instruction stringlengths 12 30k |
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What is the order of the set of distinct (up to similarity) nxn matrices over R? |
You have several questions, both about polynomial multiplication and about regular multiplication with integers.
To address the last one first: once you have multiplication by integers, multiplication by fractions will very quickly rear its head. What does multiplying by "one and a half" mean, if multiplying by 2 me... |
Let ( L, ≤ ) be a lattice, x, y, z ∈ L
I am unable to understand why ( x ∧ z ) ∧ ( y ∧ z ) = z ∧ ( y ∧ x ) is mentioned as fact in Y.N. Singh's "Mathematical Foundation of Computer Science" - Pg 157
Could I prove this somehow, or is it an axiom? |
It is well known that $\text{Ext}(\mathbb Z_p,\mathbb Z)$ is the trivial group, because $\mathbb Z_p$ is projective; this seems to be in contradiction with the Exercise 1.1 in Hilton - Stammbach, pag. 88: the two sequences
$$
0 \to \mathbb Z \xrightarrow{\mu} \mathbb Z \xrightarrow{\epsilon}\mathbb Z_3 \to 0
$$
and... |
Suppose I can calculate the extraordinary cohomology encoded in _topological_ $K$-groups of a topological space $X$ with CW structure. What information does this give me about $C^{*}$-algebras associated with $X$? What does Bott periodicity tell me about the algebras? What is the algebraic analogue of topological suspe... |
You have several questions, both about polynomial multiplication and about regular multiplication with integers.
To address the last one first: once you have multiplication by integers, multiplication by fractions will very quickly rear its head. What does multiplying by "one and a half" mean, if multiplying by 2 me... |
Suppose I can calculate the extraordinary cohomology encoded in _topological_ $K$-groups of a topological space $X$ with CW structure. What information does this give me about $C^{*}$-algebras associated with $X$? What is the algebraic analogue of topological suspension, i.e., the algebraic version of Bott Periodicity?... |
Suppose I can calculate the extraordinary cohomology encoded in _topological_ $K$-groups of a topological space $X$ with CW structure. What information does this give me about $C^{*}$-algebras associated with $X$? What is the algebraic analogue of topological suspension or the algebraic version of Bott Periodicity?
... |
You have several questions, both about polynomial multiplication and about regular multiplication with integers.
To address the last one first: once you have multiplication by integers, multiplication by fractions will very quickly rear its head. What does multiplying by "one and a half" mean, if multiplying by 2 me... |
You have several questions, both about polynomial multiplication and about regular multiplication with integers.
To address the last one first: once you have multiplication by integers, multiplication by fractions will very quickly rear its head. What does multiplying by "one and a half" mean, if multiplying by 2 me... |
Your question needs some more information:
How is their score generated (what kind of game is it)? What should your non-cheating data look like?
How do people cheat? How will their score be different (in a statistical sense) when they are not cheating?
Do you know roughly the proportion that are cheating? Or is t... |
You have two questions, the explicit one about why you would want to multiply polynomials, and an implicit one in your final paragraph about what multiplication by a non-integer might mean or why we would care to multiply by a non-integer in the first place.
To address the last one first: once you have multiplicati... |
This question is a follow up to [this][thisq] excellent mathematics stackexchange question.
Let $\mu(n)$ be the Möbius function, $\phi(n)$ Euler's totient function, $\sigma(n)$ the sum of divisors function and $\tau(n)$ the number of divisors function. Define the set $S_N,$ for a natural number $N,$ by
$$S_N = \... |
When I was trying to find closed-form representations for odd zeta-values, I used
$$ \Gamma(z) = \frac{e^{-\gamma \cdot z}}{z} \prod_{n=1}^{\infty} \Big( 1 + \frac{z}{n} \Big)^{-1} e^{\frac{z}{n}} $$
and rearranged it to
$$ \frac{\Gamma(z)}{e^{-\gamma \cdot z}} = \prod_{n=1}^{\infty} \Big( 1 + \frac{z}{n} \Big)^{... |
In a few examples i noted that the existence of k-regular graph on n vertices is :
1. True , for k or n even.
2. False , for k and n odd . But we can find a graph with n-1 vertices with
degree k and one vertex with degree k-1. There doesn't exists a k-regular graph for
k and n odd because k=deg(G)... |
While experimenting with certain sums, I came to the following sum:
$$S_n = \sum_{k=0}^n \frac{n-k+1}{(n+1) (n+2) (n-k+2)}.$$
After rewriting the summand as
$$\frac{n-k+1}{(n+1) (n+2) (n-k+2)} = \frac{n^{\underline{k}}}{(n+2)^{\underline{k}}(n-k+2)^2}$$
and then feeding the sum to Mathematica, i obtained
$$S_n... |
I cannot fully answer your questions, but hopefully I can help orient you. I know a little about C*-algebra K-theory, and less about topological K-theory, so take this with a grain of salt.
