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

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0
votes
1answer
47 views

Get dominant terms in asymptotic expansion

I'd like to find the dominant terms of an expression given the conditions $x,y >> 1$: $c_0 y+\frac{y^2 \left(4 c_0^2 y - 12 c_1 c_2^2+y^2\right)}{24 x^2 \left(\text{c1}^2+\text{c2}^2+y\right)}$ ...
1
vote
0answers
66 views

“Reduce” works fine for a non-linear system with 9 equations, but cannot solve it if 10 equations. Any ways to improve the code?

I am trying to solve a class of problems, which are basically about a solution to a system of non-linear equations subject to the constraint that some subset of solutions must be non-decreasing. I ...
2
votes
2answers
160 views

Why doesn't Mathematica pull out common factor when simplifing sums of square roots?

Why can't Mathematica pull out the common factor in the following expression when FullSimplifying, to see that it is zero? ...
3
votes
0answers
33 views

commutative matching

I've been doing some work that results in the creation of hundreds or thousands of equations with the same answer. To prevent them from collapsing to their simple answers, each has been passed through ...
3
votes
1answer
44 views

Simplifying nested KroneckerProducts

Any suggestion how to bring a nested KroneckerProduct form into just one? I mean some how converting ...
6
votes
0answers
46 views

Unexpected behaviour of Simplify

I'm evaluating an expression and to me the result should be True but Mathematica is giving me a different result. ...
3
votes
1answer
52 views

How to get Mathematica to make further simplifications to conditional expressions than it has already made?

I have the following Mathematica result under the assumption that {ax, bx, px, ay, by, py} \[Element] Reals, and after refinement by ...
4
votes
0answers
90 views

Simple arithmetic with Irrationals fails [closed]

While solving a simple puzzle that asked for a few calculations in plane geometry, I ended up with this expression: $-\frac{55}{2}+\frac{\sqrt{27233}}{2}+\frac{1}{2}(55-\sqrt{27233})$ Or, in ...
0
votes
1answer
103 views

Why doesn't mathematica replace $\frac{I_0(\kappa)}{I_0(\kappa)}$ by 1 [closed]

I have a matrix of the form: $$\left( \begin{array}{ccc} 1 & \frac{\delta I_1(\kappa )}{I_0(\kappa )} & 0 \\ \frac{I_1(\kappa ) \delta ^*}{I_0(\kappa )} & \frac{\delta (I_1(\kappa ...
1
vote
2answers
95 views
7
votes
1answer
145 views

Why don't 1. (0. + a) or (0. + 1. a) simplify?

I'm handling some mixed-numeric-analytic expressions, and I feel I'm missing some subtleties of how Mathematica handles simplification of such expressions. In particular, I was initially puzzled by ...
0
votes
2answers
138 views

Simplifying complex fractions

How can I simplify a complex fraction in order to get something of the shape (a + I b)/(c + I d)? Note that I would not like Mathematica to further simplify it ...
0
votes
1answer
82 views

How to simplify an expression with assumptions

I have a matrix of the form: Tvol // TraditionalForm $$\left( \begin{array}{ccc} 1 & \frac{\delta I_1(\kappa )}{I_0(\kappa )} & 0 \\ ...
4
votes
1answer
415 views
2
votes
2answers
113 views

How does Simplify give two answers when they are the same?

I am trying to get the CDF of a random variable using TransformedDistribution. ...
3
votes
3answers
156 views

How to evaluate $-i e^{\frac{i k}{2}} \sqrt{-e^{-i k}} = 1$?

In my calculation, there exist some expressions like $-i e^{\frac{i k}{2}} \sqrt{-e^{-i k}}$, which are not simplified to be $1$, and makes further calculations rather complicated. I tried to ...
4
votes
1answer
201 views

How to make Mathematica express an equation in terms of previously defined functions

I was given a problem for my physics class, and perhaps I have taken it too far, but I wish to finish what I started. I have a function (i warn you that this does not look pretty) ...
1
vote
0answers
94 views

what is the means of (0 -> 1) of series expansion [closed]

I use mathematica 8 to take a taylor expansion.In the Output, the expression (0->1) appears in the second term and all higher order term, and this expression is multiplied with other coefficient and ...
0
votes
1answer
90 views

Special fractions generator

Note that 13/33, 1313 / 3333 , 131313 / 333333, ... They are always equivalent fractions Fraciones generate desire to have this property based arbitrary ...
58
votes
5answers
2k views

Advice for Mathematica as Mathematician's Aid

I use Mathematica mainly as an aid in symbolic attacks on problems, usually intermediate or harder and often number theoretic. While Reduce, ...
0
votes
2answers
72 views

How to simplify noncommuting multiplication of KroneckerProducts

I'm using NCALgebra. I was wondering if there is a way to simplify KroneckerProduct[a, b]**KroneckerProduct[c, d] to become: ...
2
votes
1answer
86 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 ...
4
votes
0answers
105 views

Simplest identity that cannot be proved by FullSimplify [closed]

Apparently, FullSimplify is not able to prove all true identities, but usually it does pretty well when it comes to elementary functions. I'd like to know what are ...
4
votes
2answers
133 views

