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

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2
votes
1answer
109 views

Complicated implicit plotting [closed]

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
55 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 $(1-x)^...
0
votes
1answer
63 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
60 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
49 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
101 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
52 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
106 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
50 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
144 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
2answers
72 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
vote
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
51 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
71 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
45 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
189 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
57 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
104 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 x7-...
-1
votes
2answers
109 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? http://prntscr.com/...
3
votes
1answer
101 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
87 views

Simplifying expressions

Let's define a function $\Omega(x,y)$ ...
0
votes
2answers
57 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
83 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
93 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
89 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
58 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
vote
1answer
60 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
88 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
60 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 $$ G(...
0
votes
0answers
31 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
126 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
119 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: Collect[x + b x, b x] ...
1
vote
2answers
134 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
93 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
123 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: ...
0
votes
1answer
76 views

Simplify Re[z] in equation to more “natural” form [closed]

If you have a triangle in the complex plane with vertexes {a,b,c} (all complex numbers), the length of the altitude from A to the side BC can be computed as: ...
4
votes
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 ...
0
votes
1answer
112 views

Understanding the symbolic solutions of a system of differential equations

I'm trying to solve a simple system of differential equations but get outputs i just cant grasp, they seem way overkill. Someone said it might be because mathematica interprits the constants as non-...
5
votes
2answers
113 views

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 <...
0
votes
1answer
50 views

Quick simplification of a fraction of 2 trigonometric equations

I would like to simplify a fraction of 2 trigonometric functions ...
3
votes
1answer
35 views

Numerator not recognized

Here is a set of simple equations ...
3
votes
1answer
68 views

How to prevent extraction of constants from radical sign?

To me, the expression Sqrt[2]Sqrt[x] is more complex than Sqrt[2x]. But even if I merely input the latter, I get the former as ...
0
votes
0answers
38 views

Unexpected behavior of SameQ [duplicate]

I am new to Mathematica and I wanted to test the equality between 2 expressions using SameQ. I obtained the following result (note that I defined $r = \{x,y,z\}$, which is not shown below): It ...
2
votes
1answer
91 views

What function can transform A*Cos[x]+B*Sin[x] to Q*Sin[x+R] form? [duplicate]

I've tried several functions related to trigonometric transformations, namely TrigFactor, TrigExpand, ...
0
votes
2answers
89 views

Expression of an integral

I am doing the following integral in Mathematica with $a>0$: $$\iint e^{-\frac{(x_{1}+x_{2}-2b)^2}{4a}}dx_{1}dx_{2}$$ My code is ...
0
votes
0answers
59 views

Is this problem parametrically solvable or it can just be solved for specific $\sigma$ and $\theta$?

In order to solve This problem: What is the maximum value of coefficient fv with the constraint that the matrix is positive semi-definite?, I have used the following code (Determinant is computed by ...
1
vote
2answers
124 views

Update: Calculate Tensor products and traces with Mathematica

My goal is to algebraically simplify expressions involving tensor products and taking the trace. That is, I would like to compute $\operatorname{Tr}\left( \prod_i(id+a_i \otimes b_i) \right)$, using ...
3
votes
1answer
90 views

Factor a polynomial Root into Roots of smallest possible degree

Suppose I have a polynomial Root representing an algebraic number. I want to represent it (if possible) as a product of several polynomial ...