The $K_0$ group of a (complex) C*-algebra $A$ is defined as the Grothendieck group of a commutative monoid of equivalence clas... |
The chance to throw a 6 with once dice is 1/6
And.. 6 times 1/6 = 1
So, if I throw with 6 dices, the chance to throw at least 1 six should be 1.
But when i trow 6 dices, I sometimes don't throw any 6 at all..
How come? |
The chance to throw a 6 with one die is 1/6
And 6 times 1/6 = 1
So, if I throw with 6 dice, the chance to throw at least 1 six should be 1.
But when I throw 6 dice, I sometimes don't throw any 6 at all..
How come? |
Suppose you are given a question that goes like this:
> Consider three planets that revolve
> around a star on separate circular
> orbits sharing the same orbital plane.
> The first planet, A, takes 385 days to
> complete its orbit. The second planet,
> B, takes 814 days, while the third
> planet, C, takes 167... |
Is there formal name and proof for this formula/theorem (for now I'm calling it Orbital Collinearity Theorem)? |
How to solve $y''-\displaystyle\frac{y'}{x}=4x^{2}y$ ????
I know that the solution of this equation is : $e^{x^{2}}$, but I can not resolve.
First i thought that $z=y'$ could be, but was not .
|
how to solve this diferential equation???? $y''-\frac{y'}{x}=4x^{2}y$ |
A loan for $50,000$ has level payments to be made at the end of each year for 10 years at an annual rate of $9 \%$. (a) Find the balance at the end of $3$ years. (b) Find the interest paid in the third payment.
So I think this involves using amortization. That is, one pays the interest due first and then the princip... |
Today I was thinking about composition of functions. It has nice properties, its always associative, there is an identity, and if we restrict to bijective functions then we have an inverse.
But then I thought about commutativity. My first intuition was that bijective self maps of a space should commute but then I ... |
How do I do Recursion? |
Today I was thinking about composition of functions. It has nice properties, its always associative, there is an identity, and if we restrict to bijective functions then we have an inverse.
But then I thought about commutativity. My first intuition was that bijective self maps of a space should commute but then I ... |
How to solve $y''-\displaystyle\frac{y'}{x}=4x^{2}y$ ?
I know that the solution of this equation is: $e^{x^{2}}$, but I cannot resolve.
First I thought that $z=y'$ could be, but was not.
|
How to solve this differential equation? $y''-\frac{y'}{x}=4x^{2}y$ |
**Question**: What is the correct notion of a _product_ of integral (or rational) polytopes which induces a factorization of its Ehrhart polynomial into two primitive Ehrhart (quasi-)polynomials corresponding to its constituent polytopes, viz., $L_{P \times Q}(t) = L_{P}(t) L_{Q}(t)$?
(_Motivation_) Given two clo... |
I am trying to compute the Kolmogorov distance between two univariate gaussian distributions $\mathcal{N}(0,n)$ and $\mathcal{N}(0,2n)$ for large $n$. I have a feeling this should be simple but whatever I have tried so far doesn't work. Could anyone give me some hints?
By the Kolmogorov distance between two distri... |
**Question**: What is the correct notion of a _product_ of integral (or rational) polytopes which induces a factorization of its Ehrhart polynomial into two primitive Ehrhart (quasi-)polynomials corresponding to its constituent polytopes, viz., $L_{P \times Q}(t) = L_{P}(t) L_{Q}(t)$?
(_Motivation_) Given two close... |
**Question**: What is the correct notion of a _product_ of integral (or rational) polytopes which induces a factorization of its Ehrhart polynomial into two primitive Ehrhart (quasi-)polynomials corresponding to its constituent polytopes, viz., $L_{P \times Q}(t) = L_{P}(t) L_{Q}(t)$?
