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

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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: ...
8
votes
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 $1$, ...
1
vote
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 ...
3
votes
4answers
414 views

Mathematica not able to confirm its own solution to differential equation

I type the following into Mathematica: DSolve[q''[x] + 2 x/(x^2 - 1) q'[x] - 4*q[x]/(x^2 - 1) == 0, q[x], x] It gives me the result ...
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 ...
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 ...
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 ...
40
votes
4answers
3k views

Can I simplify an expression into form which uses my own definitions?

This seems like a simple thing to do, but I couldn't find anything relevant from Mathematica documentation. So suppose I have an expression: a*b/(a + a*Cos[a/b]) ...
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
1answer
75 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 ...
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 ...
10
votes
1answer
259 views

How to prevent simplification?

I have a question about the concept of simplification. I want to explain it with an example. When I write $4/8$ in mathematica, output is 1/2. How can I return ...
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: ...
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
votes
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
votes
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: ...
2
votes
2answers
306 views

Simplify results further

I have an extremely long result in polynomial form following some matrix operations. However, given the symmetry of the problem, I can safely say that the solution will reduce much further than is ...
0
votes
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 ...
4
votes
2answers
555 views

Simplifying expressions involving Sum

I am trying to use Mathematica to simplify a symbolic expression involving Sum. The expression is defined as follows: ...
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 ...
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 ...
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 ...
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, ...
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 ...
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
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 ...
1
vote
1answer
366 views

Collect and simplify both the coefficents and the matched patterns

(This is a far tighter version of a previous question I asked) The problem with Collect is that while Collect[exp, pattern, Simplify] will simplify the ...
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 ...
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 ...
-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? ...
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]]]
0
votes
2answers
87 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 ...