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

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2
votes
1answer
153 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
123 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
41 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 ...
7
votes
3answers
301 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
166 views

How to choose a solution of a differential equation?

I am trying to solve the following differential equation: ...
1
vote
1answer
205 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
253 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 ...
0
votes
1answer
76 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
354 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 ...
0
votes
1answer
54 views

Substituting a function in the output

I have to calculate the derivatives of the function K defined in the code: ...
10
votes
3answers
937 views

Simplifying trig expressions containing Sqrt or Abs

The following Maple code can simplify abs(sin(x)) into -sin(x) given the condition ...
4
votes
0answers
125 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
158 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
261 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
72 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) + ...
0
votes
0answers
51 views

Always the same problem with Conjugate [duplicate]

I want to compute something like : ...
2
votes
4answers
153 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 ...
5
votes
3answers
442 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
70 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 - ...
0
votes
1answer
165 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 ...
3
votes
1answer
102 views

How to make Mathematica Simplify?

Let us define r1 = 1;r2 = 2; and ...
1
vote
2answers
305 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 ...
3
votes
2answers
840 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 ...
1
vote
1answer
268 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 ...
0
votes
1answer
90 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 ...
0
votes
1answer
62 views

Resolve a conditional expression including exists and forall

I don't know the Resolve function exactly, especially when involved with Exists and ForAll, ...
1
vote
1answer
126 views

Collecting terms in an expression [duplicate]

I have an expression: ...
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 ...
0
votes
1answer
105 views

Simplifying complex expressions

I'm trying to work with complexes and I want Mathematica to know that all variables are real unless I explicitly assigned the variable with an I so I wrote: ...
2
votes
1answer
87 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. ...
0
votes
1answer
79 views
1
vote
1answer
114 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 ...
2
votes
1answer
109 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
353 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 ...
13
votes
2answers
265 views

Transform an expression to remove the singularity

I have the expression Sin[c x]/c. Clearly it is undefined at $c=0$, but that is merely a removable singularity, since $$\frac{\sin(cx)}c=x\frac{\sin(cx)}{cx}= ...
1
vote
1answer
120 views

Behaviour of Simplify when used with ArcTan and ComplexExpand along with assumptions

I am trying to simplify the slope of vectors with symbolic coordinates {x,y} using ArcTan[x,y] I am working with real X and Y I tried the following : ...
3
votes
1answer
207 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 ...
4
votes
1answer
175 views

Mathematica rule to express exponentials as multiplication

I'm sorry if this has been asked before, but it is a very simple question and I would imagine it shouldn't be terribly hard for someone that knows to answer. I'm essentially trying to tell ...
0
votes
0answers
73 views

Preventing numeric constants from being pulled out of square roots

If I input Sqrt[2 g], Mathematica automatically pulls out the 2 and returns Sqrt[2] Sqrt[g]. ...
3
votes
1answer
541 views

How to get rid of all complex numbers and functions?

For almost esthetical reasons, I always have been fascinated by infinite sums of series and I always wonder if theyhave a closed form. A couple of days ago, I found on MSE a question related to the ...
1
vote
1answer
108 views

Use Simplify option Trig->False when 3rd argument to Collect is Simplify

I would like to simplify the following expression AAA (4 Sin[x]^2 Cos[x]^2) + AAA 4 Sin[x] Cos[x] + AAA with the ...
0
votes
2answers
95 views

Can I tell Simplify to prefer nested polynomials?

I need to export expressions for numerical evaluations in a C codebase. Simplify often does a good job for this, and polynomial factorisation goes a long way. However, occasionally I would come ...
0
votes
0answers
86 views

Recognizing a generalized function as zero

Consider the following expression: HeavisideTheta[x]HeavisideTheta[-x] Mathematica will not simplify it further. But $\Theta(x)\Theta(-x)$ is zero if considered ...
5
votes
1answer
201 views

Simplification of integrals depending on a parameter [duplicate]

Assuming[Element[n, Integers], Integrate[Sin[x]*Sin[n*x],{x,0,Pi}]] returns 0, which is obviously wrong for n=1. ...
3
votes
4answers
165 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: ...
1
vote
1answer
277 views

Latest Mathematica 9.0 can't use Format.m to generate optimized Fortran code [closed]

Before updating to Mathematica 9.0, I have successfully generated beautiful Fortran code using Mark Sofroniou's Format.m package, which is posted on MathSource. ...
5
votes
3answers
303 views

Running out of variables

I am running symbolic calculations with Mathematica. Simplification of algebraic expressions is an important part of them as very often final results can be simplified considerably. Typically my ...
4
votes
2answers
172 views

Why Refine does not simplify Cos[2*Pi*FractionalPart[1/2*(i + j + k)]] to $(-1)^{i+j+k}$?

I am obtaining in Mathematica: Cos[2*Pi*FractionalPart[1/2*(i + j + k)]] We know that for $i, j, k$ being positive integers this expression after simplification ...
3
votes
2answers
147 views

Exploiting a relation among constants

Say I have two arbitrary real constants $p,q$ that satisfy $p^2+q^2=1$. Is there any way to easily declare this relation in Mathematica? Edit More specifically I have this (among others) expression: ...
0
votes
1answer
117 views

Binomial sum identities

How do you persuade Mathematica to give simple identities involving binomial sums. For example Sum[Binomial[a,i]*Binomial[b,i],{i,0,n}] where n is bigger than ...