(_Motivation_) Given two close... |
Recursion refers to a method where you figure out the "next" value in terms of previous values. For example, to solve the <a href="http://math.stackexchange.com/questions/2650/how-to-prove-the-optimal-towers-of-hanoi-strategy">Towers of Hanoi</a> puzzle, you can explain the solution recursively: to move $n$ disks, firs... |
A [classic result of Ritt][1] shows that polynomials that commute under composition must be, up to a linear homeomorphism, either both powers of $x$, both iterates of the same polynomial, or both Chebychev polynomials. Actually Ritt proved a more general rational function case - follow the link. His work was motivated... |
How to solve $y''-\displaystyle\frac{y'}{x}=4x^{2}y$ ?
I know that the solution of this equation is: $y = e^{x^{2}}$, but I cannot resolve.
First I thought that $z=y'$ could be, but was not.
|
Today I was thinking about composition of functions. It has nice properties, its always associative, there is an identity, and if we restrict to bijective functions then we have an inverse.
But then I thought about commutativity. My first intuition was that bijective self maps of a space should commute but then I ... |
**Question**: What is the correct notion of a _product_ of integral (or rational) polytopes which induces a factorization of its Ehrhart polynomial into two primitive Ehrhart (quasi-)polynomials corresponding to its constituent polytopes, viz., $L_{P \times Q}(t) = L_{P}(t) L_{Q}(t)$?
(_Motivation_) Given two close... |
I need help studying for an exam. How do I find "Big Oh," "Big Omega," and "Big Theta"?
How do I combine this with Induction?
**Prove that f(x) is O(x^n), where
f(x) = a_n*x^n + a_(n-1) *x^(n-1) + a_(n-2) *x^(n-2) + ... + a_2 * x^2 + a_1 * x + a_0**
Where a_n or a_(n-1) roughly translates to "a sub n" and "a su... |
How do I find "Big Oh," "Big Omega," and "Big Theta"? |
I have a formula which is G-force = velocity*omega/9.8. Omega is the angular velocity.
I've seen on the internet that G force is actually acceleration/9.8. I'm confused as to which formula is correct. For simulating the motion of particle taking a turn, would omega simply be velocity divided by radius of turn? Assumin... |
**Question**: What is the correct notion of a _product_ of integral (or rational) polytopes which induces a factorization of its Ehrhart (quasi-)polynomial into two primitive Ehrhart (quasi-)polynomials corresponding to its constituent polytopes, viz., $L_{P \times Q}(t) = L_{P}(t) L_{Q}(t)$?
(_Motivation_) Given t... |
I need help studying for an exam. How do I find "Big Oh," "Big Omega," and "Big Theta"?
How do I combine this with Induction?
- Prove that $f(x)$ is $O(x^n)$, where
$$f(x) = a_n x^n + a_{n-1} x^{n-1} + a_{n-2} x^{n-2} + \cdots + a_2 x^2 + a_1 x + a_0$$
- Find "Big O": (Usually log in Computer Science is assumed... |
How to proceed in this problem ? |
If $ x = \log_{12} 27 \text {, what is the the value of } \log_6 16 $ ? |
If $ x = \log_{12} 27 \text {,then what is the the value of } \log_6 16 $ ? |
Given,
1*2^1 + 2*2^2 + 3*2^3 + 4*2^4 + ... d * 2^d
= sum(r * 2^r, r from 1 to d)
How can we infer to the following solution?
= 2 (d-1) * 2^d + 2
Thank you |
I am an undergraduate learning about gauge theory and I have been tasked with working through the two examples given on pages 65 and 66 of "[Characteristic forms and geometric invariants](http://www.jstor.org/pss/1971013)" by Chern and Simon. I will recount the examples and my progress at a solution. For ease here is t... |
Given $$1\cdot 2^1 + 2\cdot 2^2 + 3\cdot 2^3 + 4\cdot 2^4 + \cdots + d \cdot 2^d = \sum_{r=1}^d r \cdot 2^r,$$
how can we infer to the following solution? $$2 (d-1) \cdot 2^d + 2. $$
Thank you |
Need help studying for an exam.
Practice Question:
If there are 200 students in the library, how many ways are there for them to be split among the floors of the library if there are 6 floors?
Hint: The students can not be told apart (they are indistinguishable).
