version 1.35, 2004/09/14 03:12:17 |
version 1.36, 2004/09/14 05:49:36 |
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% $OpenXM: OpenXM/src/kan96xx/Doc/ecart.sm1,v 1.34 2004/09/13 11:24:10 takayama Exp $ |
% $OpenXM: OpenXM/src/kan96xx/Doc/ecart.sm1,v 1.35 2004/09/14 03:12:17 takayama Exp $ |
(hol_loaded) boundp { } |
(hol_loaded) boundp { } |
{ [(parse) (hol.sm1) pushfile] extension } ifelse |
{ [(parse) (hol.sm1) pushfile] extension } ifelse |
%[(parse) (appell.sm1) pushfile] extension |
%[(parse) (appell.sm1) pushfile] extension |
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/ecartd.gb.oxRingStructure [[ ] [ ] ] def |
/ecartd.gb.oxRingStructure [[ ] [ ] ] def |
/ecart.partialEcartGlobalVarX [ ] def |
/ecart.partialEcartGlobalVarX [ ] def |
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/ecart.gb.verbose 1 def |
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/ecart.message.quiet 0 def |
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/ecartd.begin { |
/ecartd.begin { |
ecart.begin |
ecart.begin |
[(EcartAutomaticHomogenization) 1] system_variable |
[(EcartAutomaticHomogenization) 1] system_variable |
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[(EcartAutomaticHomogenization) 0] system_variable |
[(EcartAutomaticHomogenization) 0] system_variable |
} def |
} def |
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/ecart.message.quiet 0 def |
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/ecart.message { |
/ecart.message { |
ecart.message.quiet { pop } { message } ifelse |
ecart.message.quiet { pop } { message } ifelse |
} def |
} def |
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} for |
} for |
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ecart.gb.verbose { |
ecart.gb.verbose { |
(ecart.setOpt:) message |
(ecart.setOpt:) ecart.message |
(degreeShift=) messagen degreeShift message |
(degreeShift=) ecart.messagen degreeShift ecart.message |
$hdShift(startingShift)=$ messagen hdShift message |
$hdShift(startingShift)=$ ecart.messagen hdShift ecart.message |
(sugar=) messagen ecart.useSugar message |
(sugar=) ecart.messagen ecart.useSugar ecart.message |
(Other options=) messagen ans message |
(Other options=) ecart.messagen ans ecart.message |
} { } ifelse |
} { } ifelse |
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/arg1 ans def |
/arg1 ans def |
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( not to dehomogenize and homogenize) |
( not to dehomogenize and homogenize) |
]] putUsages |
]] putUsages |
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/ecart.gb.verbose 1 def |
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%ecarth.gb s(H)-homogenized outputs. GG's original version of ecart gb. |
%ecarth.gb s(H)-homogenized outputs. GG's original version of ecart gb. |
/ecarth.gb { |
/ecarth.gb { |
/arg1 set |
/arg1 set |
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[(KanGBmessage) ecart.gb.verbose ] system_variable |
[(KanGBmessage) ecart.gb.verbose ] system_variable |
$ecartd.gb dehomogenizes at each reduction step w.r.t. s (H).$ ecart.message |
$ecartd.gb dehomogenizes at each reduction step w.r.t. s (H).$ ecart.message |
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%%% Start of the preprocess |
%%% Start of the preprocess |
v tag RingP eq { |
v tag RingP eq { |
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vv {toString} map /vv set |
vv {toString} map /vv set |
vvGlobal isArray |
vvGlobal isArray |
{ } { [vvGlobal to_records pop] /vvGlobal set } ifelse |
{ } { [vvGlobal to_records pop] /vvGlobal set } ifelse |
vvGlobal {toString} map /vv set |
vvGlobal {toString} map /vvGlobal set |
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vv vvGlobal setMinus /vv set |
vv vvGlobal setMinus /vv set |
vv { /tt set [@@@.Dsymbol tt] cat } map /dd set |
vv { /tt set [@@@.Dsymbol tt] cat } map /dd set |
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vv { /tt set [@@@.Dsymbol tt] cat } map /dvv set |
vv { /tt set [@@@.Dsymbol tt] cat } map /dvv set |
dvv { 1 } map /wv1 set |
dvv { 1 } map /wv1 set |
vv { -1 } map dvv { 1 } map join /wv2 set |
vv { -1 } map dvv { 1 } map join /wv2 set |
/arg1 [wv1 wv2 ] def |
vv length 0 eq { |
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/arg1 [ ] def |
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} { |
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/arg1 [wv1 wv2 ] def |
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} ifelse |
] pop |
] pop |
popVariables |
popVariables |
arg1 |
arg1 |
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[/in-ecartd.isSameIdeal_h /aa /ii /jj /iigg /jjgg /vv /ans /k /n /f |
[/in-ecartd.isSameIdeal_h /aa /ii /jj /iigg /jjgg /vv /ans /k /n /f |
/ecartd.isSameIdeal_h.opt |
/ecartd.isSameIdeal_h.opt |
/save-ecart.autoHomogenize /wv /save-ecart.message.quiet |
/save-ecart.autoHomogenize /wv /save-ecart.message.quiet |
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/vvGlobal /rng |
] pushVariables |
] pushVariables |
[(CurrentRingp) (Homogenize_vec)] pushEnv |
[(CurrentRingp) (Homogenize_vec)] pushEnv |
[ |
[ |
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gb.verbose { (Getting in ecartd.isSameIdeal_h) message } { } ifelse |
