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ier" 1 10 255 0 255 1 2 2 2 2 2 1 1 1 3 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 
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1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 1323 "Procedure SINGULARlink provides an interface between Maple an
d Singular for the purpose of computing Groebner basis in Singular and
 returning result back to Maple. It has been succsessfully tested with
 Maple 8, 9, 9.5, and 10; and Singular 2-3-1 and 3-1-0. It can be easi
ly modified for the use of other commands in Singular than \"std\" and
 \"groebner\". \n\nProcedure SINGULARlink uses the following input arg
uments:\n\nSINGULARlink(Id,C,tord,elimorder,input_for_Singular,input_f
or_Maple,wait);\nSINGULARlink(Id,C,tord,elimorder,input_for_Singular,i
nput_for_Maple,wait,'p');\n\n- Id                             - type \+
\"list(polynom)\" - a list of polynomials [f1, f2,..., fn] that genera
te ideal Id, that is, Id = <f1, f2, ..., fn>.\n- C                    \+
          - type \"nonnegint\" - non negative characteristic for the g
round field of polynomial coefficients, set 0 for the rationals\n- tor
d                           - type \"symbol\" - one of total orders us
ed by Singular: lp, dp, Dp, ls, ds, Ds\n- elimorder                   \+
- type \"list\" - list of polynomial variables that are to be eliminat
ed in the order in which they appear in the list. This list must be id
entical to the list of polynomial variables. \n- input_for_Singular   \+
   - type \"string\" - path to a directory where input file In.txt for
 Singular will be written to" }}{PARA 0 "" 0 "" {TEXT -1 1820 "- input
_for_Maple        - type \"string\" - path to a directory where output
 file Out.txt from Singular for Maple will be written to\n- wait      \+
                     - type \"nonnegint\" or \"symbol\" - when used wi
th a positive integer it will pass on that integer to \"groebner(Id,wa
it)\" as its wait parameter; when used as symbol 'infty', procedure   \+
                                                                      \+
                                          \"groebner(Id)\" will be inv
oked\n'p'                                - (optional) type symbol 'd' \+
- for saving files to the disk; 't' for displaying In.txt to the termi
nal only (see examples below)\n\nComments:\n\n1. Global variable \"dir
pathSexe\" must be defined (see below) with a path to Singular.exe (ve
rsion 2-3-1) or to bash.exe (version 3-1-0) to execute Singular.\n2. T
he transfer directories \"input_for_Singular\" and \"input_for_Maple\"
 need not be the same. If either one does not exist, it will be create
d. These directories are not automatically deleted when Singular is fi
nished computing unless appropriate lines system(cat(\"rm -r  \",pathS
)); and system(cat(\"rm -r  \",pathM)); are unremarked. Be VERY CAREFU
L when you unremark these lines as you may accidently delete directori
es you wanted to keep!\n3. The eighth parameter 'p' is optional and ca
n only take values 't' and 'd'. When 't' is used, the input script for
 Singular is displayed to the terminal only: No transfer directory is \+
created and nothing is written to the hard disk. When 'd' is used, the
 input file In.txt is created, written to the hard disk, then Singular
 is invoked to execute it and write its output as file Out.txt. Then, \+
Out.txt file is read in and displayed to the terminal/screen. When thi
s parameter is not used, the procedure behaves like if it were used wi
th the parameter 'd'." }}{PARA 0 "" 0 "" {TEXT -1 333 "4.The output of
 this procedure is the Groebner basis returned by Singular's \"groebne
r\" command. One can easily use \"std\" command instead.  \n5. Some er
ror messaging is built in.\n6. No warranties of any kind can be made. \+
Permission is granted to use this procedure and modify it at will, alt
hough I would appreciate an acknowledgment. " }}{PARA 0 "" 0 "" {TEXT 
-1 288 "7. A complete interface module allowing a Maple user to use ot
her command  from Singular could easily be written.\n\nRafal Ablamowic
z\nDepartment of Mathematics\nTennessee Technological University\nCook
eville, TN 38501\nEmail: rablamowicz@tntech.edu\nTel: (931) 372-3569\n
Fax: (931) 372-6353\n   \n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 406 "dirpathSexe:=\"C:/cygwin/usr/local/Singular
/2-0-3/ix86-Win/Singular.exe\": #VERSION 2-3-1\ndirpathSexe:=\"C:/cygw
in/bin/bash -l C:/cygwin/bin/Singular\";             #VERSION 3-1-0\ni
