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

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0
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1answer
51 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
0answers
25 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
1answer
58 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
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0answers
25 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
32 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
73 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
89 views
5
votes
3answers
170 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
1answer
57 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}, ...
0
votes
1answer
158 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 ...
0
votes
2answers
68 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 ...
1
vote
1answer
120 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
41 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. ...
2
votes
2answers
109 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
4answers
311 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 ...
0
votes
2answers
108 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
101 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
56 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
80 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 ...
0
votes
0answers
44 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
337 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
109 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 ...
25
votes
4answers
1k views

Can I simplify an expression into form which uses my own definitions?

This seems like a simple thing to do, but I couldn't find anything relevant from Mathematica documentation. So suppose I have an expression: a*b/(a + a*Cos[a/b]) ...
2
votes
2answers
234 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
106 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: ...
1
vote
3answers
78 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 ...
3
votes
1answer
177 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
128 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
59 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
2answers
157 views

How can I separate two parts of power of Exponential functions?

How can I separate two parts of power of exponential functions in Mathematica? I have an expression similar to this one: a*b*Exp[u+v]+c*Exp[u] I want to set ...
1
vote
1answer
95 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 ...
0
votes
1answer
121 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 ...
0
votes
1answer
70 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 ...
2
votes
1answer
97 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 ...
1
vote
1answer
171 views

Collect and simplify both the coefficents and the matched patterns

(This is a far tighter version of a previous question I asked) The problem with Collect is that while Collect[exp, pattern, Simplify] will simplify the ...
3
votes
1answer
113 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
39 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
42 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
237 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
126 views
4
votes
3answers
287 views

Problems using hand-made transformation functions

I experience difficulties when using custom transformation rules. Below I give two concrete problems. I am interested in fixing each of them and in understanding what is wrong with my attitude to the ...
0
votes
1answer
163 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
1answer
112 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 ...
1
vote
0answers
57 views

Simplifying expression on power [closed]

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

Simplify function with normalized vector

I made a very simple case: testF[x_, y_, z_] = x^2 + y^2 + z^2 Simplify[testF[x, y, z]] If {x, y, z} is normalized, the simplified result should just be 1. How ...
0
votes
1answer
54 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
155 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
86 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] ...
1
vote
1answer
85 views

Equation Simplification in Mathematica

I wonder if the following equation could be further simplified by Mathematica. There are $22$ Integrals involved and many of them are in the range $y_l$ and $y_u$. I would guess that at least those ...
0
votes
1answer
52 views

Substituting a function in the output

I have to calculate the derivatives of the function K defined in the code: ...