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Dec
28
asked Newton polygon and asymptotic behavior near a singular point
Dec
28
comment Computing the monodromy for a cover of the Riemann sphere (and Puiseux expansions)
Is there any proof or reference of proofs for this method?
Dec
27
comment Composition of Number Fields
What about $\operatorname{Gal}(KL/F)\cong\operatorname{Gal}(K/F)\times\operatorname{Gal}(L/‌​F)$ where $F=K\cap L$ even when $K/F,L/F$ aren't finite but Galois?
Dec
26
comment Should diffeomorphisms preserving arc length be affine?
If $f$ preserves the (non-degenerate) symplectic structure, then $f$ is affine. I meant that I had less interest in the symplectic case, and I guessed (wrongly) for the symplectic case just because of the preceding statement.
Dec
26
comment Should diffeomorphisms preserving arc length be affine?
Informed and informative. However, the original problem arises in Lorentz quadratic form, therefore I'm more interested in the psuedo-Euclidean case. I guessed the symplectic case since it seems that the proof of my old problem also works for the symplectic structure.
Dec
26
revised Should diffeomorphisms preserving arc length be affine?
added 78 characters in body
Dec
22
asked Should diffeomorphisms preserving arc length be affine?
Dec
5
comment Show that $f\circ \gamma$ is a regular surface.
@B11b It's certainly a handwork to me.
Dec
1
comment Show that $f\circ \gamma$ is a regular surface.
You need to input $\LaTeX$ rather than images. I've edited.
Dec
1
revised Show that $f\circ \gamma$ is a regular surface.
LaTeXize
Dec
1
comment The ideal generated by $(2, x)$ in $\mathbb{Z}[x]$
@AlgebraGuy Just $(x)$. Note that $I$ is prime but not maximal iff $R/I$ is a integral domain but not a field.
Dec
1
comment Notation: $F^{*m}$ for field $F$
You're right and the notation is really ambiguous.
Dec
1
revised An imcomprehensible proof on Arnold's Lectures on PDE, contact diffeomorphism
added 70 characters in body
Dec
1
asked An imcomprehensible proof on Arnold's Lectures on PDE, contact diffeomorphism
Nov
22
comment Should isometries be linear?
$T(x)=BPx$, typo.
Nov
22
accepted Should isometries be linear?
Nov
22
comment Should isometries be linear?
A nice argument. Geometrical translation of the proof: suppose $B$ is a non-degenerate bilinear form, then $v_1,\dotsb,v_n$ are linear independent iff the Gram matrix $(B(v_j,v_k))_{jk}$ is invertible, therefore isometries map bases to bases. Suppose $\{e_k\}$ is a base, $\{f_k=Te_k\}$ is another base, then $B(Tx,f_k)=B(x,e_k)$, which naturally defines a linear map $P\colon V\to V^*;x\mapsto B(Tx,\circ)$. Since $B$ is nondegenerate, it induces an isomorphism $B\colon V^*\to V$, and $Tx=BP$.
Nov
22
revised Should isometries be linear?
added 36 characters in body
Nov
17
revised Should isometries be linear?
deleted 17 characters in body
Nov
17
revised Should isometries be linear?
added 33 characters in body