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Nov
10
revised Given $x$ and $y$ in $\mathbb{Z}[i]$, find $q$ and $r$ such that $x=qy+r$.
added 70 characters in body; edited title
Nov
10
comment Given $x$ and $y$ in $\mathbb{Z}[i]$, find $q$ and $r$ such that $x=qy+r$.
You are correct that there are very few possible $r\in\mathbb{Z}[i]$ with $|r|<2$; there are two more than you have written though.
Nov
10
comment What does it mean for two polynomials to be the same in this fundamental field extension theorem?
I think you meant to say that $\eta$ is a root of $x^2+x-1$...or I messed up my calculation.
Nov
10
comment Basis of image and kernel of a linear transformation
I am guessing (and it really is just a guess) that the "dimension theorem" that isn't supposed to be used is another name for the rank-nullity theorem. But on the other hand, it isn't so hard to show that this set is independent directly.
Nov
10
comment Basis of image and kernel of a linear transformation
Look at what kinds of polynomials appear in the image, in particular at their coefficients. Can you see how, for a polynomial in the image, the coefficient of $x^2$ is determined by the other two coefficients?
Nov
10
comment Two questions about triangle that blocked at rectangle…
By "a triangle blocked by a rectangle", I assume you mean the rectangle two of whose edges are the short edges of the triangle, and whose diagonal is the hypotenuse of the triangle? If yes, then the answer to the 1st question is yes, because the rectangle is built from two copies of the triangle, and the answer to the second question is no, because the center of the rectangle is on the hypotenuse. I'm not sure if there is a nice way to describe the centroid of the triangle in terms of the rectangle.
Nov
10
comment Two questions about triangle that blocked at rectangle…
Thanks. (To prove it wasn't a stupid question, here is a table including 16 other definitions of the center of a triangle: en.wikipedia.org/wiki/…).
Nov
10
comment Two questions about triangle that blocked at rectangle…
What do you mean by the "center" of the triangle here? There are many different definitions.
Nov
10
comment Smallest Subring of R that contains $S \cup \{a\}$
You seem to be thinking along the right lines. Can you show that any subring $S'$ containing $S\cup\{a\}$ in fact contains the set in question? This is enough to show that your set is contained in the intersection of all subrings containing $S\cup\{a\}$, and the other direction is easy since you have already shown that your set is such a subring.
Nov
10
comment Prove that $(x^3-2)$ is a maximal ideal of $\Bbb Q[x]$
To get better answers, you should add some context to your question - what have you already tried? Do you know some theorems that might help? For example, would it help you to know that $x^3-2$ is irreducible? Can you prove that it is?
Nov
7
comment Proving that $f$ is a bijection.
@egreg I'm not sure I'm following - the OP has a definition ($g(y)=x\iff f(x)=y$) in the question.
Nov
6
comment Proving that $f$ is a bijection.
It doesn't appear to be the definition the OP is using, given the phrasing of both the problem they are trying to solve and the clause beginning "I basically need to show...".
Nov
6
answered Proving that $f$ is a bijection.
Nov
6
answered Semisimple submodule
Nov
6
reviewed Approve I love maths, but my school is limited in its teachings.
Nov
5
comment Give a counterexample to show that $(AB)^{-1} \neq A^{-1}B^{-1}$
To make the same point in another way - it is not true that $AB\ne BA$ for all $A,B$, but there do exist some $A,B$ for which $AB\ne BA$ - so find a pair (that are also invertible), and you have an explicit counterexample.
Nov
5
comment Shape of the visible part of the Moon
Pas de problème. ;) I have just discovered that both of these things are "ellipse" in French, which makes your mistake even more forgivable than it already was!
Nov
5
comment Shape of the visible part of the Moon
Since you asked for language corrections - I'm pretty certain that you meant "ellipse" in "other cases". This is the shape (singular of ellipses), whereas ellipsis refers to the three dots immediately preceding the word!
Nov
5
revised Shape of the visible part of the Moon
deleted 1 character in body
Nov
5
comment re-writing a mathematical expression
@EmmaTebbs I agree this is a slightly difficult question to tag - myself and another user have now retagged it. Physics and matlab are both relevant to the context, and I also added algebra-precalc because it's essentially about manipulating expressions (although the expressions are a little more involved than those that would normally occur under this tag!).