Symmetrise a complicated expression

I am calculating the derivatives of a symmetric function $F(a_1, a_2)$ and got very complicated expressions, which I'd like to write in a symmetric form with respect to $1 \leftrightarrow 2$ (clearly ...
2
votes
1answer
71 views
2
votes
1answer
96 views

Simplify trigonometric expression

Mathematica correctly simplifies the following expression: ...
3
votes
1answer
137 views

Factor fraction, where variable occurring in both, numerator and denominator, only appears once

I have an expression like $$\frac{1+a^2+2 a \cos\left(p\right)}{\left(1+b^2\right)z-1-a^2-2 \left(a+b z\right)\cos\left(p\right)}\text{.}\tag{1}$$ Is there a combination of Mathematica functions to ...
0
votes
1answer
86 views

Using Simplify to perform substitutions [closed]

I have a matrix element $k_x$ and I want to substitute it as $-i\kappa$, I tried ...
0
votes
0answers
60 views

Simplifying sums of rational trigonometric functions

After simplifying the trigonometric functions as advised before (cf. Simplifying Expressions for FindMinimum), I obtained a sum of 62 similar expressions, the first three as in the below: ...
1
vote
1answer
207 views
6
votes
3answers
252 views

How to simplify symbolic expressions with KroneckerProduct

Having $X,Y$ being symbols for matrices, I was wondering if there is a way to simplify expressions like KroneckerProduct[X, X] + KroneckerProduct[-X, X] to ...
6
votes
2answers
212 views

ReplaceAll problem

Bug introduced in 10.1 and persisting through 10.2 or later Confirmed, as bug, by WRI: [CASE:3402234] I am trying to combine terms of the type ...
1
vote
0answers
66 views

Simplify Integer powers in inequalities

I have a fairly simple expression that I am surprised Mathematica (10.1) won't simplify ...
0
votes
0answers
108 views

More simplification tricks in Mathematica? [duplicate]

I need to simplify the following expression in order to operate on it using InverseLaplaceTransform. This result will be used in further work, so ideally I would ...
0
votes
2answers
82 views

Replacement rules do not apply for an expression inside a root

Say, you have an expression which looks like this: myexpr = (mess)+(some other mess)/( (mess)^3+(some other mess)^2 )^(1/3) Here the 'mess' in the name of terms ...
3
votes
1answer
233 views

Separating exponential terms

Suppose I have a lot of expressions multiplied by factors such as: $$e^{-i\theta[1]-i\theta[2] - i\theta[3]-i\theta[4]-i\theta[5]}$$ I would like to separate this into a product of exponentials of ...
3
votes
1answer
126 views

Simplify oversimplifies. What to do about it?

According to Mathematica 10: $$Simplify[\frac{\frac{1}{t^2}-1}{(t+\frac{1}{t})^2}]==\frac{1-t^2}{(1+t^2)^2}$$ However, the first equation does not tolerate $t=0$ because of a division by zero, but ...
5
votes
2answers
116 views

How to use ForAll to prove things about functions?

Suppose I first declare: $Assumptions = ForAll[{a,b}, b > a, f[b] > f[a]] I (wrongly, as it turns out) assume that that this would cause ...
3
votes
1answer
142 views

Equality of Reciprocal with Negative Exponent

I want MMA to tell me if two, rather large, expressions are equal. My minimum working example follows. I want MMA to tell me that the following is true:$$x^n = \left(\frac{1}{x}\right)^{-n}$$ I have ...
2
votes
1answer
113 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
2answers
76 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: ...
1
vote
1answer
60 views

How to apply Simplify only to elements of list that cause specific Warning

I have a set of replacement rules I use to analytically compute nested integrals of very long symbolic expressions since Integrate literally takes forever. To do ...
1
vote
1answer
85 views

Pulling out a prefactor from a dot product

I have three complicated vectors u, v and w as well as three simple prefactors ...
4
votes
1answer
138 views

Dealing with 6 VERY large equations. Am I doing this correctly, and can I expect a solution?

I'm new to Mathematica, but so far, everything seems straight forward and intuitive, which is really nice. However, I've come to use this software since I have to show a rather nasty 3x3 matrix is ...
5
votes
3answers
978 views

How to simplify 1 - Cos[2x] to 2 Sin[x]^2?

I want to reduce all Cos[2 x] to 1 - 2Sin[x]^2, it seems Mathematica will always simplify ...
0
votes
1answer
49 views

Expanding a function with trigonometric expressions in a controlled manner by excluding addition identities

I want to simplify a nonlinear equation with trigonometric terms. After I've expanded I don't want to loose open terms to Trigonometric Addition Formulas ...
7
votes
2answers
105 views

Simplify expression to Integer

I have the following function: f[n_]:=(n-1) E Gamma[n,1]; I know that this expression always evaluates to an Integer, but Mathematica doesn't always output the ...
1
vote
0answers
58 views

How to remove parts of an expression

I have an expression where terms Transpose[R].R appear. R is a matrix with the property Transpose[R].R=IdentityMatrix[3]. How ...