THe answer must bein terms of P(n,r), C(n,r), ... |
If there are 200 students in the library, how many ways are there for them to be split among the floors of the library if there are 6 floors? |
I recall reading somewhere that the supremum of a family of topologies on a set is simply the topology generated by the union of all topologies in the family. My question is, what does "generated" mean in this case? For instance, I know when dealing with filter bases, the generated filter is the set of all subsets cont... |
What exactly is the topology generated by the union of a family of topologies? |
Question: Let $F_n$ the sequence of Fibonacci numbers, given by $F_0 = 0, F_1 = 1$ and $F_n = F_{n-1} + F_{n-2}$ for $n \geq 2$. Show for $n, m \in \mathbb{N}$: $$F_{n+m} = F_{n-1}F_m + F_n F_{m+1}$$
My (very limited) attempt so far: after creating a small list of the values $F_0=0, F_1=1, F_2=1, F_3=2, F_4=3, F_5=5... |
Isn't this obvious (or have I missed something?)
The appropriate product of rational polytopes $P\subseteq\mathbb R^m$
and $Q\subseteq\mathbb R^n$ is surely their Cartesian product
$P\times Q\subseteq\mathbb R^{m+n}$. For a positive
integer $t$, the integer points in $t(P\times Q)$ are those of the form
$(a,b)$ ... |
Given two vectors $u, v \in \mathbb{R}^d$ represented the spherical coordinates is there a simple formula to compute the angle between the two vectors? Without loss of generality, we can assume that the vectors $u$ and $v$ have unit norm.
I am not sure that the following notation is standard, but I assume that the v... |
Apart from the mundane reasons, e.g. "you need it to do certain computations" there are also some more technical reasons:
* The Stone-Weierstrass theorem: *Let $X$ be a compact metric space and let $A$ be a $\mathbb{C}$-sub[algebra](http://en.wikipedia.org/wiki/Algebra_over_a_field) of $C(X,\mathbb{C})$. If $A$ sepa... |
Apart from the mundane reasons, e.g. "you need it to do certain computations" there are also some more technical reasons:
* The Stone-Weierstrass theorem: *Let $X$ be a compact metric space and let $A$ be a $\mathbb{C}$-sub[algebra](http://en.wikipedia.org/wiki/Algebra_over_a_field) of $C(X,\mathbb{C})$. If $A$ sepa... |
I'm in Italian guy almost in my 30. I have a regular job as a programmer. When in school I've never been much interested nor good in math and even at the university I've been studying languages, hence something more on the literary side that on the scientific one.
When in high school I've had mostly literary classes... |
I'm really embarrassed to ask this - my apologies.
In a piece of software I'm writing, I am using the following:
Y = X+(X/10*N)
That's all fine - but how do I calculate X when I know Y and N?
I know it's really basic, but for some reason I get stuck half-way through moving the equation around. |
I'm really embarrassed to ask this - my apologies.
In a piece of software I'm writing, I am using the following:
$Y = X+\frac{X}{10}N$
That's all fine - but how do I calculate X when I know Y and N?
I know it's really basic, but for some reason I get stuck half-way through moving the equation around. |
Does anyone know if it possible to reprisent a sphere with 1000 equal surfaces?
When I say equal surfaces, I am talking in terms of area. However it would also be preferable if the shape of these surfaces match.
For example, I am looking at subdivided icosahedron's, all surfaces are equal triangles in terms of sh... |
Geometry Question: Is it possible to reprisent a sphere with 1000 equal surfaces? |
I'm trying to teach myself mathematics. I only started last year with a previous knowledge of basic arithmetic. I often make a detour into regions featuring problems that are a bit too deep for me. I'm often too curious to wait until I was able to catch up on the necessary bedding. I hope you'll excuse me :-)
[Wolfr... |
Is there any "algorithm" or steps to follow to get a formula from a table of values.
Example:
Using this values:
X Result
1 3
2 5
3 7
4 9
I'd like to obtain:
Result = 2X+1
**Edit**
Maybe usi... |
Possible to imitate a sphere with 1000 congruent polygons? |
Is there any "algorithm" or steps to follow to get a formula from a table of values.
Example:
Using this values:
X Result
1 3
2 5
3 7
4 9
I'd like to obtain:
Result = 2X+1
**Edit**
Maybe usi... |
The best tool for doing this is that very, very impressive piece of software:
http://ccsl.mae.cornell.edu/eureqa
**Edit:** For your abovementioned very easy example, even WA will find the right formula:
http://www.wolframalpha.com/input/?i=3,+5,+7,+9,... |
I've got a question concerning how to proof the Pythagoras theorem using the following assumption:
x is perpendicular to y (if and only if) ||x+y||^2 = ||x||^2 + ||y||^2
Where x and y are vectors.
