Re: [sage-support] Re: Listing all k-minors of a matrix?

2010-02-02 Thread Peter K.H. Gragert
Hi,
the second solution is indeed very nice.
I tested with
 A = Matrix(QQ, 2,3, [1,2,3,4,5,6]);A
giving:
[1 2 3]
[4 5 6]
res=[A[rows,cols] for cols in Combinations(A.ncols(),2) for rows in
Combinations(A.nrows(),2)];res


[[1 2]
[4 5], [1 3]
[4 6], [2 3]
[5 6]]

this is more or less my question this output is not really readable though
correct.
for i in range(len(res)):print res[i].det()

-3
-6
-3
A.minors(2)
[-3, -6, -3]

And some different, how do Ishow output easier, is HERE a possibility to
show a picture (screen capture) of sage-sheet?

Greets
   Peter

2010/2/2 Jason Grout jason-s...@creativetrax.com

 On 02/01/2010 08:12 AM, javier wrote:

 You can see the source of the minors method using

 sage: M.minors??

 (you need to have defined M beforehand).

 By browsing at that source one can easily find the general way of
 doing it:

 sage: A = Matrix(QQ, 3, [1,2,3,4,5,6,7,8,9])
 sage: [A.matrix_from_rows_and_columns(rows, cols) for cols in
 combinations_iterator(range(A.ncols()), 2) for rows in
 combinations_iterator(range(A.nrows()),2)]
 [
 [1 2]  [1 2]  [4 5]  [1 3]  [1 3]  [4 6]  [2 3]  [2 3]  [5 6]
 [4 5], [7 8], [7 8], [4 6], [7 9], [7 9], [5 6], [8 9], [8 9]
 ]



 Or slightly easier to read:


 sage: A = Matrix(QQ, 3, [1,2,3,4,5,6,7,8,9])
 sage: [A[rows,cols] for cols in Combinations(A.ncols(),2) for rows in
 Combinations(A.nrows(),2)]

 [
 [1 2]  [1 2]  [4 5]  [1 3]  [1 3]  [4 6]  [2 3]  [2 3]  [5 6]
 [4 5], [7 8], [7 8], [4 6], [7 9], [7 9], [5 6], [8 9], [8 9]
 ]



 Thanks,

 Jason

 --
 Jason Grout


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Re: [sage-support] Profiling code in Sage

2010-02-02 Thread Robert Bradshaw

On Feb 1, 2010, at 6:14 PM, Minh Nguyen wrote:


Hi Stefan,

On Tue, Feb 2, 2010 at 1:07 PM, Stefan  
stefan.louis.no...@gmail.com wrote:


SNIP


Can anyone point me in the right direction for profiling a Python
function in Sage?


Here's an example on using prun from within Sage:

sage: %prun next_prime(10)
4 function calls in 0.000 CPU seconds

  Ordered by: internal time

  ncalls  tottime  percall  cumtime  percall filename:lineno(function)
   10.0000.0000.0000.000 {method 'next_prime' of
'sage.rings.integer.Integer' objects}
   10.0000.0000.0000.000 arith.py:772(next_prime)
   10.0000.0000.0000.000 string:1(module)
   10.0000.0000.0000.000 {method 'disable' of
'_lsprof.Profiler' objects}


For more information on the command prun(), see its doctring by
issuing the command prun?.


Note, however, that code passed to prun is not preparsed.

- Robert


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Re: [sage-support] can't build SAGE 4.3.1 for linux-powerpc32

2010-02-02 Thread Dr. David Kirkby

Douglas Mencken wrote:

I have a problem with building SAGE 4.3.1 for linux-powerpc32:
checking lex output file root... configure: error: cannot find output
from flex; giving up

My distro is Fedora 12 Constantine, I have flex 2.5.35 installed by
package management system (Package flex-2.5.35-7.fc12.ppc already
installed and latest version) and there's also lex symlink to flex:
$ ls -l `which lex`
lrwxrwxrwx 1 root root 4 2009-11-18 18:57 /usr/bin/lex - flex

Full output from make:
--
$ make
cd spkg  ./install all 21 | tee -a ../install.log
make[1]: Entering directory `/home/douglas/Desktop/SAGE/sage-4.3.1/spkg'
base/dir-0.1-install
../data/
../local/
../local/etc
../local/lib
../local/bin
../local/include
../tmp/
/home/douglas/Desktop/SAGE/sage-4.3.1/spkg/build
installed/
base/prereq-0.6-install
Starting prerequisite check.
Machine: Linux localhost 2.6.31.12-174.2.3.fc12.ppc #1 Mon Jan 18
19:36:45 UTC 2010 ppc ppc ppc GNU/Linux
prereq-0.6/
prereq-0.6/configure
prereq-0.6/configure.ac

SNIP

checking whether g++ accepts -g... yes
checking dependency style of g++... gcc3
checking how to run the C preprocessor... gcc -E
checking for flex... flex
checking lex output file root... configure: error: cannot find output
from flex; giving up
 ERROR: You do not have all of the prerequisites needed
 to build Sage from source.  See the errors above.
make[1]: *** [installed/prereq-0.6] Error 1
make[1]: Leaving directory `/home/douglas/Desktop/SAGE/sage-4.3.1/spkg'

real0m21.657s
user0m2.805s
sys 0m2.803s
Error building Sage.
--


That is odd. flex is not specifically checked for in Sage - by that, I mean the 
word flex does not appear in the configure.ac file used to create the 
configure script you are running. I suspect autoconf automatically tests for flex.


On my own system, which does not have flex, but has lex, I see:

checking for flex... no
checking for lex... lex
checking lex output file root... lex.yy
checking lex library... none needed
checking whether yytext is a pointer... no
checking for bison... no
checking for byacc... no



You could make a backup of the file spkg/base/prereq-0.6/configure, then edit 
out the following lines:


if test -f lex.yy.c; then
  ac_cv_prog_lex_root=lex.yy
elif test -f lexyy.c; then
  ac_cv_prog_lex_root=lexyy
else
  as_fn_error cannot find output from $LEX; giving up $LINENO 5
fi


and see what happens. We might find the build environment is broken in some 
other way, and flex is just a red herring.


Did you install 'flex' from source? Did you run any self-tests it may have? If 
not, I'd try both. It may be your flex is broken, and you do not know it.


