# Tagged Questions

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

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### Rewriting expression in terms of factor

I have two expressions: expr = (a - R)^2 (a + 2 R)/(2 R^3); factor = 1 - a^2/R^2; I would like to write expr in terms of <...
205 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.: <...
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### 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 ...
224 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. ...
238 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 ...
I have a bunch of expressions like this one: $\frac{e^{-\frac{7 J}{2 k T}} \left(2 e^{-\frac{2 g H \mu _B}{k T}}+e^{-\frac{g H \mu _B}{k T}}-e^{\frac{g H \mu _B}{k T}}-2 e^{\frac{2 g H \mu _B}{k T}... 1answer 253 views ### Is there a way to track the Simplify process? Is there any way to track how Mathematica actually performs Simplify, so that we can see what those "Automatic" transformation functions it applies are and how it ... 3answers 458 views ### Running out of variables I am running symbolic calculations with Mathematica. Simplification of algebraic expressions is an important part of them as very often final results can be simplified considerably. Typically my ... 1answer 94 views ### Simplify with a condition I have an expression,$-a (u + a v)$, and I would like to simplify it using the fact that$a^2 = 1$. I have tried Simplify[Expand[-a (u + a v)], a^2 == 1] but ... 3answers 123 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: $$\text{ExpandUpToLevel}\left[\left(\left(x^2+1\right)^2+1\right)^2,1\right]=\left(x^... 1answer 363 views ### Using Hold correctly with Simplify and ComplexityFunction It seems like Mathematica immediately evaluates the expression Sqrt@I to (-1)^(1/4). I'm trying to use ... 1answer 68 views ### Simplify complex answer given by DSolve[] I tried the technique in this question, but that did not work for the solution given by the MWE: DSolve[{f'[t] + f[t]*g[t] == h[t], f[0] == f0}, {f[t]}, t] How ... 1answer 102 views ### Trouble factoring an expression I've got the term -1 + 2b^2 + 2b\sqrt {b^2-1} appearing several times within several larger expressions. It is easy to see that this expression factors into {(b+\sqrt{b^2-1})^2}, but when I use <... 1answer 216 views ### Why does Mathematica not simplify this expression? Consider this simple example: ... 1answer 158 views ### How to apply tags to expression terms? I often see on this site and at the mathgroup the repeated questions on how to rearrange expression that Mathematica "likes" to keep in one form, but the user prefers in another. Consider this trivial ... 1answer 101 views ### How to tell Mathematica to avoid simplification of product of exponentials with the same base? There has been a similar question, but it doesn't solve my problem. I have this input: var = Exp[a] Exp[b] And the output is ... 0answers 53 views ### External and internal Assumptions on PiecewiseExpand and Mod After this question I'm intrigued about the different behaviors depending where and how the assumptions are given. ... 0answers 149 views ### Better way to compute triple (or higher order) convolution I have an identity that I want to verify:$$\sum_{i+j+k\ge 2}\binom{n}{i,j,k}{B_{N,i}B_{N,j}B_{N,k}}=\left(\frac{2N^2+n^2-3nN}{2N^2}\right)B_{N,n}+\left(\frac{3n^2-2n-4nN}{2N^2}\right)B_{N,n-1}+\... 2answers 192 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: ... 0answers 163 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 ... 2answers 425 views ### How can I simplify$\log(512)$to$9\log(2)$? Can you explain me about the result of Integrate. ... 3answers 197 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 ... 4answers 604 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): ... 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 ... 3answers 413 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 ... 2answers 268 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]]] ... 1answer 89 views ### Simplify$\tan(\arctan(a) - \arctan(b))$I want to simplify the expression$\tan(\arctan(a) - \arctan(b))$to$\tfrac{a-b}{1+a\cdot b}$(if$b \neq - \tfrac{1}{a}$). Right now, the output of ... 2answers 482 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 $$i(1+x^2)^{1/4} \quad ?$$ 2answers 185 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): ... 2answers 367 views ### How to expand all portions of an expression? Consider a toy expression: expr = Sin[x (a + b)]/(y (z + c)) I would like to expand all parentheses to get something like: ... 1answer 144 views ### Simplify sum of complex logs to single real log Sometimes, mathematica likes to give me complex results when, e.g, integrating a real valued function. The result might be something like ... 1answer 425 views ### Why is this not a polynomial? ... 2answers 441 views ### Why doesn't FullSimplify simplify expressions with DiracDelta? I want to simplify a complicated expression with some Dirac delta distributions, but FullSimplify does not do what I want. Specifically, I want ... 1answer 789 views ### Does the Im function work with symbolic arguments? Does the Im function work with symbolic arguments? ... 2answers 87 views ### Checking inequalities: How can$x>0,y>0$yet$x+y$indeterminate? I have the following: ... 1answer 561 views ### Can I check if an expression is positive using assumptions? I have the following notebook: ... 2answers 1k 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 ... 2answers 193 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 ... 1answer 237 views ### Can't simplify Abs[a*Cos[x]]^2 Why doesn't FullSimplify[ Abs[a*Cos[x]]^2, Assumptions -> {{a, x} ∈ Reals}] simplify to (a*Cos[x])^2 but this query <... 2answers 599 views ### Simplifying expressions involving Sum I am trying to use Mathematica to simplify a symbolic expression involving Sum. The expression is defined as follows: ... 4answers 228 views ### Another confusion with simplify After reading some of the questions concerning Simplify, I still didn't find a solution to my confusion. I want Mathematica to simplify ... 1answer 290 views ### Infinite expression encountered when simplifying ArcTan sums although the result is finite If I attempt to simplify the sum ArcTan[1/x] + ArcTan[x] with ArcTan[ Simplify[ TrigExpand[ Tan[ ArcTan[1/x] + ArcTan[x]]]]] ... 1answer 349 views ### Simplifying numerical expressions involving special functions I've encountered the following problem. There is the identity (Legendre's relation) that the special functions EllipticK[x] and ... 2answers 140 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 ... 1answer 93 views ### What options need to be set for Simplify to perform a certain manipulations similar to FullSimplify? Simplify performs algebraic transformations and is fast, while FullSimplify tries a wide range of transformations involving ... 1answer 222 views ### Simplifying conditional expressions using assumptions does not work I have a conditional expression f[x_] := x /; x ∈ Reals This works fine for normal numbers and symbols, e.g. ... 1answer 314 views ### Mathematica doesn't simplify a simple expression The question is simple as that. I have: ... 2answers 195 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 FullSimplify... 2answers 176 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: ...
Consider a series: $$\sum_{t=0}^\infty \frac{8^{-11-2t}(22+4t)!}{t!(11+t)!(11+2t)!(32+t)}$$ ...