
1answer
272 views

Another square-root simplification problem

In a certain sequence of computations, sometimes I'll get an expression of a form such as Sqrt[u^4 + 4 u^6] which it is necessary to have converted ...
2
votes
2answers
109 views

Puzzling behavior produced by Exists

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

Question on alternate forms of polynomial output

EDIT: Would it be possible to do something like let $y=ax+b$ then use Collect[] or Apart[] on the new expression? How would I go about this. I've tried using Collect[%,ax+b], Collect[%,{ax+b}], and ...
2
votes
1answer
182 views

Is there a way to simplify a symbolic expression at assignment, once-for-all?

I have a series of symbolic function calls that could be greatly simplified using some assumptions. I think I would like for these assumptions to be used in the definition of the function so that they ...
2
votes
1answer
185 views

Check for holomorphy of a function

Given a (rather complicated) function H(z), what is the best approach to check symbolically whether it is holomorphic? What I tried is checking explicitly the ...
2
votes
3answers
168 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
1answer
510 views

How to simplify Sqrt[1/x] Sqrt[x]?

In my expression, there appear terms of the form A^(B Sqrt[1/C] Sqrt[C]). Mathematica doesn't realize that this is just simply ...
2
votes
3answers
474 views

Problem with simplifying Sinc function

$Assumptions = x ∈ Reals && y ∈ Reals && a ∈ Reals && b ∈ Reals; These work: ...
2
votes
1answer
247 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
1answer
96 views

Simplification of exponential

I would like to understand why FullSimplify doesn't entirely simplify this expression ...
2
votes
4answers
98 views

how to cancel arbitrary term in fractional formula

I often encounter this kind of problem that I want the fractional formula to be looked like the way I want it to be. For example, this one $$\frac{R^2 \left(g m_1-g m_2\right)}{J+m_1 R^2+m_2 R^2}$$ ...
2
votes
3answers
129 views

How to delete a pattern from String?

Having a string like : "{Aaaa -> a, Bbbb- > b, Cccc -> , Ddddd -> c, Eeeee -> , Fffff -> e}" I want to delete the parts that contain ...
2
votes
2answers
177 views

How can Mathematica help me to find a real radical expression for roots of this polynomial?‎

The polynomial $P(x)=x^‎‏4‏‎-‎‏4‏x^‎‏2‏‎-‎‏2‏x+‎‏1$‏‎ has ‎‏4‏‎ real roots (this can be clearly checked by plotting). But solving $P(x)=‎‏0‏‎$, using ...
2
votes
2answers
397 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
143 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
1answer
70 views

Wrong result after Simplify of a complex variable with assumptions satisfying an inequality

Using Mathematica 10,Simplify[a\[Conjugate], Assumptions -> {(a + a\[Conjugate]) > 0}] returns a, i.e. treats ...
2
votes
1answer
96 views

simplifying integrals for multiple exponentials

This is somewhat related to this question, but applied to products of Exp[]. For example, I have a symbolic expression containing terms like $Exp[\int_0^1 ...
2
votes
1answer
66 views

Arrange equation in normal form

Is there a way, or if not, how could one define a function which takes an equation in any form (for example as given by FullSimplify): $$(A+X_0) x+By=3x$$ and ...
2
votes
1answer
101 views

Simplifying conditional expressions using assumptions does not work

I have a conditional expression f[x_] := x /; x ∈ Reals This works fine for normal numbers and symbols, e.g. ...
2
votes
2answers
111 views

Let mathematica combine integral limits

Is there a way to teach mathematica to combine integral limits according to $\int_a^b f dx+\int_b^c f dx=\int_a^cf dx$ to simplify expressions like $\int_0^1 f[t] dt+\int_1^x (1+f[t]) dt$ to $\int_0^t ...
2
votes
2answers
153 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
168 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
245 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
234 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
42 views

Simplify trigonometric expression

Mathematica correctly simplifies the following expression: ...
2
votes
1answer
79 views

Simplifying Expressions for FindMinimum

I am currently trying to apply the FindMinimum function to find the lowest energy of an expression. My current expression as of now is relatively complicated. It is the summation of 48 similar terms, ...
2
votes
1answer
128 views

How to parse string to expression? [closed]

When trying to make a string an expression I see some wrong results: ...
2
votes
2answers
218 views

A simple expression that Mathematica can't simplify

I'm using Mathematica 9. I encountered an expression that Mathematica couldn't simplify to a simpler form: ...
2
votes
1answer
114 views

How to get a more compact form of this probability calculation?

Inspired by the probability calculation here, I am trying to solve a little general one: $$\mathbb{P} (\sum_{i=1}^{m-1} A_i + \sum_{i=1}^{m} S_i < L < \sum_{i=1}^{m} A_i + \sum_{i=1}^{m+1} ...
2
votes
1answer
51 views

Is there a simple function identify the sign of an expression given constraints

I'm looking to find a simple function that can identify the sign of an expression given a set of constraints. I have looked around and do see that there is a few threads on this but I'm not sure I ...
2
votes
1answer
165 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
395 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
1answer
824 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
1answer
282 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
2answers
676 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
2answers
314 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
1answer
56 views

Simplifying the result of DSolve

I have a system of differential equations that can be solved with DSolve. However, the coefficients are very long there are like terms which can be combined. I used //FullSimplify in my code but the ...
2
votes
3answers
60 views

Simplifying Logs assuming arbitrary arguments real and positive

I have some expressions involving Logs which I would like to simplify. Unfortunately FullSimplify doesn't work because it assuming the arguments are general. I have no way of knowing a priori what the ...
2
votes
1answer
60 views

Simplify on a structured array

Why doesn't Simplify and FullSimplify operate on object generated using SymmetrizedArray? ...
2
votes
1answer
56 views

Prevent Simplify from using cot

I have the following problem. I got a huge equation to simplify and in there are numerous $\cos(x)$ and $\sin(x)$ terms and now it happens that Simplify changes terms like $(...+\cos(x)*a+...)$ to ...
2
votes
1answer
126 views

FullSimplify wont simplify to expression with lower SimplifyCount

I have been trying without success to get FullSimplify to work on some trigonometric expressions. It refuses to convert them to forms that are clearly much ...
2
votes
1answer
85 views

How to show that an expression is 0 if FullSimplify never finishes

I have a huge expression. And I have "checked" numerically that it is 0 for real value variables. However, due to the size and structure of the expression FullSimplify seems to be having a hard time. ...
2
votes
2answers
92 views

Parabola plotting tangential to x = const, and y= const

ContourPlot[ pm Sqrt[x - a] + pm Sqrt[y - b] == Sqrt[c], {x, 0, 2 a}, {y, 0,2 b}] plots a parabola, but only a part between points of tangency (a, 0) and (0, ...
2
votes
4answers
157 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
246 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
177 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
181 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
177 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] ...