Attachment 'NF_SEP.tex'

Download

latex error! exitcode was 1 (signal 0), transscript follows:

This is pdfTeX, Version 3.14159265-2.6-1.40.15 (TeX Live 2015/dev/Debian) (preloaded format=latex)
entering extended mode
(./latex_c3b7541409ae8736db48e05629866521ac5b4dbf_p.tex
LaTeX2e <2014/05/01>
Babel <3.9l> and hyphenation patterns for 2 languages loaded.
(/usr/share/texlive/texmf-dist/tex/latex/base/article.cls
Document Class: article 2014/09/29 v1.4h Standard LaTeX document class
(/usr/share/texlive/texmf-dist/tex/latex/base/size12.clo))
(/usr/share/texlive/texmf-dist/tex/latex/base/inputenc.sty
(/usr/share/texlive/texmf-dist/tex/latex/base/utf8.def
(/usr/share/texlive/texmf-dist/tex/latex/base/t1enc.dfu)
(/usr/share/texlive/texmf-dist/tex/latex/base/ot1enc.dfu)
(/usr/share/texlive/texmf-dist/tex/latex/base/omsenc.dfu)))
No file latex_c3b7541409ae8736db48e05629866521ac5b4dbf_p.aux.

! LaTeX Error: Can be used only in preamble.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.7 \documentclass
                  [12pt]{article}

! LaTeX Error: Can be used only in preamble.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.9 \usepackage
               {amssymb, amsmath}

! LaTeX Error: Can be used only in preamble.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.17 \begin{document}
                     
[1]
! Undefined control sequence.
<recently read> \mathbb 
                        
l.30 ...by an irreducible polynomial over $\mathbb
                                                  {Q}$, a class for number f...

! Undefined control sequence.
\Gal ->\operatorname 
                     {Gal}
l.30 ...er field $L/K$ and a subgroup $H$ of $\Gal
                                                  (L/K)$, as well as others....


LaTeX Warning: Reference `NF' on page 2 undefined on input line 30.

[2]
! Undefined control sequence.
<recently read> \mathbb 
                        
l.32 ...ce they are simultaneously rings, $\mathbb
                                                  {Z}$-modules, and in the c...

! Undefined control sequence.
<recently read> \mathbb 
                        
l.32 ...s: does one represent elements as $\mathbb
                                                  {Z}$-linear combinations o...

! Undefined control sequence.
<recently read> \mathbb 
                        
l.32 ...thbb{Z}$-linear combinations of a $\mathbb
                                                  {Z}$ basis for the order, ...


LaTeX Warning: Reference `Orders' on page 3 undefined on input line 32.

! Undefined control sequence.
<recently read> \mathfrak 
                          
l.34 ....  For an ideal $I$ of an order $\mathfrak
                                                  {O}$ over a maximal order ...

! Undefined control sequence.
<recently read> \mathfrak 
                          
l.34 ...n give generators for $I$ as an $\mathfrak
                                                  {O}$ module, generators as...

! Undefined control sequence.
<recently read> \mathbb 
                        
l.34 ...hcal{O}_K$ module or a basis as a $\mathbb
                                                  {Z}$ module.  We also want...


LaTeX Warning: Reference `Ideals' on page 3 undefined on input line 34.


LaTeX Warning: Reference `UC' on page 3 undefined on input line 36.

! Undefined control sequence.
\Gal ->\operatorname 
                     {Gal}
l.38 ...e able to work with the Galois group $\Gal
                                                  (L/K)$ not just as an abst...


LaTeX Warning: Reference `Gal' on page 3 undefined on input line 38.

! Undefined control sequence.
<recently read> \mathfrak 
                          
l.40 A number field $L/K$ and a place $\mathfrak
                                                {w}$ of $L$ over $\mathfrak{...

! Undefined control sequence.
<recently read> \mathfrak 
                          
l.40 ...lace $\mathfrak{w}$ of $L$ over $\mathfrak
                                                  {v}$ of $K$ determine a co...

! Undefined control sequence.
l.40 ...f $K$ determine a completion $L_{\mathfrak
                                                  {w}}$ over $K_{\mathfrak{v...

! Undefined control sequence.
l.40 ...tion $L_{\mathfrak{w}}$ over $K_{\mathfrak
                                                  {v}}$.  Sage should suppor...


LaTeX Warning: Reference `Comp' on page 3 undefined on input line 40.

[3]
! Undefined control sequence.
<recently read> \mathbb 
                        
l.50 ...d than Sage, they do not consider $\mathbb
                                                  {Q}$ a number field.  But ...


