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strategy improvement in intersect() using SignatureSB branch
option(redSB);
LIB "primdec.lib";
ring rng = (integer),(x,y,z),(lp(2),lp(1),C);
ideal I = 115*x*y*z^2-67*y^2*z^2,-107*x*y*z^2-10*y^2-148*z;
ideal J = 146*z^3-46*z^2+78*z-93,-119*x^2*y-105*x*y*z;
intersect(I,J);
M2 code:
R = ZZ[x,y,z]
I = ideal { 115*x*y*z^2-67*y^2*z^2, -107*x*y*z^2-10*y^2-148*z }
J = ideal { 146*z^3-46*z^2+78*z-93, -119*x^2*y-105*x*y*z }
IJ = intersect(I,J);
can you reproduce this?
more examples:
option(redSB);
LIB "primdec.lib";
ring rng = (integer),(x,y,z),(lp(2),lp(1),C);
ideal I = 97*x*z+68*y^2,-121*x^3*z-105*y;
ideal J = 132*x*y^2+123*x*z+129*z^2-6,57*x^2+72*x*y;
intersect(I,J);
example with size( std(J) )<>size(std( std(J) )) for global ordering
ring rng = (integer),(x,y,z),(dp(1),dp(2),C);
intvec op = 100663296,16787537;
option() ;
option(set, op) ;
int trial = 0;
system("random", 1310165262);
ideal I = 20*x*z+7*y^2;
ideal J = 6*x*y+20*z+6,-5*x-16*y-11,8*x*y+2*y^2;
ideal gI = std(I);
ideal ggI = std(gI);
ideal gJ = std(J);
ideal ggJ = std(gJ);
ASSUME(0, 0== size( std(reduce (I,gI ) )) );
ASSUME(0, 0== size( std(reduce (J,gJ ) )) );
ASSUME(0, size(gJ)== size(ggJ) );
? ASSUME failed: ASSUME(0, size(gJ)== size(ggJ) );
significant performance drop for some examples
the following example drops performance significantly with your patches in comparison to
recent singular spielwiese
// finishes in singular-spielwiese in a bit (correct or not?), but
// does not finish in reasonable time using SignatureSB
ring rng = integer,(x,y,z),dp;
option(redSB); option(redTail);
ideal J = -12xy-59xz+40x-22y2,
-109x-22y2z2-42,
69x2z-97x-115y-19;
ideal stdJ = std(J);
in M2: (finishes in a bit)
# default is dp ordering:
rng = ZZ[x,y,z]
I = ideal(-12*x*y-59*x*z+40*x-22*y^ 2,-109*x-22*y^ 2*z^ 2-42,69*x^2*z-97*x-115*y-19)
groebnerBasis I
Make Hilbert Poincaree Series from the Roune Slice Algorithm
intersect segfault
ring rng = (integer),(x(1)),(lp(1),C);
short = 0 ;
// int trial= 0;
system("random", 1472251352);
ideal I = 4*x(1)^3+35*x(1)^2+24*x(1),45*x(1),35;
ideal J = 18*x(1)^3+43*x(1)^2,-7*x(1)-10,-12*x(1)^2-20*x(1)+13;
ideal I_J = intersect(I,J);
<http://www.singular.uni-kl.de:8002/trac/ticket/636#comment:5>
Ticket URL: <http://www.singular.uni-kl.de:8002/trac/ticket/648#comment:1>
Change MP_INT to mpz_t
Bug in Reduce over Qring intergers
reduce() bug for local ordering in SignatureSB
ring R = integer,x,dp;
reduce(x,std(2*x));
ring S = integer,x,ls;
reduce(x,std(2*x));
output
> ring R = integer,x,dp;
> reduce(x,std(2*x));
x
>
. ring S = integer,x,ls;
> reduce(x,std(2*x));
0
std() bug for ds ordering in SignatureSB
ring rng = integer,x,ds;
short = 0 ;
ideal I = -8*x+2*x^2, -16+9*x^2-x^3;
ideal gI = std(I);
gI;
std(gI);
output
> gI;
gI[1]=16-9*x^2+x^3
gI[2]=8*x-2*x^2
gI[3]=4*x^2-9*x^3
gI[4]=2*x^4
gI[5]=x^5
> std(gI);
_[1]=16-9*x^2+x^3
_[2]=8*x-2*x^2
_[3]=4*x^2-9*x^3
_[4]=x^4
Term wird übersehen??