I have a basic understanding of linear algebra however I'm a beginner with this. The question provides hints how t... |
Let's say that we have three points: $p = (x_p,y_p)$, $q = (x_q,y_q)$ and $a = (x_a,y_a)$. How can i find point $b$ which is reflection across a line drawn through $p$ and $q$? I know it's simple to calculate, when we have $p$, $q$ etc. But I want to do this in my program, and I'm not sure, how to compute this. |
Let's say that we have three points: $p = (x_p,y_p)$, $q = (x_q,y_q)$ and $a = (x_a,y_a)$. How can i find point $b$ which is reflection of $a$ across a line drawn through $p$ and $q$? I know it's simple to calculate, when we have $p$, $q$ etc. But I want to do this in my program, and I'm not sure, how to compute this. |
How to prove that $\mathcal{O}_{\sqrt[3]{3}}$ is an euclidean domain? I heard that one should prove the following but why it is enough?
For any $ a,b,c\in\mathbb{R}$, prove that there are $ x,y,z\in\mathbb{R}$ such that $ x-a,y-b,z-c\in\mathbb{Z}$ and that
$$-1\leq x^3+3y^3+9z^3-9xyz\leq 1.$$ |
Let X be a smooth projective variety with canonical class K.
Let a be defined to be the maximum dimension of the image of X under the rational map induced by the linear system |nK| as n ranges over all positive integers.
Let b be defined to be the smallest positive integer c such that the sequence (dim(H^0 (X, nK... |
I've got a question concerning how to proof the Pythagoras theorem using the following assumption:
$x$ is perpendicular to $y$ (if and only if) $||x+y||^2 = ||x||^2 + ||y||^2$,
where $x$ and $y$ are vectors.
I have a basic understanding of linear algebra however I'm a beginner with this. The question provides hi... |
I'm asking here because no textbook or website that I know of gives a definition of the above mentioned term.
Since there's no obvious way (that I can think of) to define a normal subloop, I don't see how the definition of a simple group can be modified for the case of loops.
So - **what is the definition of a simp... |
What is a simple loop? |
With Fibonacci numbers usually there are _multiple_ ways of proving identities.
One way (which is one of my favourites) to prove your identity is the following:
Consider the following problem:
A person climbs up $\displaystyle n$ steps, by taking either one step, or two steps at a time.
The total number of ... |
What is the next term of the following sequences ?
- $ 3,8,13,24,41, \cdots $
**OPTIONS :** $\{ 70,75,80,85 \}$
- $ 4,23,60,121, \cdots $ **OPTIONS :** $\{212,221,241,242\}$
This two question is taken from a test paper of mine,I am no able to figure out the correct-answer.
|
According to [wikipedia](http://en.wikipedia.org/wiki/Discontinuous_linear_map#Axiom_of_choice), you need the Axiom of Choice to find a discontinuous map between two Banach spaces.
Does this procedure also apply for Banach algebras yielding a discontinuous multiplicative linear map?
Or, is there some obstruction,... |
Is there an algebraic homomorphism between two Banach algebras which is not continuous? |
I understand the formal definition of uniform continuity of a function,
and how it is different from standard continuity.
My question is: Is there an intuitive way to classify a function
on $\mathbb{R}$ as being
uniformly continuous, just like there is for regular continuity?
I mean, that for a "nice" function $... |
I'm trying to understand a proof in "Combinatorial Group Theory" by Lyndon & Schupp, page 26, Lemma 4.7.
Here's my problem:
$F$ is a free group with $X$ as basis. $\alpha$ in $IA(F)$ - meaning it's an automorphism of $F$ which induces the identity automorphism on $F/[F,F]$. $k$ in $F_n$ - a term in the descending... |
I'm trying to understand a proof in "Combinatorial Group Theory" by Lyndon & Schupp, page 26, Lemma 4.7.