Overfull \hbox (73.4217pt too wide) in paragraph at lines 52--53
[]\OT1/cmr/m/n/12 On the par-ent level, \OT1/cmtt/m/n/12 NumberField[]generic \
OT1/cmr/m/n/12 will have sub-classes \OT1/cmtt/m/n/12 NumberField[]absolute\OT1
/cmr/m/n/12 ,

Overfull \hbox (132.28838pt too wide) in paragraph at lines 52--53
\OT1/cmtt/m/n/12 NumberField[]relative\OT1/cmr/m/n/12 , \OT1/cmtt/m/n/12 Number
Field[]multiple\OT1/cmr/m/n/12 , \OT1/cmtt/m/n/12 NumberField[]subfield\OT1/cmr
/m/n/12 , \OT1/cmtt/m/n/12 NumberField[]fixed[]field
! Undefined control sequence.
<recently read> \mathbb 
                        
l.54 ...ingle irreducible polynomial over $\mathbb
                                                  {Q}$.  I'm not totally con...

! Undefined control sequence.
<recently read> \mathbb 
                        
l.54 ...ve extensions that happen to have $\mathbb
                                                  {Q}$ as the ground field (...

! Undefined control sequence.
<recently read> \mathbb 
                        
l.54 ...eral (no unramified extensions of $\mathbb
                                                  {Q}$, etc.  Thoughts here ...

[4]
Overfull \hbox (35.1587pt too wide) in paragraph at lines 60--61
\OT1/cmtt/m/n/12 NumberField[]relative\OT1/cmr/m/n/12 ; for $\OML/cmm/m/it/12 m
 > \OT1/cmr/m/n/12 1$ it will be very sim-i-lar to \OT1/cmtt/m/n/12 NumberField
[]multiple\OT1/cmr/m/n/12 ,

Overfull \hbox (2.58733pt too wide) in paragraph at lines 60--61
\OT1/cmr/m/n/12 quired for \OT1/cmtt/m/n/12 NumberField[]multiple\OT1/cmr/m/n/1
2 ... How-ever, \OT1/cmtt/m/n/12 NumberField[]subfield \OT1/cmr/m/n/12 comes
! Undefined control sequence.
\Gal ->\operatorname 
                     {Gal}
l.62 ...l extensions?) and a subgroup $H$ of $\Gal
                                                  (L/K)$, create the fixed s...


Overfull \hbox (64.13467pt too wide) in paragraph at lines 66--67
\OT1/cmr/m/n/12 though both types should pre-sum-ably in-herit from a sin-gle \
OT1/cmtt/m/n/12 NumberFieldElement[]generic
[5]
! Undefined control sequence.
<recently read> \mathbb 
                        
l.72 ...dule.  In particular, orders over $\mathbb
                                                  {Z}$ will be free $\mathbb...

! Undefined control sequence.
<recently read> \mathbb 
                        
l.72 ...rs over $\mathbb{Z}$ will be free $\mathbb
                                                  {Z}$ modules.

Overfull \hbox (131.86336pt too wide) in paragraph at lines 74--75
\OT1/cmr/m/n/12 of or-ders. It's not clear to me how it would be use-ful to hav
e an \OT1/cmtt/m/n/12 NumberFieldOrder[]abelian[]extension

Overfull \hbox (5.08522pt too wide) in paragraph at lines 74--75
\OT1/cmr/m/n/12 class, but all of the other cor-re-spond-ing classes, \OT1/cmtt
/m/n/12 NumberFieldOrder[]absolute\OT1/cmr/m/n/12 ,

Overfull \hbox (80.21031pt too wide) in paragraph at lines 74--75
\OT1/cmtt/m/n/12 NumberFieldOrder[]relative\OT1/cmr/m/n/12 , \OT1/cmtt/m/n/12 N
umberFieldOrder[]multiple\OT1/cmr/m/n/12 , \OT1/cmtt/m/n/12 NumberFieldOrder[]s
ubfield
[6] [7] (./latex_c3b7541409ae8736db48e05629866521ac5b4dbf_p.aux)

LaTeX Warning: There were undefined references.


LaTeX Warning: Label(s) may have changed. Rerun to get cross-references right.

 )
(\end occurred inside a group at level 1)

### semi simple group (level 1) entered at line 17 (\begingroup)
### bottom level
(see the transcript file for additional information)
Output written on latex_c3b7541409ae8736db48e05629866521ac5b4dbf_p.dvi (7 pages
, 20564 bytes).
Transcript written on latex_c3b7541409ae8736db48e05629866521ac5b4dbf_p.log.

Attached Files

To refer to attachments on a page, use attachment:filename, as shown below in the list of files. Do NOT use the URL of the [get] link, since this is subject to change and can break easily.

You are not allowed to attach a file to this page.