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

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0
votes
2answers
32 views

Taking inverse powers of an expression to that power [on hold]

I'm finding a curious behavior for Mathematica 8. The code (x^3)^(1/3) does not want to Simplify or FullSimplify. I'd prefer not to make a rule for this, because ...
0
votes
2answers
50 views

How to combine the sum of two rational polynomials into a single rational polynomial [on hold]

I have browsed the web and found no information. I have two rational polynomials $f1(x,y)$ and $f2(x,y)$. When I perform f1 + f2, I always get two separate ...
3
votes
1answer
183 views

Is this a bug in FunctionDomain (V.10)?

I used FunctionDomain[1/(x^3 + 1), x, Complexes] and got 1 + x^3 != 0 Is this a bug in FunctionDomain (V.10)? Can I receive $x \neq -1$, $x \neq ...
2
votes
3answers
152 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 ...
4
votes
1answer
84 views

Infinite expression encountered when simplifying ArcTan sums although the result is finite

If I attempt to simplify the sum ArcTan[1/x] + ArcTan[x] with ArcTan[ Simplify[ TrigExpand[ Tan[ ArcTan[1/x] + ArcTan[x]]]]] ...
0
votes
1answer
39 views

FullSimplify with assumptions

Is there a way to write a FullSimplify at the end of the line with some assumptions? That is, if I write a^2+b^2+2 a b //FullSimplify[...] is there any way to ...
0
votes
2answers
105 views

Expand 2f[x] to f[x]+f[x] (Simplify sums of ArcTan)

I'm trying to simplify an expression with sums of ArcTan, for which I've written a transformation rule that works for simple sums, so that ...
0
votes
0answers
24 views

Simplifying (A+B)* C doesn't work [duplicate]

This is simple, but it doesn't work: In[1]=FullSimplify[(A0 + B0) C0] Out[1]=(A0 + B0) C0 which should be: A0 C0+ B0 C0 It ...
0
votes
0answers
23 views

Assumptions for simplifying a long equation

I'm having trouble combining assumptions with the execution of Simplify in a long equation. The idea is to separate imaginary and real parts of a complex equation. ...
0
votes
0answers
28 views

Simplification of (Co)sine of a sum

I have a huge expression with (Co)Sine of a sum like Cos[[Theta] - 2 [Phi]] (after using \Simplify). I wanted to know if it exists a function which forces Mathematica to express the result in terms of ...
1
vote
0answers
56 views

Transform Root objects into Trigonometric expressions

Consider the Root objects roots = Table[Root[-1 + 27 #1^2 - 162 #1^4 + 243 #1^6 &, i],{i,1,6}] These can be expressed in terms trigonometric functions as ...
-1
votes
1answer
77 views

How to use Mathematica to obtain the correct simplified results? [closed]

I have a question on simplification: Given that ...
5
votes
3answers
144 views

Converting expressions to “edges” for use in TreePlot, Graph

This question is similar to this: Nested list to graph. How to "flatten" an arbitrary expression, eg expr = a[b[c, d[e][f], g], h] to a list of key-value pairs ...
0
votes
2answers
61 views

Convert an expression from one form to another

I have this expression -0.433284-0.758719 x+0.00289158 x^2-0.443672 y+0.00149027 y^2 I want to express it in terms of ...
0
votes
1answer
50 views

strange result with trigonometric triple integral [duplicate]

I'm defining functions e[k_, t_] := Cos[Pi (k - 1) t] cosIntRaw[k_, l_, m_] := Integrate[e[k, t] e[l, t] e[m, t], {t, 0, 1}] cosInt[k_, l_, m_] := Assuming[Element[{k, l, m}, ...
1
vote
1answer
116 views

Unexpected result from FullSimplify

In the following simplification why doesn't Mathematica get a zero when asked to compute "Y-Z" eventually? ...
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. ...
0
votes
1answer
111 views

How does Mathematica interpret a expression?

I'm a beginner to Mathematica. I'd read several document. But I still have a problem. For example, every expression in Mathematica are of the form ...
2
votes
2answers
87 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 ...
0
votes
2answers
89 views

Simplifying an expression containing radicals

Now I'm trying to use Mathematica to simplify an expression like this: $P \sqrt{-P + \sqrt{M^2 + P^2}} + \sqrt{(M^2 + P^2) (-P + \sqrt{M^2 + P^2})} - M \sqrt{P + \sqrt{M^2 + P^2}}$ where ...
0
votes
3answers
85 views

Why is 1. x (Times[1.`, x]) not simplified to x?

This is maybe a silly question, but I could not think of any logical reason why it is not simplified automatically. I was working with a big linear equation system with some constrained inequalities ...
0
votes
1answer
54 views

Inequality test returned unevaluated

I tried, Refine[Sin[k]^2/(k^2 + k + 1) < 1/(k^2), Element[k, Integers]] $\frac{\text{Sin}[k]^2}{1+k+k^2}<\frac{1}{k^2}$ It returns unevaluated. I ...
1
vote
1answer
65 views

Simplify results further

I have an extremely long result in polynomial form following some matrix operations. However, given the symmetry of the problem, I can safely say that the solution will reduce much further than is ...
0
votes
1answer
49 views

How to evaluate Floor[1/2 + Arg[z]/(2π)] with Re[z] > 0

I want to do a series expansion of an expression containing Gamma functions with specific arguments. An example is the following: ...
0
votes
0answers
39 views

Symbolic manipulation of the moments of an unknown distribution

I'm curious as to whether it's possible to get Mathematica to simplify/manipulate/expand basic expectations, conditional expectations, sums of random variables, etc. A simple example might be: ...
1
vote
1answer
65 views

How to obtain a useful answer from integration when Simplify is insufficient?