ring rng = (0),(x,y,z),(ls(3),C);
system("random", 157161605);
ideal I =
68/23_z-142/133_y_z-64/37_x_y+65/71_x_y_z^2+1/3_x^2_y_z,-2/7_x_y_z-61/91_x_y^2_z;
ideal J = 3/53_x_z+47/44_x_y^2_z,-40/107_x_z^2+22_x_z^3;
ideal gI = std(I);
ideal ggI = std(gI);
ideal gJ = std(J);
ideal ggJ = std(gJ);
ASSUME(0, 0== size( std(reduce (I,gI ) )) );
$;
Add hdepth_1 computation
Negative Coeffcient
Interred Bug
Bug in radicalZ and primdecZ
Not actually a bug: the third component is irrelevant.
segfault in std computation using SignatureSB branch
Hello Adi,
I get a segfault for the following example:
option(redSB);
LIB "primdec.lib";
LIB "wrappers.lib";
ring rng = (integer),(x,y,z),(lp(2),lp(1),C);
int trial = 0;
system("random", 1181381080);
ideal I = 124*x^2+99*x*y,58*x*y+31*y+120*z,65*x^2*z+54*y^2*z+58*y*z+95*y;
ideal J = 52*x*y^3*z+102*y^2,4*x*y^2*z+19*y^3*z-103*y-30;
ideal gI = std(I);
can you reproduce this?
(I merged recent Singular into SignatureSB and didn't use your last commit)
medium size failing examples
ring rng = (integer),(x,y),rp;
short = 0 ;
ideal I = -4*y^2+x-1,2*y^2+6*x*y-5*y;
ideal gI = std(I);
ideal ggI = std(gI);
gI;
ggI;
reduce (I,gI );
reduce (I,ggI );
ASSUME(0, 0== size( std(reduce (I,gI ) )) );
////////////////////////////////////////////////
LIB "primdec.lib";
ring rng = (integer),(x,y),(lp(1),lp(1),C);
short = 0 ;
ideal J = -x^2-3*x,6*x*y^2+10*x*y+5*y^2;
ideal gJ = std(J);
ideal ggJ = std(gJ);
ASSUME(0, 0== size( std(reduce (J,gJ ) )) );
ASSUME(0, idealsEqual(gJ,ggJ ));
ASSUME(0, size(gJ)== size(ggJ) );
Kernel Restructuration
Mstd code review
segfault in qring over integers
ring rng = (integer),(x,y,z),(dp(3),C);
ideal Q = x,yz2+5;
qring QR = std(Q);
poly a = z;
ideal J = 5,z,x;
ideal aJJ = quotient( a*J, J );
Quotient Bug
Bug
ring r = integer,(a,d,g,h,i,j),ws(-1,-1,-1,-1,-1,-1);
ideal inI= gh+2i, dh+j, d+2g+aj, d+2g+ai;
ideal g= std(inI);
M2 - (not sure if correct)
rng = ZZ[a,d,g,h,i,j, MonomialOrder=>RevLex, Weights=>{-1,-1,-1,-1,-1,-1},Global=>false]
inI = ideal(g_h+2_i,d_h+j,d+2_g+a_j,d+2_g+a*i)
groebnerBasis inI
ring rng = (integer),(x,y,z),(ws(-1,-1,-1),C);
ideal I = 6yz-6,6xy-6yz-8y;
ideal gI =std(I);
sba(): tail not reduced
example:
ring rng = (integer),(x,y,z),dp;
option(redSB);
option(redTail);
ideal I = 24*z^2+33*y,-20*y-42,-29*y-39*z;
ideal gI = std(I);
ideal ggI = std(gI);
ideal sI = sba(I);
ideal ssI = sba(sI);
sI;
ssI;
output:
> sI;
sI[1]=y+351z-546
sI[2]=3z-44142
sI[3]=182154
> ssI;
ssI[1]=182154
ssI[2]=3z-44142
ssI[3]=y+63756
(351 = 3*117)
ẁhat happens with this example?
option(prot);
ring rng = (integer),(x(1),x(3),x(4),x(5)),(dp(4),C);
short = 0;
ideal Q = x(4)^2-x(3)*x(5),
x(3)*x(4)-x(5),
x(3)^2-x(4),
x(1)^2-121*x(5)^2-11*x(5)-1;
Q = std(Q);
qring qr = Q;
ideal a = x(5)-2;
ideal j = 6,x(5)-2,x(4)+2,x(3)-2,x(1)+3;
ideal aJJ = quotient(a*j,j); // ?