Dave


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[sage-support] Strange behaviour of trig_expand

2010-02-02 Thread Nicolas
Here is some to-my-opinion strange behaviour of trig_expand :

#Declare real variables
var('a b c')
assume([a,'real'],[b,'real'],[c,'real'])
assumptions()
--- [a is real, b is real, c is real]

#Case 1
sin(a+b).trig_expand()
--- sin(a)*cos(b) + sin(b)*cos(a)

#Case 2
sin((a+b)/2).trig_expand()
--- sin(1/2*a)*cos(1/2*b) + sin(1/2*b)*cos(1/2*a)

#Case 3
sin((a+b)/c).trig_expand()
--- sin((a + b)/c)

#Case 4
sin((a/c+b/c)).trig_expand()


In case 3, the expansion is not done. I wonder if it would be possible
to do it. Obviously, if the sine argument was rational expanded before
trig expansion, it would work but none seem to work on the whole
expression.

Any idea ?

PS: I am actually using this in an expression where doing this
expansion would simplify a lot and I would have expected simplify_full
to see it... which it does not, I suspect because of this.
--- sin(a/c)*cos(b/c) + sin(b/c)*cos(a/c)

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[sage-support] Re: Strange behaviour of trig_expand

2010-02-02 Thread Nicolas
Oops, case  4 ended at the end of the message...

On 2 fév, 15:06, Nicolas nicolas.fresseng...@gmail.com wrote:
 Here is some to-my-opinion strange behaviour of trig_expand :

 #Declare real variables
 var('a b c')
 assume([a,'real'],[b,'real'],[c,'real'])
 assumptions()
 --- [a is real, b is real, c is real]

 #Case 1
 sin(a+b).trig_expand()
 --- sin(a)*cos(b) + sin(b)*cos(a)

 #Case 2
 sin((a+b)/2).trig_expand()
 --- sin(1/2*a)*cos(1/2*b) + sin(1/2*b)*cos(1/2*a)

 #Case 3
 sin((a+b)/c).trig_expand()
 --- sin((a + b)/c)

 #Case 4
 sin((a/c+b/c)).trig_expand()

 
 In case 3, the expansion is not done. I wonder if it would be possible
 to do it. Obviously, if the sine argument was rational expanded before
 trig expansion, it would work but none seem to work on the whole
 expression.

 Any idea ?

 PS: I am actually using this in an expression where doing this
 expansion would simplify a lot and I would have expected simplify_full
 to see it... which it does not, I suspect because of this.
 --- sin(a/c)*cos(b/c) + sin(b/c)*cos(a/c)

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[sage-support] Re: Strange behaviour of trig_expand

2010-02-02 Thread kcrisman
Dear Nicolas,

If you do

sage: a = sin((a+b)/c)
sage: a.trig_expand??

you will see the source code, which simply uses one of Maxima's
expansion routines, whose behavior should be documented on the Maxima
Sourceforge site.  My suspicion is that Maxima declines to expand this
because c might be zero, though there could be another reason.  We
have several Maxima experts who also read this list and might have
more detailed information, but this would be the first place I would
start.  One idea might be to apply another simplification/expansion to
whatever you feed into your trig functions, before you expand the
rest.


Good luck, and please follow up with more details, or specific
proposals for how we can improve our documentation to help make it
clearer how this works. Thank you!

- kcrisman

On Feb 2, 9:06 am, Nicolas nicolas.fresseng...@gmail.com wrote:
 Here is some to-my-opinion strange behaviour of trig_expand :

 #Declare real variables
 var('a b c')
 assume([a,'real'],[b,'real'],[c,'real'])
 assumptions()
 --- [a is real, b is real, c is real]

 #Case 1
 sin(a+b).trig_expand()
 --- sin(a)*cos(b) + sin(b)*cos(a)

 #Case 2
 sin((a+b)/2).trig_expand()
 --- sin(1/2*a)*cos(1/2*b) + sin(1/2*b)*cos(1/2*a)

 #Case 3
 sin((a+b)/c).trig_expand()
 --- sin((a + b)/c)

 #Case 4
 sin((a/c+b/c)).trig_expand()

 
 In case 3, the expansion is not done. I wonder if it would be possible
 to do it. Obviously, if the sine argument was rational expanded before
 trig expansion, it would work but none seem to work on the whole
 expression.

 Any idea ?

 PS: I am actually using this in an expression where doing this
 expansion would simplify a lot and I would have expected simplify_full
 to see it... which it does not, I suspect because of this.
 --- sin(a/c)*cos(b/c) + sin(b/c)*cos(a/c)

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[sage-support] Re: exponential and simplify

2010-02-02 Thread kcrisman


On Feb 1, 11:53 pm, Simon simonjty...@gmail.com wrote:
 Thank you both for your replies.
 It's interesting that in Andrej's examples, the e^x and exp(x) form do
 not yield the same result,
 since in maxima (which I know next to nothing about) we have
 (%i1) declare(m, integer);
 (%o1)                                done
 (%i2)  rectform(exp(2*m*%i*%pi));
 (%o2)                                  1
 (%i3)  rectform(%e^(2*m*%i*%pi));
 (%o3)                                  1

 Is this a problem with the sage conversion?
 Note these two different behaviours:

 sage: var('m'); assume(m, 'integer')
 m
 sage: e^(i*2*pi*m)._maxima_().rectform()
 e^(2*I*pi*m)
 sage: exp(i*2*pi*m)._maxima_().rectform()
 1

 but (this was tested in a new sage/maxima session)

 sage: var('m'); maxima('declare(m, integer)')
 m
 done
 sage: maxima(e^(i*2*pi*m)).rectform()
 1
 sage: maxima(exp(i*2*pi*m)).rectform()
 1

Interesting.  This might be due to the fact that _maxima_() uses the
calculus copy of Maxima (with certain standard assumptions we like
in Sage, such as domain being complex), while maxima(foo) just uses
vanilla Maxima.  This has arisen before, though I am not sure how many
people will read the documentation of maxima? before using it, and we
really do want to have the ability to launch a separate Maxima session
like this.

It is also possible that the Pynac representation of e^(i*2*pi*m)
differs from that of exp(i*2*pi*m) in such a way that _maxima_ would
address it differently with respect to the assumption, but that seems
less likely to me than the first possibility.  I apologize for not
being able to diagnose this better right now.

- kcrisman

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[sage-support] Re: Listing all k-minors of a matrix?

