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

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1
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0answers
30 views

`QPochhammer` function simplification?

Consider the function which in Mathematica is denoted as QPochhammer[a,q,n], and its infinite product cousine: which in Mathematica reads ...
8
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1answer
96 views

Adding irrelevant assumptions changes the result of Simplify

I've run into this problem a number of times. A typical example is Simplify[Sign[k], {0 < A, 0 < B, A*Exp[2*y] < k, y > 1}] which evaluates to $1$, ...
4
votes
1answer
71 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 ...
0
votes
0answers
27 views

Finding results using qualifiers?

I have set of recursive function definitions and assumptions $\forall n.t1(n+1)=t1(n)-Y*S(n)$ $\forall n.t2(n+1)=t2(n)+S(n)$ and assumption $\forall n.n<K\rightarrow L1=L2*t2(n)+t1(n)$ I want ...
0
votes
1answer
52 views

Not simplify an easy equation with “Simplify”

I've a problem with the function Simplify. I've this equations x^2 + 2 x + 1 == 0 and 4 x^2 == 0. If I use Simplify, it returns ...
0
votes
2answers
25 views

Simplifying polynomials with conditions on variables

I'm working with polynomials of 5 variables $a,b,p,q,r$ which have a condition $a+b=p+q+r$. I'd like to minimize the number of variables in the answer. However, FullSimplify can't handle even simple ...
1
vote
1answer
52 views

FullSimplify fail with general assumption

Assume I want to simplify this: -a^(-1) ** b^(-1) + (b ** a)^(-1) given assumption: $\frac{1}{b\_\text{**}a\_}=\frac{1}{a\_}\text{**}\frac{1}{b\_}$ Then it ...
3
votes
3answers
125 views

How to obtain this expression in terms of real functions

I know that this expression (2 (ArcCot[E^(-((I ϕ)/2)) r] + ArcCot[E^((I ϕ)/2) r]))/π is real, because is the sum of a real series, in particular: ...
0
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0answers
51 views

Handling Inequality with condition

I have verifying inequality using Mathematica using Simplify command For Example I want to check whether inequality a<f ...
0
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1answer
34 views

Complex number simplifications

My Mathematica notebook is not simplifying some expressions which do look trivial. I mean that one of my outputs contains: ...
3
votes
3answers
434 views

Simplify big numbers in a second order equation

How can I simplify big exponents like $10^{39}$ in the solution of a second order equation: ...
0
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1answer
35 views

Option for Simplify command in mathematica

What does Simplify[%[[1]], %[[2]]] mean in following code? I mean [[1]] and [[2]] exactly what does refer to? ...
1
vote
2answers
78 views

Double sum in mathematica

It may look like a stupid question, but I was really confused by how double sums works in mathematica: After simplification, the function actually has nothing to do with n2? Also, when I manually ...
2
votes
0answers
72 views

Complicated implicit plotting - can it be tackled?

I'm quite new to Mathematica and have already spent tons of time on problems of this type, browsing through tutorials and topics here. I'm now coming to conclusion that it cannot be done and am about ...
0
votes
1answer
53 views

Simplify assuming $x$ is small [closed]

I would like to assume that $x$ is small so that values of the order $x^2$ (and higher orders) are negligible. For example, I would like Mathematica to return $1-2m$ when I ask it to simplify ...
0
votes
1answer
46 views

Metric Simplify & grouping

I'm changing a basis from one metric to another. When simplifying the result Mathematica doesn't seem to grasp all the possible simplification: ...
0
votes
3answers
59 views

how to take complex conjugate of a real variable

I have a function defined as follows: g[θ_] := 1/k (Exp[-I δ0] Sin[δ0] + 3 Exp[I δ1] Sin[δ1 Cos[θ] + 5/2 Exp[I δ2 (3 (Cos[θ])^2 - 1)) and I compute ...
1
vote
2answers
48 views

Simplify Expressions used to define Region

For example, RegionPlot[{x + y > 1, x - y > 1, y - x > 1, -x - y > 1}, {x, -2, 2}, {y, -2, 2}] can be somehow written as: ...
2
votes
1answer
95 views

