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{SECT 0 {EXCHG {PARA 203 "" 0 "" {TEXT 210 61 "Introduction to the DR \+
(Dixon Projection / Resultant) Package" }}{PARA 205 "" 0 "" {TEXT 206 
25 "(C) 2007 Manfred Minimair" }}{PARA 209 "" 0 "" {TEXT -1 0 "" }}
{PARA 209 "" 0 "" {TEXT 200 11 "Description" }}{PARA 209 "" 0 "" 
{TEXT 207 207 "This package provides the function RProject which compu
tes the Dixon projection of a list of multivariate polynomials. The fu
nction implements Kapur/Saxena/Yang's approach (see D. Kapur, T. Saxen
a, L. Yang, " }{TEXT 256 56 "Algebraic and Geometric Reasoning Using D
ixon Resultants" }{TEXT 207 110 ". International Symposium on Symbolic
 and Algebraic Computation (ISSAC), July 1994, Oxford University, Engl
and" }{TEXT 207 2 ")." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 
"" {TEXT -1 144 "The package uses code written by Arthur Chtcherba for
 constructing Dixon matrices and by Hoon Hong for computing determinan
ts of maximal minors." }}{PARA 209 "" 0 "" {TEXT -1 0 "" }}{PARA 209 "
" 0 "" {TEXT 200 16 "Calling Sequence" }}{PARA 208 "" 0 "" {TEXT 208 
31 "DR:-DProject(polylist, varlist)" }}{PARA 208 "" 0 "" {TEXT 208 31 
"DR[DProject](polylist, varlist)" }}{PARA 208 "" 0 "" {TEXT 208 27 "DP
roject(polylist, varlist)" }}{PARA 209 "" 0 "" {TEXT -1 0 "" }}{PARA 
209 "" 0 "" {TEXT 200 10 "Parameters" }}{PARA 208 "" 0 "" {TEXT 208 
49 "polylist     - list of (multivariate) polynomials" }}{PARA 208 "" 
0 "" {TEXT 208 64 "varlist       - list of variables of the polynomial
s in polylist" }}{PARA 209 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 19 "infolevel[DR] := 2;" }}{PARA 0 "" 0 "" {TEXT -1 73 "cause
s the package to print some progress information for the computation" 
}}{PARA 209 "" 0 "" {TEXT -1 0 "" }}{PARA 209 "" 0 "" {TEXT 200 8 "Exa
mples" }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 204 14 "read \"dr.mpl
\";" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#DRG`6)%1DResDetRankMinorG%-D
ResMaxMinorG%)DProjectG%-DetRankMinorG%)MaxMinorG%2InstantiateMatrixG%
&DixonGb6#%+thismoduleG6$%-IsNonZeroRowG%6PermutationFromMatrixG6\"6)%
1DResDetRankMinorG%-DResMaxMinorG%)DProjectG%-DetRankMinorG%)MaxMinorG
%2InstantiateMatrixG%&DixonGF4F4F4F4%,_m151407548G6$%-IsNonZeroRowG%6P
ermutationFromMatrixG" }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 204 
45 "f1 := randpoly([x1,x2,p1,p2],dense,degree=2);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#f1G,>\"##)!\"\"*&\"\"(\"\"\")%#x1G\"\"#F*F'*(\"#AF*F
,F*%#x2GF*F**(\"#bF*F,F*%#p1GF*F'*(\"#%*F*F,F*%#p2GF*F'*&\"#()F*F,F*F*
*&\"#cF*)F0F-F*F'*(\"#iF*F0F*F6F*F'*&\"#(*F*F0F*F**&\"#tF*)F3F-F*F'*(
\"\"%F*F3F*F6F*F'*&\"#$)F*F3F*F'*&\"#5F*)F6F-F*F'*&F=F*F6F*F*" }}}
{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 204 45 "f2 := randpoly([x1,x2,p1
,p2],dense,degree=1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#f2G,,\"#v!
\"\"*&\"#!)\"\"\"%#x1GF*F**&\"#WF*%#x2GF*F'*&\"#rF*%#p1GF*F**&\"#<F*%#
p2GF*F'" }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 204 45 "f3 := randpo
ly([x1,x2,p1,p2],dense,degree=3);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>
%#f3G,bo\"#&*\"\"\"**\"#vF'%#x1GF'%#x2GF'%#p1GF'F'**\"#sF'F*F'F,F'%#p2
GF'F'*&\"#WF'F*F'F'*&\"#\\F'F+F'!\"\"*&\"#5F'F,F'F4*&\"#xF'F/F'F'*(\"
\"'F'F*F'F+F'F'*(\"#PF'F*F'F,F'F'*(\"#()F'F*F'F/F'F'*(\"#HF'F+F'F,F'F4
*(\"#6F'F+F'F/F'F'*(\"#oF'F,F'F/F'F'*&\"#]F')F*\"\"#F'F4*&F6F')F+FHF'F
'*&\"#\")F')F,FHF'F4*&\"#^F')F/FHF'F4*(\"\"(F'FGF'F+F'F4*(\"#SF'FGF'F,
F'F4*(\"#UF'FGF'F/F'F'*(\"#BF'F*F'FJF'F'*(\"#uF'F*F'FMF'F'*(FXF'F*F'FP
F'F4*(\"#)*F'FJF'F,F'F'*(FXF'FJF'F/F'F4*(\"#hF'F+F'FMF'F4*(F&F'F+F'FPF
'F'*(FTF'FMF'F/F'F'*(\"#\"*F'F,F'FPF'F'**\"##*F'F*F'F+F'F/F'F4**\"\")F
'F+F'F,F'F/F'F4*&F6F')F*\"\"$F'F4*&F@F')F+FeoF'F'*&\"#ZF')F,FeoF'F4*&
\"#JF')F/FeoF'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "infolev
el[DR] := 2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%*infolevelG6#%#DRG
\"\"#" }}}{EXCHG {PARA 209 "> " 0 "" {MPLTEXT 1 204 33 "DR:-DProject([
f1,f2,f3],[x1,x2]);" }}{PARA 6 "" 1 "" {TEXT -1 52 "DResDetRankMinor: \+
Dixon matrix of size 9 x 9 set up." }}{PARA 6 "" 1 "" {TEXT -1 51 "  D
etRankMinor: Working on column 1................" }}{PARA 6 "" 1 "" 
{TEXT -1 51 "  DetRankMinor: Working on column 2................" }}
{PARA 6 "" 1 "" {TEXT -1 51 "  DetRankMinor: Working on column 3......