gb.verbose { (Getting in ecartd.isSameIdeal_h) message } { } ifelse |
%% comparison of hilbert series has not yet been implemented. |
%% comparison of hilbert series has not yet been implemented. |
/save-ecart.message.quiet ecart.message.quiet def |
/save-ecart.message.quiet ecart.message.quiet def |
aa length 3 eq { } |
aa length 3 eq , aa length 4 eq , or { } |
{ ([ii jj vv] ecartd.isSameIdeal_h) error } ifelse |
{ ([ii jj vv] ecartd.isSameIdeal_h) error } ifelse |
/ii aa 0 get def |
/ii aa 0 get def |
/jj aa 1 get def |
/jj aa 1 get def |
/vv aa 2 get def |
/vv aa 2 get def |
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aa length 4 eq { |
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/vvGlobal aa 3 get def |
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vvGlobal isString { [vvGlobal to_records pop] /vvGlobal set } |
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{ vvGlobal { toString } map /vvGlobal set } ifelse |
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} { /vvGlobal [ ] def } ifelse |
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ii length 0 eq jj length 0 eq and |
ii length 0 eq jj length 0 eq and |
{ /ans 1 def /LLL.ecartd.isSame_h goto } { } ifelse |
{ /ans 1 def /LLL.ecartd.isSame_h goto } { } ifelse |
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vv ecart.stdOrder /wv set |
[vv vvGlobal] ecart.stdBlockOrder /wv set |
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vvGlobal length 0 eq { |
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/rng [vv wv ] def |
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}{ |
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/rng [vv wv [(partialEcartGlobalVarX) vvGlobal]] def |
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} ifelse |
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/save-ecart.autoHomogenize ecart.autoHomogenize def |
/save-ecart.autoHomogenize ecart.autoHomogenize def |
/ecart.autoHomogenize 0 def |
/ecart.autoHomogenize 0 def |
[ii vv wv] ecartd.gb /iigg set |
[ii] rng join ecartd.gb /iigg set |
[jj vv wv] ecartd.gb /jjgg set |
[jj] rng join ecartd.gb /jjgg set |
save-ecart.autoHomogenize /ecart.autoHomogenize set |
save-ecart.autoHomogenize /ecart.autoHomogenize set |
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iigg getRing ring_def |
iigg getRing ring_def |
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0 1 n 1 sub { |
0 1 n 1 sub { |
/k set |
/k set |
iigg k get |
iigg k get |
[jjgg vv wv] ecartd.reduction 0 get |
[jjgg] ecartd.reduction 0 get |
(0). eq not { /ans 0 def /LLL.ecartd.isSame_h goto} { } ifelse |
(0). eq not { /ans 0 def /LLL.ecartd.isSame_h goto} { } ifelse |
gb.verbose { (o) messagen } { } ifelse |
gb.verbose { (o) messagen } { } ifelse |
} for |
} for |
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0 1 n 1 sub { |
0 1 n 1 sub { |
/k set |
/k set |
jjgg k get |
jjgg k get |
[iigg vv wv] ecartd.reduction 0 get |
[iigg] ecartd.reduction 0 get |
(0). eq not { /ans 0 def /LLL.ecartd.isSame_h goto} { } ifelse |
(0). eq not { /ans 0 def /LLL.ecartd.isSame_h goto} { } ifelse |
gb.verbose { (o) messagen } { } ifelse |
gb.verbose { (o) messagen } { } ifelse |
} for |
} for |
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[(ecartd.isSameIdeal_h) |
[(ecartd.isSameIdeal_h) |
[([ii jj vv] ecartd.isSameIdeal_h bool) |
[([ii jj vv] ecartd.isSameIdeal_h bool) |
(ii, jj : ideal, vv : variables) |
(ii, jj : ideal, vv : variables) |
$The ideals ii and jj will be compared in the ring h[0,1](D).$ |
$The ideals ii and jj will be compared in the ring h[0,1](D_0).$ |
$ii and jj are re-parsed.$ |
$ii and jj are re-parsed.$ |
$Example 1: [ [((1-x) Dx + h)] [((1-x)^2 Dx + h (1-x))] (x)] ecartd.isSameIdeal_h $ |
$Example 1: [ [((1-x) Dx + h)] [((1-x)^2 Dx + h (1-x))] (x)] ecartd.isSameIdeal_h $ |
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([ii jj vv vvGlobal] ecartd.isSameIdeal_h bool) |
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$ Ideals are compared in Q(x')_0 [x''] <Dx',Dx'',h> $ |
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( where x'' is specified in vvGlobal.) |
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(cf. partialEcartGlobalVarX option) |
]] putUsages |
]] putUsages |
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/ecartd.isSameIdeal_noh { |
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/arg1 set |
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[/aa /ii /jj /iigg /jjgg /vv /ans /k /n /f |
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/ecartd.isSameIdeal_h.opt |
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/save-ecart.autoHomogenize /wv /save-ecart.message.quiet |
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/vvGlobal /rng |
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] pushVariables |
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[(CurrentRingp) (Homogenize_vec)] pushEnv |
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[ |
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/aa arg1 def |
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gb.verbose { (Getting in ecartd.isSameIdeal_noh) message } { } ifelse |
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%% comparison of hilbert series has not yet been implemented. |
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/save-ecart.message.quiet ecart.message.quiet def |
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aa length 3 eq , aa length 4 eq , or { } |
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{ ([ii jj vv] ecartd.isSameIdeal_noh) error } ifelse |
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/ii aa 0 get def |
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/jj aa 1 get def |
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/vv aa 2 get def |
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aa length 4 eq { |
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/vvGlobal aa 3 get def |
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vvGlobal isString { [vvGlobal to_records pop] /vvGlobal set } |
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{ vvGlobal { toString } map /vvGlobal set } ifelse |
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} { /vvGlobal [ ] def } ifelse |
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ii length 0 eq jj length 0 eq and |
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{ /ans 1 def /LLL.ecartd.isSame_h goto } { } ifelse |
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[vv vvGlobal] ecart.stdBlockOrder /wv set |
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vvGlobal length 0 eq { |
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/rng [vv wv ] def |
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}{ |
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/rng [vv wv [(partialEcartGlobalVarX) vvGlobal]] def |
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} ifelse |
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/save-ecart.autoHomogenize ecart.autoHomogenize def |
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/ecart.autoHomogenize 0 def |
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[ii] rng join ecartd.gb /iigg set |
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[jj] rng join ecartd.gb /jjgg set |
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save-ecart.autoHomogenize /ecart.autoHomogenize set |
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iigg getRing ring_def |
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getOptions /ecartd.isSameIdeal_h.opt set |
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/ans 1 def |
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iigg 0 get /iigg set |
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jjgg 0 get /jjgg set |
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%%Bug: not implemented for the case of module. |
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/save-ecart.message.quiet ecart.message.quiet def |
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/ecart.message.quiet 1 def |
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gb.verbose { (Comparing) message iigg message (and) message jjgg message } |
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{ } ifelse |
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gb.verbose { ( ii < jj ?) messagen } { } ifelse |
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iigg length /n set |
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0 1 n 1 sub { |
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/k set |
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iigg k get |
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[jjgg] ecartd.reduction_noh 0 get |
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(0). eq not { /ans 0 def /LLL.ecartd.isSame_noh goto} { } ifelse |
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gb.verbose { (o) messagen } { } ifelse |
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} for |
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gb.verbose { ( jj < ii ?) messagen } { } ifelse |
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jjgg length /n set |
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0 1 n 1 sub { |
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/k set |
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jjgg k get |
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[iigg] ecartd.reduction_noh 0 get |
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(0). eq not { /ans 0 def /LLL.ecartd.isSame_noh goto} { } ifelse |
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gb.verbose { (o) messagen } { } ifelse |
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} for |
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/LLL.ecartd.isSame_noh |
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gb.verbose { ( Done) message } { } ifelse |
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save-ecart.message.quiet /ecart.message.quiet set |
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ecartd.isSameIdeal_h.opt restoreOptions |
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/arg1 ans def |
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] pop |
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popEnv |
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popVariables |
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arg1 |
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} def |
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[(ecartd.isSameIdeal_noh) |
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[([ii jj vv] ecartd.isSameIdeal_noh bool) |
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(ii, jj : ideal, vv : variables) |
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$The ideals ii and jj will be compared in the ring D_0.$ |
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$ii and jj are re-parsed.$ |
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$Example 1: [ [((1-x) Dx + 1)] [((1-x)^2 Dx + (1-x))] (x)] ecartd.isSameIdeal_noh $ |
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([ii jj vv vvGlobal] ecartd.isSameIdeal_noh bool) |
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$ Ideals are compared in Q(x')_0 [x''] <Dx',Dx''> $ |
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( where x'' is specified in vvGlobal.) |
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(cf. partialEcartGlobalVarX option, ecartd.reduction_noh, ecartd.isSameIdeal_h) |
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$Example 2: [ [(1-z) (1-x-y-z)] [(1-x) (1-y)] (x,y,z) [(x)]] $ |
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$ ecartd.isSameIdeal_noh $ |
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]] putUsages |
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(ecartd.isSameIdeal_noh ) messagen-quiet |
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/ecart.01Order { |
/ecart.01Order { |
/arg1 set |
/arg1 set |
[/in-ecart.01Order /vv /tt /dvv /wv1 /wv2 |
[/in-ecart.01Order /vv /tt /dvv /wv1 /wv2 |
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$Example 1: [ [((1-x) Dx + 1)] (x)] ecart.homogenize01Ideal $ |
$Example 1: [ [((1-x) Dx + 1)] (x)] ecart.homogenize01Ideal $ |
]] putUsages |
]] putUsages |
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% Example: [(x,y,z) (x)] ecart.stdBlockOrder |
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% [[(Dy) 1 (Dz) 1] [(y) -1 (z) -1 (Dy) 1 (Dz) 1] [(x) 1 (Dx) 1]] |
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% Example: [(x,y,z) [ ]] ecart.stdBlockOrder |
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/ecart.stdBlockOrder { |
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/arg1 set |
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[/vv /vvGlobal /tt /dd /rr] pushVariables |
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[ |
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/vv arg1 0 get def |
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/vvGlobal arg1 1 get def |
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{ |
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vv isArray |
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{ } { [vv to_records pop] /vv set } ifelse |
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vv {toString} map /vv set |
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vvGlobal isArray |
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{ } { [vvGlobal to_records pop] /vvGlobal set } ifelse |
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vvGlobal {toString} map /vvGlobal set |
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vvGlobal length 0 eq { |
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vv ecart.stdOrder /rr set exit |
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} { } ifelse |
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vv vvGlobal setMinus /vv set |
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vv ecart.stdOrder /rr set |
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vvGlobal { /tt set [@@@.Dsymbol tt] cat } map /dd set |
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[[ |
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0 1 vvGlobal length 1 sub { |
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/tt set |
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vvGlobal tt get , 1 |
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} for |
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0 1 dd length 1 sub { |
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/tt set |
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dd tt get , 1 |
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} for |
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]] rr join /rr set |
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exit |
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} loop |
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/arg1 rr def |
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] pop |
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popVariables |
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arg1 |
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} def |
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( ) message-quiet |
( ) message-quiet |
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