2010-02-02 Thread Jason Grout

On 02/02/2010 03:57 AM, Peter K.H. Gragert wrote:

Hi,
the second solution is indeed very nice.
I tested with
  A = Matrix(QQ, 2,3, [1,2,3,4,5,6]);A
giving:
[1 2 3]
[4 5 6]
res=[A[rows,cols] for cols in Combinations(A.ncols(),2) for rows in
Combinations(A.nrows(),2)];res


[[1 2]
[4 5], [1 3]
[4 6], [2 3]
[5 6]]

this is more or less my question this output is not really readable
though correct.
for i in range(len(res)):print res[i].det()

-3
-6
-3
A.minors(2)
[-3, -6, -3]

And some different, how do Ishow output easier, is HERE a possibility to
show a picture (screen capture) of sage-sheet?




You can upgrade your sage in order to take advantage of the nice 
printing you saw in our output:



sage: A = Matrix(QQ, 2,3, [1,2,3,4,5,6]);A
[1 2 3]
[4 5 6]
sage: res=[A[rows,cols] for cols in Combinations(A.ncols(),2) for rows 
in Combinations(A.nrows(),2)];res

[
[1 2]  [1 3]  [2 3]
[4 5], [4 6], [5 6]
]
sage: [det(m) for m in res]
[-3, -6, -3]

Thanks,

Jason


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[sage-support] Deleting Sage on Mac

2010-02-02 Thread kcrisman
Dear support,

Has anyone ever had the following problem on Mac?  I get this on both
PPC and Intel.

One has some Sage installations.  One builds/downloads new ones.  One
puts the old ones in the Trash, and then tries to Empty Trash.  Then
one gets a whole bunch of messages like:

The operation cannot be completed because the item libpari-gmp.dylib
is in use

Also for many .so files like real_lazy.so, and even python and sage-
sage. Note that in these cases Sage has not been in use for many hours
or even days, and the Terminal is closed.

I've deleted these now, so I can't reproduce it again, but it did
happen twice, which maybe counts.

Are there processes running in the background that never stop, even
after Sage is terminated?  I only know how to use top very naively, so
I didn't see any processes that seemed suspicious.  Anyway, if there
are, that would seem to be bad.

- kcrisman

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[sage-support] Re: Deleting Sage on Mac

2010-02-02 Thread kcrisman
Here is the result of ps, which I forgot about:

  PID  TT  STAT  TIME COMMAND
22503  p1  S  0:00.04 -bash
23320  p1- S  9:50.62 python /Users/.../sage-4.1.2.rc1.alpha3-copy/
local/bin/sage-cleaner
 5846  pb  Ss+0:00.03 bash /Users/.../sage-4.1.2.rc2/sage -python -
u
 5853  pb  S+ 0:00.04 bash /Users/.../sage-4.1.2.rc2/local/bin/
sage-sage -python -u
 5865  pb  S+ 0:00.09 python -u
 3113  pc  Ss+0:00.03 bash /Users/.../sage-4.1.2.rc1.alpha3-copy/
sage -python -u
 3120  pc  S+ 0:00.04 bash /Users/.../sage-4.1.2.rc1.alpha3-copy/
local/bin/sage-sage -python -u
 3144  pc  S+ 0:00.08 python -u
 5593  q0  Ss 0:00.03 bash /Users/.../sage-4.1.2.rc2/sage -twistd
--pidfile=tmpO_Yq8b/twistd.pid
 5600  q0  S  0:00.04 bash /Users/.../sage-4.1.2.rc2/local/bin/
sage-sage -twistd --pidfile=tmpO_
 5614  q0  S  0:07.65 python /Users/.../sage-4.1.2.rc2/local/bin/
twistd --pidfile=tmpO_Yq8b/twis
 2860  q1  Ss 0:00.03 bash /Users/.../sage-4.1.2.rc1.alpha3-copy/
sage -twistd --pidfile=tmpRsQnL
 2867  q1  S  0:00.04 bash /Users/.../sage-4.1.2.rc1.alpha3-copy/
local/bin/sage-sage -twistd --p
 2880  q1  S  0:07.93 python /Users/.../sage-4.1.2.rc1.alpha3-copy/
local/bin/twistd --pidfile=tm

Note again that on this computer, Sage hasn't been run (and, afaik,
was closed properly) in at least a week.  And certainly
sage-4.1.2.rc1/2 hadn't been run for months!  Maybe it was a problem
specific to those - or a bad termination of them?  In which case I
apologize for wasting bandwidth.  But if someone knows what I did
wrong, hopefully I can avoid doing it in the future, and maybe we can
put a check in for it if people are similarly unlucky.

- kcrisman

On Feb 2, 10:32 am, kcrisman kcris...@gmail.com wrote:
 Dear support,

 Has anyone ever had the following problem on Mac?  I get this on both
 PPC and Intel.

 One has some Sage installations.  One builds/downloads new ones.  One
 puts the old ones in the Trash, and then tries to Empty Trash.  Then
 one gets a whole bunch of messages like:

 The operation cannot be completed because the item libpari-gmp.dylib
 is in use

 Also for many .so files like real_lazy.so, and even python and sage-
 sage. Note that in these cases Sage has not been in use for many hours
 or even days, and the Terminal is closed.

 I've deleted these now, so I can't reproduce it again, but it did
 happen twice, which maybe counts.

 Are there processes running in the background that never stop, even
 after Sage is terminated?  I only know how to use top very naively, so
 I didn't see any processes that seemed suspicious.  Anyway, if there
 are, that would seem to be bad.

 - kcrisman

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Re: [sage-support] Profiling code in Sage

2010-02-02 Thread Minh Nguyen
Hi Robert,

On Tue, Feb 2, 2010 at 10:20 PM, Robert Bradshaw
rober...@math.washington.edu wrote:

SNIP

 Note, however, that code passed to prun is not preparsed.

Good point. I think this is tracked at ticket #2054

http://trac.sagemath.org/sage_trac/ticket/2054

-- 
Regards
Minh Van Nguyen

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[sage-support] Re: Strange behaviour of trig_expand

2010-02-02 Thread Nicolas
Thanks for your answer !

Following your idea, ny playing around in maxima, I found that :

trigreduce(sin((a+b)/c))
 sin(b/c+a/c)

Therefore
trigexpand(trigreduce(sin((a+b)/c)))
 cos(a/c)*sin(b/c)+sin(a/c)*cos(b/c)
Which is what is wanted

but I did not find any trigreduce in sage

Any idea how I can do that directly in sage ?


