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

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2
votes
2answers
301 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
126 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
87 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
186 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
136 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
66 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
204 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
112 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
155 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 ...
1
vote
1answer
101 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
118 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
203 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
116 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
45 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
265 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 ...
4
votes
3answers
352 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
203 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
143 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
58 views

Simplifying expression on power [closed]

I want to understand the behavior of Mathematica for the following code. ...
0
votes
1answer
200 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
68 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
226 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
93 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
95 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
53 views

Substituting a function in the output

I have to calculate the derivatives of the function K defined in the code: ...
0
votes
1answer
342 views

How Simplify and Assume can be combined on matrix products?

What I am trying to do is to simplify some expressions involving matrices! The problem is that Simplify[] considers the simplifications based on alphabetical order and everything is Commutative. For ...
8
votes
2answers
642 views

How can I get Mathematica to simplify $\Vert\{1,\sin(t),\cos(t)\}\Vert_2$ to $\sqrt{2}$?

Context Norm[{1, Sin[t], Cos[t]}] Norm[{1, Sin[t], Cos[t]}] // Simplify (* Sqrt[1 + Abs[Cos[t]]^2 + Abs[Sin[t]]^2] Sqrt[1 + Abs[Cos[t]]^2 + Abs[Sin[t]]^2] *) ...
1
vote
1answer
234 views

Why doesn't FullSimplify work properly on this?

I wish to simplify the simple expression fac[n_] := Sum[R^i, {i, 0, n}]; as much as possible for various $n$. FullSimplify or ...
4
votes
0answers
109 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
2answers
147 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 ...
1
vote
1answer
249 views

Get Cos[2 x] in “Solve”

My goal is to get an analytical solution of x ( $\lambda$ in the problem), when $\epsilon$ (f[x] in the problem) is maximum (use inverse form). I found that if I can use trigonometric identity ...
1
vote
1answer
68 views

Solve never terminates with simultaneous equation set

I have the following set of simultaneous equations that I want to solve symbolically. The two unknowns are $a$ and $d$. $a=\frac{c*(d/10)}{1 + (f/130) + (d/50)} - \frac{a}{1 + (a/100) + (d/100) + ...
2
votes
4answers
129 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 ...
0
votes
0answers
51 views
0
votes
0answers
30 views

Is it possible to obtain vector differentiation results in terms of vectors rather than components? [duplicate]

When doing certain operations on vectors in Mathematica it is quite desirable to convert the results back into coordinate-free notation. Unfortunately, after going through the Documentation Center and ...
0
votes
1answer
123 views

Impose an specific Trigonometric expansion with TrigExpand

Is there a way to impose in mathematica an specific trigonometric expansion with TrigExpand? I have various double-angle expressions for cosine and sine in my ...
0
votes
1answer
66 views

How to simplify or improve my code (or how to Flatten inside the matrix)?

I believe that it may be simplified, but I have no ideas anymore.. I need to flatten inside each element of array. F.ex. {{1}, 128552, 6, 1} ---> {1, 128552, 6, 1} Input data (Z - requests, t - ...
1
vote
1answer
275 views

How to tell Mathematica not to simplify an expression

While there is this question with a very similar title, it does not answer my question, which is: I have part of an input, in my case Re[Exp[I*x]] which ...
0
votes
0answers
74 views
1
vote
1answer
256 views

Prevent FullSimplify from converting trigonometric expressions to exponential

There's an option for FullSimplify, which is Trig, and with it I could prevent a trigonometric identities from being used. I'm ...
3
votes
2answers
697 views

Mathematica won't simplify the expression with obvious common factor of a fraction

I have an expression obtain from an integral, which is: Integrate[ϵ^2/Sqrt[(ϵ - u)^2 + Δ^2], ϵ] // FullSimplify The denominator and numerator of the result have ...
8
votes
2answers
344 views

How can I get $(r^{1/x})^x$ to simplify to $r$?

Simplify and FullSimplify do not simplify this kind of expression: $(r^\frac{1}{x})^x$. Consider ...
1
vote
1answer
164 views

Factor a Vector

Does there exist a function in Mathematica that simply takes out a common factor from a vector/list of expressions? This seems like such a simple operation that I am surprised that I could not find it ...
1
vote
1answer
210 views

Function simplification: factoring $f(r,x)$ into $f1(r) \times f2(x)$ [closed]

I have a function of two variables $f(r,x,c)$, where $r$ and $x$ are variables and $c$ is a constant that appears in the function. I would like to write it as a product of two functions $f1(r,c) ...
0
votes
1answer
87 views

Decompose Expression into Segments

Say I have an expression test = 3 x1^2 - 2 x3^-3 and I would like to decompose the expression into {3 x1^2, -(2/x3^3)}, I can do ...
-7
votes
1answer
136 views

Simplify looks ugly [closed]

I use Simplify mostly to make expressions look neat. However, Mathematica often does not produce expression in, what I consider, the optimal way. Look at this: ...
0
votes
1answer
69 views

Log does not reduce expressions [closed]

When solving an analytical expression, I need to take the Log of something. However, Mathematica seems unable to reduce a simple Log of an exponential: ...
9
votes
3answers
1k views

Why does Simplify[b-a] give -a+b and not b-a?

Simplify[b - a] results in -a + b. I prefer b - a, which is a bit simpler (3 symbols instead ...