Here's my problem:
$F$ is a free group with $X$ as basis. $x \in X$. $\alpha \in IA(F)$ - meaning it's an automorphism of $F$ which induces the identity automorphism on $F/[F,F]$. $k \in F_n$ - a term in the d... |
Why in a Hausdorff sequentially compact space the size of the closure of a countable subset is less than $c$ ? I can see why this is true when the space if first countable but we are not assuming so. |
While experimenting with certain sums, I came to the following sum:
$$S_n = \sum_{k=0}^n \frac{n-k+1}{(n+1) (n+2) (n-k+2)}.$$
After rewriting the summand as
$$\frac{n-k+1}{(n+1) (n+2) (n-k+2)} = \frac{n^{\underline{k}}}{(n+2)^{\underline{k}}(n-k+2)^2}$$
and then feeding the sum to Mathematica, i obtained
$$S_n... |
Why in a Hausdorff sequentially compact space the size of the closure of a countable subset is less or equal than $c$ ? I can see why this is true when the space if first countable but we are not assuming so. |
So what can go wrong? We can certainly define a function g(x)=something nice except when x=c, something different at c. Then $\lim_{x\rightarrow c} g(x) \neq g(c)$ Can you rule out this behavior in $f'(x)$? Or maybe $f'(x)$ has a step at $c$. Why can't it? |
I am adding lots of answers here, sorry. I think since they are giving different information, they are best put separately.
If you have not had experience with this, you may be interested in how people derive formulas for these problems. Difference calculus is a nice method to use. Kelley and Peterson's textbook [1]... |
While some of the other answers look good, there are two particular related uses for polynomial multiplication which I didn't see while skimming.
One is related to probabilities. We can use a polynomial to represent the possible outcomes of a random process (so long as there are finitely many), where there is a vari... |
This is really several questions. In increasing order of depth:
1. Why multiply polynomials? Because they are functions, and multiplication is a natural or desirable operation on functions.
2. Why multiply functions? Because the values of the functions are integers, or rational numbers, or real numbers, or ob... |
While some of the other answers look good, there are two particular related uses for polynomial multiplication which I didn't see while skimming.
One is related to probabilities. We can use a polynomial to represent the possible outcomes of a random process (so long as there are finitely many), where there is a vari... |
While some of the other answers look good, there are two particular related uses for polynomial multiplication which I didn't see while skimming.
One is related to probabilities. We can use a polynomial to represent the possible outcomes of a random process (so long as there are finitely many), where there is a vari... |
This is really several questions. In increasing order of depth:
1. Why multiply polynomials? Because they are functions, and multiplication is a natural or desirable operation on functions.
2. Why multiply functions? Because the values of the functions are integers, or rational numbers, or real numbers, or ob... |
You are right that you are kind of assuming what you want, because you cannot even write down $f'(c)$ until you prove it exists; this can be fixed if you replace $f'(c)$ by a specific limit, and the specific limit you want is probably $B$.
Here is half a proof, following the Hint of Robin Chapman:
Consider first ... |
You are right that you are kind of assuming what you want, because you cannot even write down $f'(c)$ until you prove it exists; this can be fixed if you replace $f'(c)$ by a specific limit, and the specific limit you want is probably $B$.
Here is the beginning of half a proof, following the Hint of Robin Chapman:
... |
I have 2 matrices and have been trying to multiply them but to no avail. Then I found this [online][1] site and trying feeding it the values but yet no success.
- R' . T
is what i would like to do but R is a 3x3 (3 rows, 3 cols) matrix and T is a 1 x 3 matrix (1 row, 3 cols).
Any idea how to go ahead with ... |
How to multiply a 3x3 matrix with a 1x3 matrix? |
You can only multiply an $n\times m$ matrix by a $p\times q$ matrix, in that order, if $m=p$. That is, only if the number of columns of the first factor is equal to the number of rows of the second factor. So you *cannot* multiply a $3\times 3$ matrix by a $1\times 3$ matrix; on the other hand, you *can* multiply a $1\... |
I'm trying to understand a proof in "Combinatorial Group Theory" by Lyndon & Schupp, page 26, Lemma 4.7.
Here's my problem:
$F$ is a free group with $X$ as basis. $x \in X$. $\alpha \in IA(F)$ - meaning it's an automorphism of $F$ which induces the identity automorphism on $F/[F,F]$. $k \in F_n$ - a term in the d... |
This is initially a funny question, because I've found this on old notes but I do not find/recover my own derivation... But then it's more general.
Q1:
I considered the function
$ f(x) = \frac {2x^2+3x}{(x+1)^2} $
I expressed this by a powerseries $ f_1(x) = -3x+4x^2-5x^3+ 6x^4 -\ldots $
and stated ... |
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