Mathematica doesn't know about the absorption identity? [closed]

The well-known binomial absorption identity states that $$n\binom{n-1}{k-1} = k \binom{n}{k}$$ However, Mathematica gives ...
0
votes
1answer
48 views

Inverse of a Fourier matrix [closed]

I am trying to find the inverse of a Fourier matrix but I am getting confusing results. If R is a Fourier matrix, then ...
0
votes
2answers
96 views

Solving recursion relation from power series

I am interested in solving differential equations in the form of power series. Let's say we have following equation: $$f^{\prime \prime} (\rho) + \left( \frac{2 e^{-k \rho}}{\rho} - \varepsilon ...
0
votes
0answers
46 views

Force expression in certain form

Is there a function in Mathematica to force an expression to be transformed into a given form. For example f[x] is a function of ...
8
votes
2answers
139 views

Collect/Factor a fraction

Is there a way to tell Mathematica to factor things only containing a specific combination of a fraction, example: $$\tag{1}f = \frac{a+m\cdot a+b+n\cdot b+c+k\cdot c+d+e}{ab}$$ Is there a way to ...
1
vote
1answer
39 views

Simplifying expressions containing unit of zero magnitude

I have obtained the following form as a part of a computation: k (Quantity[0, "Kilohertz"]) + Quantity[1/500, "Kilohertz"] This is typeset as Here, ...
1
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0answers
57 views

Output in FunctionExpand for function of Gamma

I used of this code: α Gamma[α] // FunctionExpand and get output: Gamma[1 + α] Also I used of this code: ...
0
votes
1answer
44 views

Two Variable First Order Approximation [duplicate]

I found that using Series and Normal command, I am able to approximate the first order of x or y, but If I also get rid of x*y (cross term), Series command does not work any more. Let's define some ...
3
votes
0answers
68 views

Can Mathematica reliably determine the equality of any two constructible numbers?

A constructible number is any number which can be expressed with only natural numbers and the operators $+$, $-$, $\times$, $/$, $\sqrt{}$ (square root only). Is Mathematica's ...
2
votes
0answers
44 views

How to remove parentheses from algebraic expression? [closed]

Suppose I have an expression like $x+x+y(x+y(x+y))$. I used Simplify command and get $y^3+x(2+y+y^2)$. How to remove parentheses to get every summand explicitly? ...
3
votes
2answers
180 views

How can I get Mathematica to simplify this i * sqrt expression

In[11]:= FullSimplify[I Sqrt[-1 + w^2], Element[w, Reals], Assumptions -> 0 <= w <= 1] Out[11]= I Sqrt[-1 + w^2] Is it possible to have Mathematica ...
2
votes
2answers
56 views

Expanding and simplifying expressions

I have some complicated expression, for example: (-a^3 (-1 + b^2) - 3 a b^2 (2 + b^2) d c)/(b^2 (d c)^(3/2)) All variables are positive. I want to expand it and ...
-1
votes
2answers
96 views

linear system equation ( trying to solve ) [closed]

I am trying to solve this system 3.7 x1+51.5 x10+71.3 x11-84. x2-16. x3-57.7 x4+89.7 x5-54.9 x6-85.8 x7+57.8 x8-51.3 x9==-36.8 -86.3 x1+5.7 x10-0.2 x11-39.9 x2+52.6 x3-45.6 x4+78. x5+90.7 x6-86.2 ...
-1
votes
2answers
96 views

Square root of a square root [closed]

Calculate square root of: Sqrt[3] Sqrt[3 - Sqrt[5]] (Sqrt[15/2] + Sqrt[3/2]) The response of the square root is 6. Edit: Can anyone go? ...
3
votes
1answer
96 views

Simplifying a complicated expression (with no variables)

I am trying to obtain some exact analytical results without resorting to numerical approximations, and I ended up with a pretty huge expression that Mathematica is really struggling with. It has no ...
0
votes
1answer
84 views