nput_for_Singular:=\"C:/cygwin/home/Singular\";\ninput_for_Maple:=\"C:
/Maple8\";\ntransfer_directoryM:=\"C:/transferM\":\ntransfer_directory
S:=\"C:/transferS\":\ninput_for_Maple:=transfer_directoryM;\ninput_for
_Singular:=transfer_directoryS;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%,dirpathSexeGQMC:/cygwin/bin/bash~-l~C:/cygwin/bin/Singular6\"" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%3input_for_SingularGQ8C:/cygwin/home
/Singular6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%0input_for_MapleGQ*C
:/Maple86\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%0input_for_MapleGQ-C:
/transferM6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%3input_for_Singular
GQ-C:/transferS6\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 11238 "SINGULARlink:=\nproc(Id::list(polynom),C::nonneg
int,tord::symbol,elimorder::list,\ninput_for_Singular::string,input_fo
r_Maple::string,wait::\{nonnegint,symbol\}) \nlocal i,j,pathS,pathS2,p
athM,pathM2,vars,varsfound,F,p,ele,s,N,pathS_filename,\n      pathM_fi
lename,executeinputfile,first,line,last,fseq,dirpathSexeloc,direction;
\nglobal dirpathSexe;\n###############################################
####################################################################\n
#Input arguments are as follows:\n#Id   - a list with polynomials that
 are to generate ideal Id\n#C    - non negative characteristic for the
 ground field of polynomial coefficients, set 0 for the rationals\n#el
imorder = list with elimination order\n#tord - total order accepted by
 Singular: \n#       lp = lex order \n#       dp = degrevlex order \n#
       Dp = deglex order\n#       ls = negative lex order\n#       ds \+
= negative degree reverse lex order\n#       Ds = negative degree lex \+
order\n#input_for_Singular - path where input file In.txt for Singular
 will be saved by Maple\n#input_for_Maple    - path where input file O
ut.txt for Maple will be saved by Singular\n#wait - number of seconds \+
Singular will compute at most or 'infty' for infinite number of second
s\n###################################################################
################################################\nif not member(tord,
\{lp,dp,Dp,ls,ds,Ds\}) then\n   error `third argument total order must
 be one of lp, dp, Dp, ls, ds, or Ds`\nend if;\n######################
######################################################################
########\nF:=map(expand,Id);\nvarsfound:=sort(convert(indets(F),list))
;\nvars:=elimorder;\nN:=nops(vars):\nif nops(varsfound)<>N then \n   e
rror `number of variables found in polynomials is different from the n
umber of variables in elimination list` end if;\nif convert(varsfound,
set) minus convert(vars,set) <> \{\} then \n   error `extra variables \+
found in polynomials that do not appear in elimination list`\nend if;
\nif convert(vars,set) minus convert(varsfound,set) <> \{\} then \n   \+
error `extra variables found in elimination list that do not appear in
 polynomials`\nend if;\n##############################################
#######################################################\nif C>0 then p
:=C else p:=0 end if; #reassigning C to p\n###########################
######################################################################
####\n#Path and filename where input file for Singular will be saved t
o\n###################################################################
##################################\npathS:=input_for_Singular;        \+
    #path where input file In.txt for Singular will be saved\npathS_fi
lename:=cat(pathS,\"/In.txt\"); #path w/filename where input file for \+
Singular will be saved\n##############################################
#######################################################\npathM:=input_
for_Maple;               #path where input file Out.txt for Maple will
 be saved\npathM_filename:=cat(pathM,\"/Out.txt\");#path w/filename wh
ere input file for Maple will be saved\n##############################
######################################################################
#\ndirection:=0:\nif nargs=8 then direction:=args[nargs] end if; #swit
ch for error messages\n###############################################
######################################################\n#Changing the \+
name of the input_for_Maple directory so that it could be created, if \+
needed:\nif SearchText(\"C:/\",pathM)=0 then pathM2:=pathM \nelif\n   \+
SearchText(\"C:/\",pathM)=1 then pathM2:=cat(\"C:\\\\\",substring(path
M,4..-1)); #directory to create\nelse error `write directory to create
 for Maple input as, for example, \"C:/transferM\" `\nend if:\n#######