On 2 fév, 16:15, kcrisman kcris...@gmail.com wrote:
 Dear Nicolas,

 If you do

 sage: a = sin((a+b)/c)
 sage: a.trig_expand??

 you will see the source code, which simply uses one of Maxima's
 expansion routines, whose behavior should be documented on the Maxima
 Sourceforge site.  My suspicion is that Maxima declines to expand this
 because c might be zero, though there could be another reason.  We
 have several Maxima experts who also read this list and might have
 more detailed information, but this would be the first place I would
 start.  One idea might be to apply another simplification/expansion to
 whatever you feed into your trig functions, before you expand the
 rest.

 Good luck, and please follow up with more details, or specific
 proposals for how we can improve our documentation to help make it
 clearer how this works. Thank you!

 - kcrisman

 On Feb 2, 9:06 am, Nicolas nicolas.fresseng...@gmail.com wrote:

  Here is some to-my-opinion strange behaviour of trig_expand :

  #Declare real variables
  var('a b c')
  assume([a,'real'],[b,'real'],[c,'real'])
  assumptions()
  --- [a is real, b is real, c is real]

  #Case 1
  sin(a+b).trig_expand()
  --- sin(a)*cos(b) + sin(b)*cos(a)

  #Case 2
  sin((a+b)/2).trig_expand()
  --- sin(1/2*a)*cos(1/2*b) + sin(1/2*b)*cos(1/2*a)

  #Case 3
  sin((a+b)/c).trig_expand()
  --- sin((a + b)/c)

  #Case 4
  sin((a/c+b/c)).trig_expand()

  
  In case 3, the expansion is not done. I wonder if it would be possible
  to do it. Obviously, if the sine argument was rational expanded before
  trig expansion, it would work but none seem to work on the whole
  expression.

  Any idea ?

  PS: I am actually using this in an expression where doing this
  expansion would simplify a lot and I would have expected simplify_full
  to see it... which it does not, I suspect because of this.
  --- sin(a/c)*cos(b/c) + sin(b/c)*cos(a/c)

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[sage-support] failed to built sage-4.3.1 on fedora 11

2010-02-02 Thread ggrafendorfer
Hi,

I tried to built sage-4.3.1 on fedora 11 (amd phenom II X4),
when compiling pari a problem arised.

here are the relevant lines of install.log:

==
Shall we try to build pari 2.3.3 (released) now (y/n)? [n]
Ok. Type make install when you are ready
Bye !
Building and install PARI
make[2]: Entering directory `/scratch/bin/sage-4.3.1/spkg/build/
pari-2.3.3.p7/src'
Making gp in Olinux-x86_64
make[3]: Entering directory `/scratch/bin/sage-4.3.1/spkg/build/
pari-2.3.3.p7/src/Olinux-x86_64'
../config/genkernel ../src/kernel/x86_64/asm0.h  parilvl0.h
cat ../src/kernel/gmp/tune.h ../src/kernel/gmp/int.h ../src/kernel/
none/level1.h  parilvl1.h
cat parilvl0.h parilvl1.h  pariinl.h
gcc  -c -O1 -Wall -fno-strict-aliasing -fomit-frame-pointer-I. -
I../src/headers -I../src/language -I/scratch/bin/sage-4.3.1/local/
include -o gp.o ../src/gp/gp.c
cd ../src/desc  /usr/bin/perl merge_822 ../functions/*/*  def-linux-
x86_64-4090.tmp
mv ../src/desc/def-linux-x86_64-4090.tmp ../src/desc/pari.desc
cd ../src/desc  /usr/bin/perl gen_proto gp pari.desc  gp_init-linux-
x86_64-4090.tmp
mv ../src/desc/gp_init-linux-x86_64-4090.tmp ../src/gp/gp_init.h
gcc  -c -O1 -Wall -fno-strict-aliasing -fomit-frame-pointer-I. -
I../src/headers -I../src/graph -o gp_init.o ../src/gp/gp_init.c
gcc  -c -O1 -Wall -fno-strict-aliasing -fomit-frame-pointer-I. -
I../src/headers -I../src/language -I/scratch/bin/sage-4.3.1/local/
include -o gp_rl.o ../src/gp/gp_rl.c
cd ../src/desc  /usr/bin/perl gen_proto highlevel pari.desc 
highlvl-linux-x86_64-4090.tmp
mv ../src/desc/highlvl-linux-x86_64-4090.tmp ../src/gp/highlvl.h
gcc  -c -O1 -Wall -fno-strict-aliasing -fomit-frame-pointer-I. -
I../src/headers -DDL_DFLT_NAME=NULL -o highlvl.o ../src/gp/highlvl.c
gcc  -c -O1 -Wall -fno-strict-aliasing -fomit-frame-pointer-I. -
I../src/headers -o whatnow.o ../src/gp/whatnow.c
gcc  -c -O1 -Wall -fno-strict-aliasing -fomit-frame-pointer-I. -
I../src/headers -I../src/graph -o plotport.o ../src/graph/plotport.c
g++ -c -O1 -Wall -fno-strict-aliasing -fomit-frame-pointer-I. -I../
src/headers -I/usr/local/include  -o plotfltk.o ../src/graph/
plotfltk.c
../src/graph/plotfltk.c:27:19: error: FL/Fl.H: No such file or
directory
../src/graph/plotfltk.c:28:26: error: FL/Fl_Window.H: No such file or
directory
../src/graph/plotfltk.c:29:24: error: FL/fl_draw.H: No such file or
directory
../src/graph/plotfltk.c:31: error: expected class-name before '{'
token
../src/graph/plotfltk.c:45: error: 'Fl_Color' does not name a type
../src/graph/plotfltk.c:48: error: 'Fl_Color' does not name a type
../src/graph/plotfltk.c: In constructor 'Plotter::Plotter(long int*,
long int*, long int*, long int, const char*)':
../src/graph/plotfltk.c:56: error: class 'Plotter' does not have any
field named 'Fl_Window'
../src/graph/plotfltk.c:60: error: 'color' was not declared in this
scope
../src/graph/plotfltk.c:60: error: 'FL_WHITE' was not declared in this
scope
../src/graph/plotfltk.c:61: error: 'FL_BLACK' was not declared in this
scope
../src/graph/plotfltk.c:62: error: 'FL_BLUE' was not declared in this
scope
../src/graph/plotfltk.c:63: error: 'rgb_color' was not declared in
this scope
../src/graph/plotfltk.c:64: error: 'FL_RED' was not declared in this
scope
../src/graph/plotfltk.c:65: error: 'FL_GREEN' was not declared in this
scope
../src/graph/plotfltk.c: In function 'void DrawPoint(void*, long int,
long int)':
../src/graph/plotfltk.c:73: error: 'fl_point' was not declared in this
scope
../src/graph/plotfltk.c: In function 'void DrawLine(void*, long int,
long int, long int, long int)':
../src/graph/plotfltk.c:79: error: 'fl_line' was not declared in this
scope
../src/graph/plotfltk.c: In function 'void DrawRectangle(void*, long
int, long int, long int, long int)':
../src/graph/plotfltk.c:85: error: 'fl_rect' was not declared in this
scope
../src/graph/plotfltk.c: In function 'void DrawPoints(void*, long int,
plot_points*)':
../src/graph/plotfltk.c:92: error: 'fl_point' was not declared in this
scope
../src/graph/plotfltk.c: In function 'void SetForeground(void*, long
int)':
../src/graph/plotfltk.c:97: error: 'Fl_Color' was not declared in this
scope
../src/graph/plotfltk.c:97: error: 'color' was not declared in this
scope
../src/graph/plotfltk.c:97: error: expected primary-expression before
')' token
../src/graph/plotfltk.c:97: error: expected ';' before 'data'
../src/graph/plotfltk.c:98: error: 'fl_color' was not declared in this
scope
../src/graph/plotfltk.c: In function 'void DrawLines(void*, long int,
plot_points*)':
../src/graph/plotfltk.c:105: error: 'fl_line' was not declared in this
scope
../src/graph/plotfltk.c: In function 'void DrawString(void*, long int,
long int, char*, long int)':
../src/graph/plotfltk.c:111: error: 'fl_draw' was not declared in this
scope
../src/graph/plotfltk.c: In member function 'void Plotter::draw()':
../src/graph/plotfltk.c:118: error: 'class Plotter' has no 

[sage-support] Re: Strange behaviour of trig_expand

2010-02-02 Thread andrejv
On Feb 2, 3:06 pm, Nicolas nicolas.fresseng...@gmail.com wrote:
 Here is some to-my-opinion strange behaviour of trig_expand :

 #Declare real variables
 var('a b c')
 assume([a,'real'],[b,'real'],[c,'real'])
 assumptions()
 --- [a is real, b is real, c is real]

 #Case 1
 sin(a+b).trig_expand()
 --- sin(a)*cos(b) + sin(b)*cos(a)

 #Case 2
 sin((a+b)/2).trig_expand()
 --- sin(1/2*a)*cos(1/2*b) + sin(1/2*b)*cos(1/2*a)

 #Case 3
 sin((a+b)/c).trig_expand()
 --- sin((a + b)/c)

 #Case 4
 sin((a/c+b/c)).trig_expand()

 
 In case 3, the expansion is not done. I wonder if it would be possible
 to do it. Obviously, if the sine argument was rational expanded before
 trig expansion, it would work but none seem to work on the whole
 expression.

 Any idea ?

 PS: I am actually using this in an expression where doing this
 expansion would simplify a lot and I would have expected simplify_full
 to see it... which it does not, I suspect because of this.
 --- sin(a/c)*cos(b/c) + sin(b/c)*cos(a/c)

Sage will expand (x+y)/2 into x/2 + y/2, so trig_expand does what you
expect. But it leaves (x+y)/a as (x+y)/a, so trig_expand does not
change it.

sage: sin((x+y)/2)
sin(1/2*x + 1/2*y)
sage: sin((x+y)/2).trig_expand()
sin(1/2*x)*cos(1/2*y) + sin(1/2*y)*cos(1/2*x)
sage: sin((x+y)/a)
sin((x + y)/a)
sage: sin((x+y)/a).trig_expand()
sin((x + y)/a)

I don't know how to change sin((x+y)/a) to sin(x/a + y/a) in Sage,
maybe someone else can help you with that.

HTH, Andrej

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[sage-support] Re: Cannot run Sage

2010-02-02 Thread Drini


On Jan 30, 7:06 am, Alex Ghitza aghi...@gmail.com wrote:
 On Sat, 30 Jan 2010 18:01:45 +1100, Alex Ghitza aghi...@gmail.com wrote:

  I will make a new binary distribution and upload it somewhere, and I'll
  send you the link when that's done.

 It's basically done; I am getting it compressed with lzma right now, so
 it should be ready in about 30 minutes, and available at

 http://sage.math.washington.edu/home/ghitza/sage-archlinux-32bit-4.3

 Best,
 Alex



Is it still up? If not, a fix is available somewhere? I just ran into
this problem (arch 32bit also) today

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[sage-support] How to contour_plot piecewise defined function?

2010-02-02 Thread Eugene Goldberg
Hi!

I've got a few functions like this:

f1(x,y)=sin(x)+cos(y)
f2(x,y)=sin(y)+cos(x)

and I need to plot counter graphics like:

contour_plot(lambda x,y:f1(x,y),(x,0,3),(y,0,14))+contour_plot(lambda
x,y:f2(x,y),(x,3,6),(y,0,14))

can i do this easily using piecewise function?

g=Piecewise([ [(0,3),f1], [(3,6),f2] ])

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Re: [sage-support] failed to built sage-4.3.1 on fedora 11

2010-02-02 Thread Minh Nguyen
Hi Georg,

On Wed, Feb 3, 2010 at 4:10 AM, ggrafendorfer
georg.grafendor...@gmail.com wrote:

SNIP

 ../src/graph/plotfltk.c:193: error: 'class Plotter' has no member
 named 'show'
 ../src/graph/plotfltk.c:194: error: 'Fl' has not been declared
 make[3]: *** [plotfltk.o] Error 1
 make[3]: Leaving directory `/scratch/bin/sage-4.3.1/spkg/build/

The pari spkg specifically uses the option --graphic=none to configure
pari 2.3.3. However, that option is ignored in this case. The upshot
is that pari should not be configured to use graphics libraries. The
library fltk is one of them.


 I'm not experienced with fedora, can anybody tell me which package is
 missing and should be installed, or whatever is going on here.

Ticket #7979 [1] is tracking the issue. The ticket has an updated
spkg. A workaround is to delete the following pari package on your
system

SAGE_ROOT/spkg/standard/pari-2.3.3.p7.spkg

Then download the updated spkg at #7979 and put the updated spkg under

SAGE_ROOT/spkg/standard/

This should replace the previous version .p7 of the pari spkg. Then
from SAGE_ROOT, run make again to resume the compilation of Sage. Hope
that helps.


[1] http://trac.sagemath.org/sage_trac/ticket/7979

-- 
Regards
Minh Van Nguyen

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Re: [sage-support] Profiling code in Sage

2010-02-02 Thread Mike Hansen
On Tue, Feb 2, 2010 at 7:50 AM, Minh Nguyen nguyenmi...@gmail.com wrote:
 Hi Robert,
 Note, however, that code passed to prun is not preparsed.

 Good point. I think this is tracked at ticket #2054

 http://trac.sagemath.org/sage_trac/ticket/2054

I've put a patch up which fixes this by doing something similar to #797.

--Mike

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[sage-support] Re: Strange behaviour of trig_expand

2010-02-02 Thread ma...@mendelu.cz
On 2 ún, 18:11, andrejv andrej.vodopi...@gmail.com wrote:

 I don't know how to change sin((x+y)/a) to sin(x/a + y/a) in Sage,
 maybe someone else can help you with that.

This is expand from Maxima
sage: sin((a+b)/c)._maxima_().expand().sage()
sin(a/c + b/c)

Robert

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[sage-support] orthogonal subspace?

2010-02-02 Thread VictorMiller
I can't find a method for a vector space (or perhaps a subspace of a
vector space) for orthogonal subspace.  Since vector space seem to
be equipped with an inner product this seems like a natural function
to have.  Am I missing something?  If not, I vote that it should be
added.

Victor

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[sage-support] Re: Strange behaviour of trig_expand

2010-02-02 Thread ma...@mendelu.cz


On 2 ún, 17:38, Nicolas nicolas.fresseng...@gmail.com wrote:
 Thanks for your answer !

 Following your idea, ny playing around in maxima, I found that :

 trigreduce(sin((a+b)/c))
  sin(b/c+a/c)

 Therefore
 trigexpand(trigreduce(sin((a+b)/c)))
  cos(a/c)*sin(b/c)+sin(a/c)*cos(b/c)
 Which is what is wanted

 but I did not find any trigreduce in sage

 Any idea how I can do that directly in sage ?


sage: sin((a+b)/c)._maxima_().trigreduce().trigexpand().sage()
sin(a/c)*cos(b/c) + sin(b/c)*cos(a/c)
sage: sin((a+b)/c)._maxima_().expand().trigexpand().sage()
sin(a/c)*cos(b/c) + sin(b/c)*cos(a/c)


btw: I attemepted to include trigreduce by 
http://trac.sagemath.org/sage_trac/ticket/7334
. However, there was an idea not to add new functions to Sage, but
rewrite simpification rules in Sage. See the discussion attached to
trac 7334 and the link to sage-devel:
http://groups.google.cz/group/sage-devel/browse_thread/thread/3899a578da747009
and look forward to Sage 4.3 :)

Robert

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Re: [sage-support] orthogonal subspace?

2010-02-02 Thread Mike Hansen
Hello,

On Tue, Feb 2, 2010 at 12:08 PM, VictorMiller victorsmil...@gmail.com wrote:
 I can't find a method for a vector space (or perhaps a subspace of a
 vector space) for orthogonal subspace.  Since vector space seem to
 be equipped with an inner product this seems like a natural function
 to have.  Am I missing something?  If not, I vote that it should be
 added.

This is http://trac.sagemath.org/sage_trac/ticket/7522.  I think some
work was done on it a few weeks ago, but I'm not sure what the current
status is.

--Mike

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Re: [sage-support] Re: Cannot run Sage

2010-02-02 Thread Alex Ghitza
On Tue, 2 Feb 2010 09:16:52 -0800 (PST), Drini pdsanc...@gmail.com wrote:
 
 Is it still up? If not, a fix is available somewhere? I just ran into
 this problem (arch 32bit also) today
 

Yes, try

http://modular.math.jmu.edu/linux/32bit/sage-4.3.1-fat-archlinux-i686-Linux.tar.lzma

(Other mirrors might have it as well by now.)


Best,
Alex

-- 
Alex Ghitza -- Lecturer in Mathematics -- The University of Melbourne
-- Australia -- http://www.ms.unimelb.edu.au/~aghitza/

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[sage-support] Fwd: using sage -tp vs testall

2010-02-02 Thread Minh Nguyen
Hi folks,

The following forwarded message is from someone who wasn't able to
directly send to this list.

-- 
Regards
Minh Van Nguyen


-- Forwarded message --
From: ross k ros...@gmail.com
Date: Wed, Feb 3, 2010 at 8:40 AM
Subject: Fwd: using sage -tp vs testall
To: Minh Nguyen nguyenmi...@gmail.com


Minh

Sorry to send this to you directly.
Tried sending this to sage-devel but I think I need to request
membership before I can post there

all the best
Ross
-- Forwarded message --
From: ross k ros...@gmail.com
Date: Wed, Feb 3, 2010 at 7:50 AM
Subject: using sage -tp vs testall
To: sage-de...@googlegroups.com


Hi

The thrust of this post is how do I use sage -tp properly...

I just got access to a new machine (Not sure at the moment but its
either 4 or 8 core).

Id like to do the equivalent to sage -testall using sage -tp
Is the equivalent command sage -long -optional?
(When I looked at sage -advanced, in the description of -testall,
theres mention of testing examples as well, but not in the description
of -tp)
How do I do ALL the tests using -tp and if I have say a 4 core machine
what options do I pass to -tp

In particular, how do I work out how many threads to use?

Finally if I re-run the tests that fail in parallel but pass
non-parallel (as mentioned in included email below), should I
consider them as passed or report them?

Despite the multiple questions, Im really just asking, how do I use
sage -tp properly...

Hope this makes sense and was the right forum

Ross


 Hi Alex,

 On Mon, Feb 1, 2010 at 11:54 PM, Alex Ghitza aghi...@gmail.com wrote:

 SNIP

   The following tests failed:
          sage -t  -long devel/sage/sage/parallel/decorate.py # Segfault
 
   This only seems to happen when I run the whole testsuite.  If I try to
   run this test on its own, it always passes.  (I had the same issue in
   alpha0.)  It could just be something that only comes up under stress --
   I was testing things in parallel with 16 threads.  Anyway, I don't
   think we can do much about it right now.

 The above failure often comes up when performing parallel doctests on
 mod.math. I have seen it many times during the Sage 4.3.2 release
 milestone. However, when it is run by itself, not part of a parallel
 doctest of the whole Sage library, it would pass. Sometimes it would
 also pass during a parallel doctest on mod.math.

 --
 Regards
 Minh Van Nguyen

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[sage-support] Re: using sage -tp vs testall

2010-02-02 Thread Minh Nguyen
Hi Ross,

On Wed, Feb 3, 2010 at 8:50 AM, Minh Nguyen nguyenmi...@gmail.com wrote:

SNIP

 The thrust of this post is how do I use sage -tp properly...

See the Developers' Guide, especially the sections Parallel testing
many modules [1] and Parallel testing the whole Sage library [2].


 Id like to do the equivalent to sage -testall using sage -tp
 Is the equivalent command sage -long -optional?

Not quite. The option -testall is equivalent to doctesting the whole
Sage library and standard documentation using -t. So if you want to
do

./sage -testall

you could issue the following equivalent command:

./sage -t devel/sage-main/

You can think of them as synonymous with each other. The incantation
./sage -testall is much shorter than explicitly specifying the the
main branch of your Sage installation.


 How do I do ALL the tests using -tp and if I have say a 4 core machine
 what options do I pass to -tp

If you want to use 4 threads for parallel doctesting, you could do

./sage -tp 4 devel/sage-main/

or replace devel/sage-main/ with the directory to you want to perform
parallel doctest on. For example, the command

./sage -tp 4 devel/sage-main/sage

only performs parallel doctest on the whole Sage library. See the
chapter Parallel Testing the Sage Library [3] of the Developers'
Guide for more information.


 In particular, how do I work out how many threads to use?

On a multiuser system such as a machine within the Sage cluster, I
often use about a quarter of the total number of cores on that
machine. This allows other developers to run parallel build/doctests.
The number of threads to use for parallel doctesting depends on your
machine (and how nice you want to be :-).


 Finally if I re-run the tests that fail in parallel but pass
 non-parallel (as mentioned in included email below), should I
 consider them as passed or report them?

Please report such situations.


 Despite the multiple questions, Im really just asking, how do I use
 sage -tp properly...

The Developers' Guide has a chapter on parallel doctesting. In any
case, don't hesitate to ask if it doesn't make sense or lacks
clarification.


[1] 
http://www.sagemath.org/doc/developer/doctesting.html#parallel-testing-many-modules

[2] 
http://www.sagemath.org/doc/developer/doctesting.html#parallel-testing-the-whole-sage-library

[3] http://www.sagemath.org/doc/developer/doctesting.html

-- 
Regards
Minh Van Nguyen

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[sage-support] Re: Cannot run Sage

2010-02-02 Thread Harald Schilly
On Feb 2, 10:01 pm, Alex Ghitza aghi...@gmail.com wrote:
 (Other mirrors might have it as well by now.)

I'm afraid, no. They have shut down the master server more than a day
ago, I don't know what has happened ... :(

H

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Re: [sage-support] How to contour_plot piecewise defined function?

2010-02-02 Thread David Joyner
I personally don't see how off the top of my head, but if
you figure out a way to do it, please post it!

Maybe reading to source code of Piecewise and/or contour_plot
might help?


On Tue, Feb 2, 2010 at 1:00 PM, Eugene Goldberg omegat...@gmail.com wrote:
 Hi!

 I've got a few functions like this:

 f1(x,y)=sin(x)+cos(y)
 f2(x,y)=sin(y)+cos(x)

 and I need to plot counter graphics like:

 contour_plot(lambda x,y:f1(x,y),(x,0,3),(y,0,14))+contour_plot(lambda
 x,y:f2(x,y),(x,3,6),(y,0,14))

 can i do this easily using piecewise function?

 g=Piecewise([ [(0,3),f1], [(3,6),f2] ])

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[sage-support] Re: can't build SAGE 4.3.1 for linux-powerpc32

2010-02-02 Thread Douglas Mencken
Dave, thank you for reply!
Building flex from source solved this issue. So it is definitely the
problem with Fedora repos.
And sorry for your time.

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[sage-support] Re: Strange behaviour of trig_expand

2010-02-02 Thread kcrisman


On Feb 2, 3:10 pm, ma...@mendelu.cz ma...@mendelu.cz wrote:
 On 2 ún, 17:38, Nicolas nicolas.fresseng...@gmail.com wrote:



  Thanks for your answer !

  Following your idea, ny playing around in maxima, I found that :

  trigreduce(sin((a+b)/c))
   sin(b/c+a/c)

  Therefore
  trigexpand(trigreduce(sin((a+b)/c)))
   cos(a/c)*sin(b/c)+sin(a/c)*cos(b/c)
  Which is what is wanted

  but I did not find any trigreduce in sage

  Any idea how I can do that directly in sage ?

 sage: sin((a+b)/c)._maxima_().trigreduce().trigexpand().sage()
 sin(a/c)*cos(b/c) + sin(b/c)*cos(a/c)
 sage: sin((a+b)/c)._maxima_().expand().trigexpand().sage()
 sin(a/c)*cos(b/c) + sin(b/c)*cos(a/c)

 btw: I attemepted to include trigreduce 
 byhttp://trac.sagemath.org/sage_trac/ticket/7334
 . However, there was an idea not to add new functions to Sage, but
 rewrite simpification rules in Sage. See the discussion attached to
 trac 7334 and the link to 
 sage-devel:http://groups.google.cz/group/sage-devel/browse_thread/thread/3899a57...
 and look forward to Sage 4.3 :)

This is another reason for us not to get all finicky about structure,
but just add the functionality.  If we wait for someone to
recategorize simplification/expansion (or to write it natively in
Sage), problems like this will keep showing up.  The philosophy of
Sage was to do it, not to wait for perfection, I think.

Sorry for being grumpy, but this has come up many times in the few
months since we last had this discussion.

- kcrisman

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[sage-support] Re: orthogonal subspace?

2010-02-02 Thread kcrisman


On Feb 2, 3:23 pm, Mike Hansen mhan...@gmail.com wrote:
 Hello,

 On Tue, Feb 2, 2010 at 12:08 PM, VictorMiller victorsmil...@gmail.com wrote:
  I can't find a method for a vector space (or perhaps a subspace of a
  vector space) for orthogonal subspace.  Since vector space seem to
  be equipped with an inner product this seems like a natural function
  to have.  Am I missing something?  If not, I vote that it should be
  added.