Simplifying expressions

Let's define a function $\Omega(x,y)$ ...
0
votes
2answers
55 views

Put a trigonometric equation in the form A*cos(theta)+B*sin(theta)+C=0 [closed]

eq = (Cos[Θ[t]]cf - Cos[γ1[t]] mf + Cos[γ2[t]] mf)^2/cf^2 + (Sin[Θ[t]]cf + Sin[γ1[t]] mf - Sin[γ2[t]] mf + xP1[t] - xP2[t])^2/cf^2 Can you help me to simplify and ...
7
votes
0answers
73 views

Need explanation on strange behavior of Simplify under given assumption

This is quite surprising to me. Simplify[a == b, {a == {1}, b == {1}}] a == b does not evaluate the equality, while ...
2
votes
1answer
77 views

How to estimate the running time of a programme on mathematica [closed]

I am solving a system of 6 linear equations containing six unknowns using mathematica. It is taking too much time and still running after 3 hours. can I estimate the approximate running time? Is there ...
3
votes
0answers
84 views

How to force Series[] to compute expansions by considering non commutative multiplication?

I wish to compute the Taylor series expansion of the following iteration method $x_{k+1}=x_k-f'(x_k)^{-1}f(x_k)$ up to four terms of error ($e_k=x_k-\alpha$). When this is a scalar iteration, I very ...
3
votes
1answer
55 views

Simplifying a trigonometric function with arctan

Why is this trigonometric expression with $\arctan$ not simplified ? ArcTan[Tan[γ[t] - θ[t]]]
2
votes
1answer
66 views
1
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1answer
43 views

Using Collect to group derivatives together

Is there a way to combine derivatives that are a result from the product rule back together using Collect. For example, I'd like to collect x Dt[y,b] + y Dt[x,b] ...
2
votes
1answer
82 views

Getting wrong result when Integrating under an assumption [duplicate]

The simple integral $$\int_0^b \cos\left(\frac{2\pi m(y-\eta)}{b}\right) \cos\left(\frac{2\pi \eta}{b}\right)\mathrm{d}\eta$$ can be easily evaluated by Mathematica as, ...
0
votes
1answer
52 views

How to evaluate and simplify series expansions of long partial derivatives involving trigonometry?

I have 4 maps defined on a plane, i.e. on $\mathbb{R}^{2}$. Let's call them $F,G,H,J$. Let $(s,t) \in \mathbb{R}^{2}$. Define $F(s,t) = (f_{1}(s,t), f_{2}(s,t)).$ Likewise, in components, write $$ ...
0
votes
0answers
30 views

Simplify expression?

Suppose I have expressions that involve terms like: p1.p1+p2.p2+p3.p3+p4.p4 p1, p2, p3, and p4 are all elements of an array: ...
1
vote
2answers
123 views

Simplifying ArcTan[Cos[u], Sin[u]]

I am trying to evaluate the following expression in Mathematica: $$ \bigg| \frac{\left(1-z^{-2}\right)^n}{\left(1-z^{-1}\right) \left(2-z^{-n}-z^{-1}\right)} \bigg|^2 $$ Here $z$ is the complex ...
6
votes
1answer
115 views

How to Collect a variable multiplied by a constant?

I'd like to use Collect to get terms that have a variable multiplied by a constant. For example I'd like: ...
1
vote
2answers
131 views

Express roots of quadratic equation in a specific form [closed]

By solving this equation, I got two roots as follows: Solve[1 + Subscript[a, 1]*s + Subscript[a, 2]*s^2 == 0, s] Is there a way to express it in the form below ...
2
votes
4answers
84 views

How to fix unsimplifed Sqrts?

The following code produces two values for the variable p. But the results contain Sqrt[k^2]. This should just be reduced to k, because the sign ambiguity is ...
4
votes
0answers
69 views

strange FullSimplify result, why zero? [duplicate]

This came up looking at this How to speed up calculation of this equation (FindRoot). Is there some sense to why FullSimplify gives zero here? ...
4
votes
2answers
118 views

Why doesn't FullSimplify find simpler expression given a set of transformation rules?

I've defined a set of rules, which I want to use with FullSimplify, as follows: ...