######################################################################
#######################\n#Changing the name of the input_for_Singular \+
directory so that it could be created, if needed:\nif SearchText(\"C:/
\",pathS)=0 then pathS2:=pathS \nelif\n   SearchText(\"C:/\",pathS)=1 \+
then pathS2:=cat(\"C:\\\\\",substring(pathS,4..-1)); #directory to cre
ate\nelse error `write directory to create for Singular as, for exampl
e, \"C:/transferS\" `\nend if:\n######################################
######################################################################
##\n#NOTE: If you don't like these messages to appear, remark the next
 fourteen lines.\nif direction='d' or direction=0 then\n   if system(c
at(\"mkdir \",pathM2))=0 then\n      print(`Transfer directory for Map
le has been made ... proceeding... waiting for Singular results...`)\n
   else\n      print(`Transfer directory for Maple already exists... p
roceeding... waiting for Singular results...`)\n   end if;\n   if syst
em(cat(\"mkdir \",pathS2))=0 then\n      print(`Transfer directory for
 Singular has been made ... proceeding... waiting for Singular results
...`)\n   else\n      print(`Transfer directory for Singular already e
xists... proceeding... waiting for Singular results...`)\n   end if;\n
elif direction='t' then\n     print(`Trying to create and display inpu
t file for Singular... proceeding...`)\nend if;\n#####################
######################################################################
####################\n#Produce input file for Singular ...\n##########
######################################################################
############################### \nif nargs=8 then \n   if evalb(args[n
args]='t') then writeto(terminal) elif\n      evalb(args[nargs]='d') t
hen writeto(pathS_filename) else \n      error `last optional argument
 needs to be 't' (for displaying to terminal) or 'd' (for saving to di
sk)`\n   end if;\nelse writeto(pathS_filename) #redirect Maple output \+
to input file for Singular as default\nend if:\n######################
######################################################################
####################\n# Define the ring (with term order)\n###########
####################################\nprintf(`ring R =`);\nprintf(cat(
` `,p,`,`));\ns:=cat(`(`,seq(cat(vars[i],`,`),i=1..(N-1)),vars[N],`)`)
;\nprintf(\"%Q\",s);\nprintf(`,`);\nprintf(\"%q\",tord);\nprintf(\"%A
\\n\",`;`);\n###############################################\n# Define
 the ideal . . . \n###############################################\npr
intf(\"%Q\\n\",`ideal I =`) ; \nfor i to nops(F) do\nele:=F[i];\nif ty
pe(ele,monomial) then \n   printf(\"%A\\n\",ele);\n   printf(\"%A\\n\"
,`,`);\nelse # split into summands, otherwise line might get chopped! \+
\n   printf(\"%A\\n\",op(1,ele)); \n   for j from 2 to nops(ele) do\n \+
      printf(\"%A %A\\n\",`+`,op(j,ele)) \n   end do;\nif i < nops(F) \+
then printf(\"%A\\n\",`,`) end if;\nend if\nend do; \nprintf(\"%A\\n\"
,`;`);\n###############################################\n# Now prepare
 input file for Singular . . . \n#####################################
##########\nprintf(\"%Q\\n\",`short=0;`);\n###########################
########################\n#options:\n#################################
##################\nprintf(\"%Q\\n\",`option(redSB);`);\n#############
######################################\nif evalb(wait='infty') then \n
   printf(\"%Q\\n\",`ideal J = groebner(I);`); #unremark this line if \+
you want to use groebner command\n   #printf(\"%Q\\n\",`ideal J = std(
I);`);     #unremark this line if you want to use std command\nelse\n \+
  printf(\"%Q\",`int wait=`);\n   printf(\"%Q\",wait);\n   printf(\"%A
\\n\",`;`);\n   printf(\"%Q\\n\",`ideal J = groebner(I,wait);`); \nend
 if;\ns:=cat(\"\\\":w \",pathM_filename,\"\\\"\",`,`,\"J\");\ns:=cat(`
write(`,s,`);`);\nprintf(\"%A\\n\",s);\nprintf(\"%Q\\n\",`quit;`); #qu
it Singular when finished\n###########################################
#########\n# Finished writing input file for Singular\n###############
#####################################\nwriteto(terminal); #redirect Ma
ple output to terminal\n##############################################
###########################\n## Call Singular and execute its input fi
le if direction <> 't' ...\n##########################################
###############################\nif direction='t' then return NULL end
 if;\nif assigned(dirpathSexe) then\n   dirpathSexeloc:=dirpathSexe: #
assign global path to Singular.exe\n   else\n   ######################
#######################################\n   #try a standard path under
 a typical Windows installation\n   ##################################
##########################################\n   #For version 2-3-1 use:
   \n   dirpathSexeloc:=\"C:/cygwin/usr/local/Singular/2-0-3/ix86-Win/
Singular.exe\":\n   ##################################################
##########################\n   #For version 3-1-0 use:\n   dirpathSexe
loc:=\"C:/cygwin/bin/bash -l C:/cygwin/bin/Singular\":         \nend i
f;\n##################################################################
#######\nexecuteinputfile:=cat(dirpathSexeloc,\" < \", pathS_filename)
;\nsystem(executeinputfile);\nif %<>0 then\n   #######################
######################################################################
#\n   #If you want to delete pathS directory in case of the error, unr
emark the following line but \n   #BE CAREFUL WHAT YOU DELETE as you m
ay need this directory for checking file In.txt:\n   #system(cat(\"rm \+
-r \",pathS)); ##to remove the directory pathS: BE CAREFUL!!!!\n   ###
######################################################################
#####################\n   error `something went wrong while executing \+
Singular:\ncould not find a path on your system to Singular.exe. The p
ath must be \nassigned to a global variable dirpathSexe, for example,
\ndirpathSexe:=\"C:/cygwin/usr/local/Singular/2-0-3/ix86-Win/Singular.
exe\": for version 2-3-1, or\ndirpathSexe:=\"C:/cygwin/bin/bash -l C:/
cygwin/bin/Singular\" for version 3-1-0` \nfi;\n######################
######################################################\n# Retrieve res
ults from Out.txt created by Singular line by line as strings\n#######
#####################################################################
\n#read(pathM_filename); #this DOES NOT work yet due to [] in Out.txt
\n####################################################################
########\nfirst := readline(pathM_filename);\nline := readline(pathM_f
ilename);\nwhile line <> 0 do\n   last := line;\n   line := readline(p
athM_filename)\nend do;\n#############################################
###############################\nfseq:=parse(first); #changing text in
put from Singular into Maple algebraic\n##############################
############################################## \nF:=[fseq];\nif F=[] t
hen \n   print(`Singular has not returned any results... increase 'wai
t' time or make it 'infty'`)\nend if;\n###############################
##########################################################\n#If you wa
nt to delete pathS directory, unremark the following line but BE CAREF
UL \n#WHAT YOU DELETE as you may need this directory for checking file
 In.txt:\n####system(cat(\"rm -r  \",pathS)); #To remove pathS directo
ry: BE CAREFUL WHAT YOU DELETE!\n#####################################
####################################################\n################
######################################################################
###\n#If you want to delete pathM directory, unremark the following li
ne but BE CAREFUL \n#WHAT YOU DELETE as you may need this directory fo
r checking file Out.txt:\n####system(cat(\"rm -r  \",pathM)); #To remo
ve pathM directory: BE CAREFUL WHAT YOU DELETE!\n#####################
####################################################################\n
F:=map(expand,F);\nreturn F; \nend proc:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 251 "Example 1: T
o test option 't' in the above procedure. When used with option  't', \+
the procedure outputs the In.txt file containing input for Singular to
 the terminal/screen. It does not write it to the hard disk not it inv
okes Singular to execute it:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 136 "f:=2*x^10+4*x^9;\ng:=4*y-8-x;\nh:=f*g^2+z^4;\nk:=-5*x^10+x^9*
z^2;\nL:=map(expand,[f,g]);\nvars:=sort(convert(indets(L),list));\nN:=
nops(vars);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,&*&\"\"#\"\"\")%
\"xG\"#5F(F(*&\"\"%F()F*\"\"*F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%\"gG,(*&\"\"%\"\"\"%\"yGF(F(\"\")!\"\"%\"xGF+" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%\"hG,&*&,&*&\"\"#\"\"\")%\"xG\"#5F*F**&\"\"%F*)F,\"\"
*F*F*F*),(*&F/F*%\"yGF*F*\"\")!\"\"F,F7F)F*F**$)%\"zGF/F*F*" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"kG,&*&\"\"&\"\"\")%\"xG\"#5F(!\"\"*&)F*
\"\"*F()%\"zG\"\"#F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG7$,&*&
\"\"#\"\"\")%\"xG\"#5F)F)*&\"\"%F))F+\"\"*F)F),(*&F.F)%\"yGF)F)\"\")!
\"\"F+F5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%varsG7$%\"xG%\"yG" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG\"\"#" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 82 "SINGULARlink([f,g,h],0,lp,[x,y,z],input_for_Singul
ar,input_for_Maple,'infty','t');" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%`oTrying~to~create~an
d~display~input~file~for~Singular...~proceeding...G" }}{PARA 6 "" 1 "
" {TEXT -1 22 "ring R = 0,(x,y,z),lp;" }}{PARA 6 "" 1 "" {TEXT -1 9 "i
deal I =" }}{PARA 6 "" 1 "" {TEXT -1 6 "2*x^10" }}{PARA 6 "" 1 "" 
{TEXT -1 7 "+ 4*x^9" }}{PARA 6 "" 1 "" {TEXT -1 1 "," }}{PARA 6 "" 1 "
" {TEXT -1 3 "4*y" }}{PARA 6 "" 1 "" {TEXT -1 4 "+ -8" }}{PARA 6 "" 1 
"" {TEXT -1 4 "+ -x" }}{PARA 6 "" 1 "" {TEXT -1 1 "," }}{PARA 6 "" 1 "
" {TEXT -1 11 "32*x^10*y^2" }}{PARA 6 "" 1 "" {TEXT -1 13 "+ -160*x^10
*y" }}{PARA 6 "" 1 "" {TEXT -1 12 "+ -16*x^11*y" }}{PARA 6 "" 1 "" 
{TEXT -1 10 "+ 192*x^10" }}{PARA 6 "" 1 "" {TEXT -1 9 "+ 36*x^11" }}
{PARA 6 "" 1 "" {TEXT -1 8 "+ 2*x^12" }}{PARA 6 "" 1 "" {TEXT -1 12 "+
 64*x^9*y^2" }}{PARA 6 "" 1 "" {TEXT -1 12 "+ -256*x^9*y" }}{PARA 6 "
" 1 "" {TEXT -1 9 "+ 256*x^9" }}{PARA 6 "" 1 "" {TEXT -1 5 "+ z^4" }}
{PARA 6 "" 1 "" {TEXT -1 1 ";" }}{PARA 6 "" 1 "" {TEXT -1 8 "short=0;
" }}{PARA 6 "" 1 "" {TEXT -1 14 "option(redSB);" }}{PARA 6 "" 1 "" 
{TEXT -1 22 "ideal J = groebner(I);" }}{PARA 6 "" 1 "" {TEXT -1 35 "wr
ite(\":w C:/transferM/Out.txt\",J);" }}{PARA 6 "" 1 "" {TEXT -1 5 "qui
t;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 332 "Example 2: To test option 'd' in the above proced
ure. When used with option  'd', the procedure creates and saves file \+
In.txt file containing input for Singular to the hard disk, it then in
vokes Singular to execute it and write its output file Out.txt for Map
le, and then reads and displays the file Out.txt to the terminal/scree
n:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 136 "f:=2*x^10+4*x^9;\n
g:=4*y-8-x;\nh:=f*g^2+z^4;\nk:=-5*x^10+x^9*z^2;\nL:=map(expand,[f,g]);
\nvars:=sort(convert(indets(L),list));\nN:=nops(vars);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%\"fG,&*&\"\"#\"\"\")%\"xG\"#5F(F(*&\"\"%F()F*\"
\"*F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gG,(*&\"\"%\"\"\"%\"yGF
(F(\"\")!\"\"%\"xGF+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hG,&*&,&*&
\"\"#\"\"\")%\"xG\"#5F*F**&\"\"%F*)F,\"\"*F*F*F*),(*&F/F*%\"yGF*F*\"\"
)!\"\"F,F7F)F*F**$)%\"zGF/F*F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"
kG,&*&\"\"&\"\"\")%\"xG\"#5F(!\"\"*&)F*\"\"*F()%\"zG\"\"#F(F(" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG7$,&*&\"\"#\"\"\")%\"xG\"#5F)F)*
&\"\"%F))F+\"\"*F)F),(*&F.F)%\"yGF)F)\"\")!\"\"F+F5" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%%varsG7$%\"xG%\"yG" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%\"NG\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "SINGULARl
ink([f,g,h],0,dp,[x,y,z],input_for_Singular,input_for_Maple,'infty','d
');" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%gpTransfer~dire