 This ishttp://trac.sagemath.org/sage_trac/ticket/7522.  I think some
 work was done on it a few weeks ago, but I'm not sure what the current
 status is.


You are right that it is natural to have!  This ticket just needs to
be turned into a documented patch.  Neither Jason nor I have had time
to do this, but as you can see one could do it by hand for now, and
hopefully someone will do it properly soon.  Apologies (at least to
myself) for not having done so myself by now.

- kcrisman

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[sage-support] openMPI and MPI4PY?

2010-02-02 Thread calcpage

Are openMPI and MPI4PY included in the SAGE distribution?

I see MPI4PY mentioned here:
http://www.sagemath.org/doc/numerical_sage/mpi4py.html

Also, this blog
http://www.sagemath.org/doc/numerical_sage/mpi4py.html
says that openMPI is included when you install SAGE.

I don't see how that's possible as I just spent several days trying to 
figure out how to setup openMPI on my cluster.  Between setting up 
public key ssh authentication and torque servers, it was not trivial.


TIA,
A. Jorge Garcia
http://calcpage.tripod.com

Teacher  Professor
Applied Mathematics, Physics  Computer Science
Baldwin Senior High School  Nassau Community College


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Re: [sage-support] Re: sage blog

2010-02-02 Thread calcpage
All I know is this is my feed:

http://calcpage.tripod.com/shadowfax/rss.xml

does that help?

HTH,
A. Jorge Garcia
http://calcpage.tripod.com

Teacher  Professor
Applied Mathematics, Physics  Computer Science
Baldwin Senior High School  Nassau Community College



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[sage-support] how to cast finite field elements into p-adic ring

2010-02-02 Thread dmharvey
Hi,

After I create the residue field of a p-adic ring, how do I cast
elements of the field back into the ring? Any lift is fine. The
obvious thing doesn't work:

sage: R.z = Zq(9)
sage: F = R.residue_class_field()
sage: F
Finite Field in z0 of size 3^2
sage: a = F.gen()
sage: R(a)
---
TypeError



Also, is it possible to change the name of the generator of the
residue field?

david

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Re: [sage-support] openMPI and MPI4PY?

2010-02-02 Thread Minh Nguyen
Hi,

On Wed, Feb 3, 2010 at 1:36 PM,  calcp...@aol.com wrote:
 Are openMPI and MPI4PY included in the SAGE distribution?

No. Both Open MPI and mpi4py are not part of the Sage standard
repository. For what's available in the repository of standard
packages, see the page for standard spkg's [1]. However, if you want
to use Open MPI and mpi4py, they are available as optional spkg's [2].


 I see MPI4PY mentioned here:
 http://www.sagemath.org/doc/numerical_sage/mpi4py.html

 Also, this blog
 http://www.sagemath.org/doc/numerical_sage/mpi4py.html
 says that openMPI is included when you install SAGE.

 I don't see how that's possible as I just spent several days trying to
 figure out how to setup openMPI on my cluster.

The numerical guide [3] is rather outdated. No one has yet volunteered
to update/rewrite it.


[1] http://www.sagemath.org/packages/standard/

[2] http://www.sagemath.org/packages/optional/

[3] http://www.sagemath.org/doc/numerical_sage/

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Regards
Minh Van Nguyen

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Re: [sage-support] Re: sage blog

2010-02-02 Thread Minh Nguyen
Hi,

On Wed, Feb 3, 2010 at 1:50 PM,  calcp...@aol.com wrote:
 All I know is this is my feed:

 http://calcpage.tripod.com/shadowfax/rss.xml

 does that help?

That actually feeds every update from your blog to an aggregator.
People who subscribe to Planet Sage often do so for Sage specific
posts. To aggregate any update from a blog, regardless of whether it's
Sage specific or otherwise, would really annoy subscribers.

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Regards
Minh Van Nguyen

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[sage-support] Text Editor for Sage

2010-02-02 Thread Georges
Hi All,

I'm new to Sage/Sun VirtualBox (Windows Vista x64).  I can open sage:
prompt, Sage Notebook (Firefox icon), no problem.  I'm trying to
work on some programming (Sage Tutorials Release 4.3.1, Chapter 5).
The question I have is how do I create/open/edit a sage file.  Is
there a simple text editor, like Window's notepad that I can use to
write the code.

For example, the tutorial suggests that I create a file called
example.sage with the following content:

print Hello World
print 2^2

I can't figure out how to complete this task.  I tried right clicking
on the VirtualBox desktop and select Create from Template, then
Empty File.  It'll let me create a file called example.sage.
Double clicking on it opens a window telling me that I should
associate it with some application which I don't have (So far, I only
see Firefox Web Browser, Orage, and Sun Java 6 Web Start).  I tried to
find example.sage in Windows, by searching for it, but that yield no
result.

So do I need another application, like another .ovf file for text
editing?

Please help,

Thank you!

Georges

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[sage-support] Re: how to cast finite field elements into p-adic ring

2010-02-02 Thread Rado
Something seems to be broken in extensions of p-adics. Here are two
examples:

sage: R.z = Zq(9)
sage: R.residue_system()

TypeError: cannot convert x to a p-adic element

and

sage: el=R.random_element()
sage: el.slice(el.valuation(),el.valuation()+1)

TypeError:
'sage.rings.padics.padic_ZZ_pX_CA_element.pAdicZZpXCAElement' object
cannot be interpreted as an index

Otherwise I saw there is a parameter res_name to be passed to
constructor:

sage: R.z = Zq(9,res_name=x)

but then x is not really bound to anything.

sage: x*3
3*x

Sorry, can't be of much help. Even this trick didn't work

sage: R2.z = Zq(9,1)
sage: R(z)
NotImplementedError: Conversion from different p-adic extensions not
yet supported

Rado

On Feb 2, 9:04 pm, dmharvey dmhar...@cims.nyu.edu wrote:
 Hi,

 After I create the residue field of a p-adic ring, how do I cast
 elements of the field back into the ring? Any lift is fine. The
 obvious thing doesn't work:

 sage: R.z = Zq(9)
 sage: F = R.residue_class_field()
 sage: F
 Finite Field in z0 of size 3^2
 sage: a = F.gen()
 sage: R(a)
 ---
 TypeError

 

 Also, is it possible to change the name of the generator of the
 residue field?

 david

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