.........." }}{PARA 6 "" 1 "" {TEXT -1 51 "  DetRankMinor: Working on \+
column 4................" }}{PARA 6 "" 1 "" {TEXT -1 51 "  DetRankMino
r: Working on column 5................" }}{PARA 6 "" 1 "" {TEXT -1 51 
"  DetRankMinor: Working on column 6................" }}{PARA 6 "" 1 "
" {TEXT -1 51 "  DetRankMinor: Working on column 7................" }}
{PARA 6 "" 1 "" {TEXT -1 51 "  DetRankMinor: Working on column 8......
.........." }}{PARA 6 "" 1 "" {TEXT -1 51 "  DetRankMinor: Working on \+
column 9................" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,Z*&\"F+?z
PA13J1=WRSy&)[UJ\"\"\"\"%#p1GF&F&*&\"E+?22W6$\\S:'G3;4o&*3gF&%#p2GF&F&
*(\"F+?F1zj\"o)p#)yI\"*pV#er;F&F'F&F*F&!\"\"*&\"E++w$)=`>%[faxSM'*o<H%
F&)F'\"\"#F&F&*&\"F+!oRf-#yw<!zl&\\^U]0s$F&)F*F1F&F&*(\"F+?&f+s-I\"GNY
!=bIu%oC$F&F0F&F*F&F&*(\"F++%=0.*oF(ecQ'3\"3\"=I)[F&F'F&F4F&F-*&\"F+!3
'3D(fh?J&GT1emuSl\"F&)F'\"\"$F&F-*&\"F+?v-C(Qb!Hw29;5&*y\"fkF&)F*F<F&F
-*&\"F++SW.UCunF/'G9iwY7TF&)F'\"\"%F&F-*&\"F+?fg'f#>Z>-D,&y)*Gt7LF&)F*
FCF&F&*(\"F+gpD(e$opqItl%)p6YRb\"F&F;F&F*F&F&*(\"E+!)oQ9(etpk^o;S!Rb/&
*F&F0F&F4F&F-*(\"F++/N.47$\\zb6UF51f%=*F&F'F&F?F&F&*(\"F+S1ks2*epVvD9f
8n/]@F&F0F&F?F&F-*(\"F+!)[RG1M0_Me+&f%4v1$>F&F;F&F4F&F&*(\"F+?&Rj>&ep'
p<J]D1+J)*pF&FBF&F*F&F&*(\"F+!oVTye*Ha'y>6(zOrJJ'F&F'F&FFF&F-*(\"F+!39
\\``0:_([3X6t+fU#F&FBF&F4F&F-*(\"F+?2j-nYdRmC*4k:q%Gg\"F&)F'\"\"&F&F*F
&F&*(\"F+![;f!Q+]%*4G]L7,^GM\"F&)F*FZF&F'F&F&*(\"E+?z2c(f8Vxh6rZ[TN@)F
&FFF&F0F&F&*(\"E+g,Qu,N%\\c!46!Q+apI(F&F;F&F?F&F-*&\"F+!)oMT6SIV,RY3&)
R!*e*HF&FYF&F-*&\"E++kk^-*z$H_!p^&z$p_Z(F&FgnF&F-*&\"E+S#=h]\"z)Q=Mt1d
lIn;#F&)F'\"\"'F&F-*&\"D+S]j45(GRm1mK<.8r5F&)F*FcoF&F-\"E+SAy@,9pk,%G(
o'e<m&*)F-" }}}{EXCHG }{EXCHG }{EXCHG {PARA 209 "" 0 "" {TEXT 200 21 "
Additional procedures" }}{PARA 209 "" 0 "" {TEXT 208 385 "The package \+
also exports the procedurs DResDetRankMinor and DResDetMaxMinor. By de
fault DProject is DResDetRankMinor. The function DResDetMaxMinor has t
he same calling sequence as DResDetRankMinor. It computes the determin
ant of a maximal minor by using the determinant function from the Line
arAlgebra package, whereas DResDetRankMinor uses a customized Gaussian
 elimination procedure." }}}}{MARK "9 0 0" 2 }{VIEWOPTS 1 1 0 1 1 
1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }