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

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0
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1answer
47 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
70 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
182 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
100 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
104 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
100 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
85 views

Simplifying expressions

Let's define a function $\Omega(x,y)$ ...
0
votes
2answers
56 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
79 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
83 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
57 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
50 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
57 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
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
125 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
118 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
133 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
122 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
75 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
86 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
111 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
108 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
49 views

Quick simplification of a fraction of 2 trigonometric equations

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

Numerator not recognized

Here is a set of simple equations ...
3
votes
1answer
67 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
88 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
121 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
82 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 ...
10
votes
1answer
127 views

Use of some functions of the Developer Utility Package, such as BesselSimplify

The Developer Utilities Package contains several functions that look interesting: BesselSimplify GammaSimplify ...
1
vote
0answers
35 views

How to simplify a ratio [closed]

I have a ration of the form $\frac{p^2}{(p^2+1)^2}$. I can simplify it using $p^2=p^2+1-1$, and to get $\frac{p^2}{(p^2+1)^2}=\frac{1}{p^2+1}-\frac{1}{(p^2+1)^2}$. How can I create the rule to do it ...
4
votes
1answer
42 views

What do I need to know about simplifying expressions involving Symbolic Tensors?

I want to use Mathematica to show that the inner product of a vector with itself is equal to the square of its norm. This is what I tried: ...
0
votes
1answer
52 views

Different Results from Simplify, dependent on explicit vs computed rules

Can anybody explain why these two pieces of code are giving me different results? Heres the inputs: ...
1
vote
2answers
107 views

Imaginary part of complex number, nothing works?

I want to find the imaginary part of the complex number (a+i*b). say I have a function in the following form: ...
4
votes
1answer
83 views

Simplify Class invariant $G(25)$

How to simplify $$\frac{\sqrt[3]{\vartheta _3\left(0,e^{-5 \pi }\right)}}{\sqrt[12]{2} \sqrt[6]{\vartheta _2\left(0,e^{-5 \pi }\right) \vartheta _4\left(0,e^{-5 \pi }\right)}}$$ This is a ...
0
votes
1answer
44 views

Simplify doesn't simplify multiple conditions from Reduce

Consider the following simple example where I try to solve an equation and then apply a bounded interval to find the right result out of an infinite amount of solutions: ...
0
votes
3answers
73 views

How to select coefficient of an exponential function

Suppose I have these set of equations: sol = DSolve[{ x'[t] == -RandomReal[]*x[t] + y[t], y'[t] == x[t] - *y[t] , x[0] == 1, y[0] == 0}, {x[t], y[t]}, t] The ...
1
vote
2answers
75 views

How can I eliminate a parameter by substitution and simplification?

I have this equation k = (a b c t)/(Sqrt[(f + t)^2]) and I want to set p = t/(t + f) In which way I can eliminate ...
4
votes
4answers
225 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 ...
1
vote
2answers
118 views

How to get the $0$ result for this limit?

Consider the following series: $$\sigma (\text{x$\_$})\text{:=}\sqrt{\sum _{k=0}^{x-1} \frac{(x! x!) (-1)^{x-k}}{(x-k) (k! (2 x-k)!)}+\frac{\pi ^2}{12}}$$ From the following codes, it seems that the ...
1
vote
1answer
133 views

NIntegrate (Helium Singlet and Triplet) [closed]

I have two integrals that I am calculating using nested NIntegrate. One is for the singlet helium atom and another for triplet. (here, I am calculating variationally the approximate energies and ...