I have been trying to integrate a function AND get an output that is sufficiently simple as to be usable. Simply using the Simplify and ...
2
votes
2answers
79 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
2answers
170 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 ...
1
vote
1answer
266 views

Simplify square roots

If I simplify an equation like Sqrt[A^5]+5*Sqrt[A^3]-Sqrt[A] then I get (A^2+5A-1)*Sqrt[A] with no problems. But when I need to simplify Sqrt[(A^5) (1 + a) ] + 5 Sqrt[A^3 (1 + a)] - Sqrt[A (1 + a)] as ...
2
votes
2answers
85 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: ...
0
votes
0answers
57 views

Inconsistent behavior of Assuming[] in combination with Simplify[]

The following integral gives the correct result ...
-1
votes
1answer
48 views

Place symbols from small to big

I am wondering how to compare the different values of ω I derived in this code, and place them in order as follows. (use Print ...
3
votes
1answer
170 views

Strange behavior of Reduce with a cubic equation

This equation: $(\frac{-a}{x})^2=\sqrt{\frac{1}{x}}$ at $a > 0$ and $x > 0$ has a clear solution $x=a^{4/3}$, doesn't it? However, ...
5
votes
2answers
112 views

FullSimplify inconsistent

I'm having problems using FullSimplify to simplify a differential equation. The expression is simplifying just as I would like when I express a variable ...
1
vote
1answer
45 views

Simplification of linear algebra [duplicate]

I have a few vectors defined as V1 = Array[v1,3] V2 = Array[v2,3] V3 = Array[v3,3] And I am trying to solve a very simple equation along the lines of ...
1
vote
1answer
73 views

How to simplify an expression into the sum of small fractions

I'm trying to simplify the following expression $$\frac{n.r \ p.q - (n.p + n.q) (p.r + q.r)}{(n.p + n.q)\ p.q}\to \frac{n.r}{n.p+p.q}-\frac{p.r+q.r}{p.q}$$ When I put it into Mathematica and use ...
1
vote
3answers
71 views

FullSimplify assumptions for function body

I'd like to pass an assumption to FullSimplify so whenever it gets a function that is squared and square rooted would return me only the function body, without ...
0
votes
1answer
59 views

Working with means and variances

My goal is to work out on the following equation: $$Mean(P)(1-Mean (P))\left (h + (1 - 2 h) (1 - \frac {Var (P)} {Mean (P) (1 - Mean (P))}) (1 - Mean (P)) + \frac {Var (P)} {Mean (P) (1 - Mean ...
0
votes
1answer
86 views

Factor vector out of a matrix

I am wondering how to factor a[1],a[2],...,a[4] out of sim so that I can write sim as 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 ...
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 ...
1
vote
0answers
38 views

Finding simpler implied formulas while preserving contradiction

I have two Presburger formulas A and B such that A∧B≡False. From these I need to find "simpler" formula A′ (as simple as I can make it) such that A→A′ and A′∧B≡False. Is there any simple way to ...
0
votes
0answers
38 views

Can you tell (Full)Simplify to introduce a case distinction?

I got this term¹ as a partial result $\qquad\displaystyle T = -1 + (-1)^{\frac{1}{3} \cdot (1 - 2 n)} - (-1)^{\frac{2}{3} - \frac{4 n}{3}}$ which Mathematica refuses to (full)simplify further, even ...
7
votes
3answers
214 views

Simplify with Assumptions Sqrt[(expr)^2]

While trying to simplify expressions in the form Sqrt[(expr)^2] when expr>0 I noticed a peculiar behavior that was not ...
1
vote
1answer
106 views

How to choose a solution of a differential equation?

I am trying to solve the following differential equation: ...
1
vote
1answer
77 views

Simplifying fractions

What ComplexityFunction (or other technique) can I use to have Mathematica pull things out of fractions? I have a rational function of several variables and I'd ...
0
votes
1answer
121 views

How to simplify power series in terms of functions

For example, after some computations mathematica outputs $$ \sum_{k=0}^{\infty} \frac{k g_k z^{k+4}}{(1-z)^3} $$ and we assume that $$G(z)= \sum_{k=0}^{\infty} g_k z^k $$ so the question is: how ...
1
vote
0answers
54 views

Simplifying expression on power [closed]

I want to understand the behavior of Mathematica for the following code. ...
0
votes
1answer
51 views

TeXForm without simplification

I'd like to be able to feed an expression into Mathematica, and have Mathematica convert that expression to TeXForm WITHOUT ANY SIMPLIFICATION WHATSOEVER. As a trivial example, currently, if I enter ...
2
votes
1answer
78 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 ...