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

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6
votes
1answer
343 views

Forcing Mathematica to use certain simplification rule

I'm trying to force Mathematica to use following transformation function ...
6
votes
1answer
801 views

Why does this sum not simplify properly?

I was trying to get Mathematica to simplify some moderately ugly sums and I ran into some pretty weird behaviour, which I tracked down to the following example. I'm working with ...
6
votes
1answer
74 views

How to simplify expressions by closing open inequalities?

Recently I have often acquired results which consist of combinations of 0, 1 and 2-dimensional (in)equalities. For instance, consider a very simple case with ineq1 ...
6
votes
2answers
61 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 ...
6
votes
2answers
227 views

Simplify 2D polyhedral Regions like Interval

I don't think there's a built in "RegionSimplify" for polyhedral Regions and derived akin to how Interval automatically simplifies its argument expression: ...
6
votes
1answer
155 views

Moles/Liters doesn't get simplified to Molar even though Molar*Liters gets simplified to Moles

Why can't Mathematica 9 simplify mol/L to M, when it can simplify M*L to mol? ...
6
votes
2answers
217 views

How to simplify only the lowest level of a nested expression [closed]

I have a large expression that takes forever to simplify if I apply FullSimplify[...]. The expression has lots and lots of brackets that luckily already groups ...
6
votes
0answers
232 views

Using FunctionExpand to evaluate symbolic derivatives

Some symbolic derivatives of certain special function are not expanded automatically, but FunctionExpand often helps to get a derivative-free closed form ...
5
votes
2answers
402 views

Simplify — is this simplest result Mathematica can provide?

I have a question about Simplify: When I do a simplification the returned result is not as simple as I want. When I ask for the Norm of an complex expression, ...
5
votes
3answers
705 views

Removing Abs from Abs[a + Exp[I*c]b]^2

Title says it all. Mathematica produces sometimes expressions of the form Abs[a + Exp[I*c]b]^2 where all three quantities a, b and c are positive real numbers. ...
5
votes
2answers
260 views

Inequality with assumptions not simplifying

Can someone explain to me why the following does not simplify to True (as all constituents are positive)? ...
5
votes
1answer
245 views

Validating simplifications analytically

I have a rather complex expression which I would like to simplify and check my work along the way (Mathematica does not simplify very basic things and it is frustrating me). In the following example, ...
5
votes
2answers
389 views

How to find monotonically increasing intervals of a function

I tried this code, but not working Clear[f]; f[x_] := x^3 - 3 x + 2; ForAll[{x1, x2}, x1 < x2, f[x1] < f[x2]] Reduce[%, {x1, x2}, Reals] I expected the ...
5
votes
2answers
324 views

on simplifying an expression

After some integration process, I ended up with the following expression: ...
5
votes
2answers
547 views

Replacements/Substitutions in Mathematica

I am a new user of Mathematica and have some questions about the simplifications of calculated expressions. I am unable to attach an image of the session, but my Mathematica commands are: ...
5
votes
2answers
833 views

How to group the powers of one variable?

Consider the following expression: $\sqrt{a x} \sqrt{b x}$ What do I use to make it simplify to: $\sqrt{ab} x$ I tried actually everything (Simplify, FullSimplify, Collect and so on...) and such ...
5
votes
3answers
182 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 ...
5
votes
5answers
149 views

Isolating cross terms

I have a set of expressions that contains terms like $\frac{1}{(x + a + b)(c+d)}$. I would like to simplify the denominator so that products of $a,b,c,d$ are dropped, but $x c$ and $x d$ are kept. ...
5
votes
2answers
181 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 ...
5
votes
2answers
109 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 ...
5
votes
3answers
740 views

How to prevent Mathematica combining similar terms?

For example, given: x + 2 x y - x y + y I need to put it in this form: x (1 + 2 y) - y (x - 1). But Mathematica will simplify ...
5
votes
2answers
1k views

Log of products to sum of logs

I have a log of products: $$\log \left(\prod _{i=1}^n \left( g(a(i,i)) \prod _{k=1}^i f(a(i,k))\right)\right)$$ That I turn into a sum of logs (I know everything involved is nice enough): $$\sum ...
5
votes
2answers
348 views

Simplifying general solutions of differential equations (driven harmonic oscillator)

Solving general differential equations in Mathematica usually leads to somewhat unsightly results. As an example, consider the solution of the driven, damped harmonic oscillator: ...
5
votes
3answers
4k views

Mathematica not simplifying square root expressions even with assumptions

I have the following expression: expr=(Sqrt[2]r Sqrt[(4+r^2) (2+r (r+Sqrt[4+r^2]))])/(4+r (r+Sqrt[4+r^2])) Then ...
5
votes
1answer
167 views

Simplifying a b = 1 in non-commutative products?