ctory~for~Maple~already~exists...~proceeding...~waiting~for~Singular~r
esults...G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%jpTransfer~directory~fo
r~Singular~already~exists...~proceeding...~waiting~for~Singular~result
s...G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%,(%\"xG\"\"\"*&\"\"%F&%\"yG
F&!\"\"\"\")F&*$)%\"zGF(F&,8*&\"\"#F&)F)\"#5F&F&*&\"#RF&)F)\"\"*F&F**&
\"$U$F&)F)F+F&F&*&\"%w<F&)F)\"\"(F&F**&\"%[gF&)F)\"\"'F&F&*&\"&7T\"F&)
F)\"\"&F&F**&\"&[G#F&)F)F(F&F&*&\"&W`#F&)F)\"\"$F&F**&\"&K%=F&)F)F1F&F
&*&\"%OzF&F)F&F*\"%O:F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "
SINGULARlink([f,g,h],0,dp,[z,y,x],input_for_Singular,input_for_Maple,'
infty');" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%gpTransfer~directory~for~
Maple~already~exists...~proceeding...~waiting~for~Singular~results...G
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%jpTransfer~directory~for~Singular
~already~exists...~proceeding...~waiting~for~Singular~results...G" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#7%,(*&\"\"%\"\"\"%\"yGF'F'\"\")!\"\"%
\"xGF**$)%\"zGF&F',&*$)F+\"#5F'F'*&\"\"#F')F+\"\"*F'F'" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "SINGULARlink([f,g,h],0,lp,[z,y,x],i
nput_for_Singular,input_for_Maple,30);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#%gpTransfer~directory~for~Maple~already~exists...~proceeding...~
waiting~for~Singular~results...G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%j
pTransfer~directory~for~Singular~already~exists...~proceeding...~waiti
ng~for~Singular~results...G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7%,&*$)
%\"xG\"#5\"\"\"F)*&\"\"#F))F'\"\"*F)F),(*&\"\"%F)%\"yGF)F)\"\")!\"\"F'
F3*$)%\"zGF0F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "Example 3. Testing some error mess
ages:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "SINGULARlink([f,g,
h],0,LP,[z,y,x],input_for_Singular,input_for_Maple,30);" }}{PARA 8 "" 
1 "" {TEXT -1 93 "Error, (in SINGULARlink) third argument total order \+
must be one of lp, dp, Dp, ls, ds, or Ds\n" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 73 "SINGULARlink([f,g,h],0,lp,[z,y,X],input_for_Singula
r,input_for_Maple,30);" }}{PARA 8 "" 1 "" {TEXT -1 101 "Error, (in SIN
GULARlink) extra variables found in polynomials that do not appear in \+
elimination list\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "SINGU
LARlink([f,g,h],0,lp,[z,y,x],input_for_Singular,input_for_Maple,'infty
','p');" }}{PARA 8 "" 1 "" {TEXT -1 121 "Error, (in SINGULARlink) last
 optional argument needs to be 't' (for displaying to terminal) or 'd'
 (for saving to disk)\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "
SINGULARlink([f,g,h],-1,lp,[z,y,x],input_for_Singular,input_for_Maple,
30);" }}{PARA 8 "" 1 "" {TEXT -1 105 "Error, invalid input: SINGULARli
nk expects its 2nd argument, C, to be of type nonnegint, but received \+
-1\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 
"" 0 "" {TEXT -1 34 "End\n\nCookeville, December 21, 2005" }}}}{MARK "
25 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 
1 }