Yesterday, I try to define some rules for non-communicative multiplication, here. I find some quite helpful rules, but things still do not work properly; the distributive rule can't be applied (e.g.: ...
5
votes
2answers
155 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 ...
5
votes
1answer
204 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. ...
5
votes
1answer
422 views

How to express an expression with only ArcTan and ArcTanh?

I have an expression which is simply (j/k) x^(j/k) LerchPhi[x,1,j/k)] where 0 < j < k. Manually I have been able ...
5
votes
2answers
165 views

Trigonometric simplification

How can I simplify 1/2 (Sqrt[3] Cos[x] - Sin[x]) in order to get Cos[x + Pi/6] on Mathematica? I saw that Wolfram|Alpha lists ...
5
votes
1answer
170 views

Restrict Mathematica command to what is inside parentheses

I have a bunch of expressions like this one: $\frac{e^{-\frac{7 J}{2 k T}} \left(2 e^{-\frac{2 g H \mu _B}{k T}}+e^{-\frac{g H \mu _B}{k T}}-e^{\frac{g H \mu _B}{k T}}-2 e^{\frac{2 g H \mu _B}{k ...
5
votes
1answer
243 views

Is there a way to track the Simplify process?

Is there any way to track how Mathematica actually performs Simplify, so that we can see what those "Automatic" transformation functions it applies are and how it ...
5
votes
2answers
625 views

a problem about simplifing conjugate

the situation is as follows ...
5
votes
1answer
3k views

Remove annoying Conjugate

Here is an expression ...
5
votes
3answers
316 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 ...
5
votes
3answers
91 views

Expand just first level of an expression

Is there a way to build a function to expand just the first level of powers and products of an expression? Edit: ...
5
votes
1answer
54 views

Simplify complex answer given by DSolve[]

I tried the technique in this question, but that did not work for the solution given by the MWE: DSolve[{f'[t] + f[t]*g[t] == h[t], f[0] == f0}, {f[t]}, t] How ...
5
votes
1answer
380 views

Simplification of double symbolic sums containing a DiscreteDelta without explicit summation range

I am trying to get Mathematica to automatically do simplifications like the following: $$\sum\limits_{q}^{q\in qV}\sum\limits_{q'}^{q'\in q'V}{f(q)g(q')\delta(q-q')}=\sum_{q}^{q\in qV}{f(q)g(q)}.$$ ...
5
votes
1answer
200 views

Why does Mathematica not simplify this expression?

Consider this simple example: ...
5
votes
1answer
145 views

How to apply tags to expression terms?

I often see on this site and at the mathgroup the repeated questions on how to rearrange expression that Mathematica "likes" to keep in one form, but the user prefers in another. Consider this trivial ...
5
votes
2answers
123 views

Simplification due to recognition of dummy indices in sums?

Today I noticed something weird concerning implicit sums. Apparently, Mathematica cannot recognize dummy indices as such and simplify accordingly. Consider: ...
5
votes
0answers
96 views

Faster way to perform SameQ[Reduce[…], Reduce[…]]

I'm have some expressions that I need to confirm the equality of. SameQ[Reduce[...], Reduce[...]] works like a charm for the more simple expressions, however when ...
4
votes
2answers
371 views

How can I simplify $\log(512)$ to $9\log(2)$?

Can you explain me about the result of Integrate. ...
4
votes
3answers
190 views

Output to preserve dot product

I am fairly new to Mathematica and I am faced with a problem. I tried to search for the solution but it seems that I don't know how to formulate the short search request. I need to perform a matrix ...
4
votes
3answers
158 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 ...
4
votes
4answers
494 views

Simplifying just parts of an expression

I'm having trouble with the simplifications of certain expressions. A typical example of this is the following (all my variables are positive real numbers): ...
4
votes
4answers
1k views

Simplifying a trigonometric expression

I'm sure this has been addressed before, but I can't find it! I want Mathematica to simplify Sqrt[1 - Sin[π/6 - θ]^2] to ...
4
votes
3answers
392 views

How to transform power of -1 into exponential [duplicate]

After FullSimplify, Mathematica usally gives some coefficients like ((-1)^(1/5)) But I don't want this form, I want ...
4
votes
2answers
195 views

Simplifying If statements

How can I get Mathematica to simplify the true and false clauses for If[] statements? For example: bar[a_] := a FullSimplify[If[a > b, bar[a], bar[b]]] ...
4
votes
2answers
413 views

Force a negative square root to be interpreted as an I

I have expressions like $$\sqrt{-\sqrt{1+x^2}} $$ how can I force mathematica to systematically rewrite this as $$i(1+x^2)^{1/4} \quad ? $$
4
votes
2answers
174 views

HornerForm of polynomials in terms of E^(i x)

I want to know how to get the HornerForm of the following expression in terms of E^(I x): ...