correct result can be obtained by
// correct result
proc quotient_alternative(i,j1,j2)
"USAGE: quotient_alternative(i,j1,j2);
@* i,j1,j2 = ideals
RETURN: the quotient ideal (j1:j2) in the ring r/i
EXAMPLE: example quotient_alternative; shows an example"
{
/*ASSUME( 0 , isCommutative( ) );
ASSUME( 0 , hasGlobalOrdering( basering ) );
if ( baseringIsExtensionField() ||
not ( baseringHasIntegerCoefficientRing() ||
baseringHasRationalCoefficientField() ||
baseringHasPrimeCoefficientField()
)
)
{
ERROR("quotient_alternative does not support given ring type");
}
*/
def BAS = basering;
int j,k;
ideal q = 1;
for(j = 1; j <= ncols(j2); j++)
{
ideal s = j2[j], -j1, -i;
matrix m = matrix(syz(s));
m = m[1,1..ncols(m)];
matrix n[1][ncols(m)] = m[1,1..ncols(m)];
ideal qq = n;
qq = simplify(qq,2);
q = std( intersect(q,qq) );
for(k=1; k <= ncols(q); k++)
{
if (leadcoef(q[k]) < 0)
{
//ERROR("quotient_alternative::Warning: negative leadcoef occured");
q[k] = -q[k];
}
}
kill m,n,qq,s;
}
return(q);
}
// option(prot);
ring rng = (integer),(s,x,y,z),(dp(4),C);
ideal Q = y^2-x*z, x*y-z, x^2-y, s^2-121*z^2-11*z-1 ;
Q = std(Q);
ideal a = z-2;
ideal j = 6,z-2,y+2,x-2,s+3;
ideal aJJ = quotient_alternative(Q, a*j,j) ;
aJJ;
M2 code?
R = ZZ[s,x,y,z]
Q = ideal {y^2-x*z, x*y-z, x^2-y, s^2-121*z^2-11*z-1 }
S = R/Q
A = ideal{z-2}
J = ideal(6,z-2,y+2,x-2,s+3);
AJJ = quotient(A*J,J)
// lift AJJ to R and compute gb
gens gb lift( AJJ, R )
simplified bug in std() over integers with ws ordering
ring r = integer,(a,d,g,h,i,j),ws(-1,-1,-1,-1,-1,-1);
ideal inI= gh+2i, dh+j, d+2g+aj, d+2g+ai;
ideal g= std(inI);
# M2 - (not sure if correct)
rng = ZZ[a,d,g,h,i,j, MonomialOrder=>RevLex, Weights=>{-1,-1,-1,-1,-1,-1},Global=>false]
inI = ideal(g*h+2*i,d*h+j,d+2*g+a*j,d+2*g+a*i)
toString entries groebnerBasis inI
64Bits Bugs
simple failing examples over ZZ
ring rng = integer,x,lp;
short = 0 ;
option(noredSB) ;
option(noredTail) ;
ideal I = -8*x^3+7*x^2-7*x, 8*x^2+10*x-2;
ideal gI = std(I);
ideal ggI = std(gI);
reduce (I,gI ); // <>0 !!
gI;
ggI;
output
> ring rng = integer,x,lp;
> short = 0 ;
> option(noredSB) ;
> option(noredTail) ;
> ideal I = -8*x^3+7*x^2-7*x, 8*x^2+10*x-2;
> ideal gI = std(I);
> ideal ggI = std(gI);
> reduce (I,gI ); // <>0 !!
_[1]=371464849600
_[2]=0
> gI;
gI[1]=3200
gI[2]=2*x-5554
gI[3]=x^2+6023*x
> ggI;
ggI[1]=1600
ggI[2]=2*x-2354
ggI[3]=x^2+2823*x
Ticket URL: <http://www.singular.uni-kl.de:8002/trac/ticket/653>
examples ok now:
The patches in SignatureSB fixes several bugs, but now I hit a new one:
//options: redefine loadLib usage prompt
ring rng = (integer),(x(1),x(2),x(3),x(4),x(5)),(dp(5),C);
ideal I = x(4)^2-x(3)*x(5),x(3)*x(4)-x(5),x(3)^2-x(4),x(1)^2-121*x(5)^2-11*x(5)-1,2*x(3)^3-3*x(3)*x(4)+x(5),-4*x(1)*x(4)^2-2*x(1)*x(3)*x(5),2*x(1)*x(3)*x(4)+2*x(1)*x(5),2*x(1)*x(3)^2-4*x(1)*x(4),484*x(4)^2*x(5)+242*x(3)*x(5)^2+22*x(4)^2+11*x(3)*x(5),-8*x(1)*x(3)*x(4)+2*x(1)*x(5),4*x(1)*x(3)^2,-2*x(1)*x(3),968*x(3)*x(4)*x(5)+44*x(3)*x(4)-242*x(5)^2-11*x(5),-4*x(1)*x(3)^2-2*x(1)*x(4),4*x(1)*x(3),-2*x(1),484*x(3)^2*x(5)+22*x(3)^2+242*x(4)*x(5)+11*x(4);
ideal J = std(I); // error
update: seems ok now
ring rng = (integer),(x,y),(dp(2),C);
ideal I = xy-2x-8y,y-2,x-8;
ideal J = std(I);
finishes now
ring rng = (integer),(x,y),(dp(2),C);
poly a = 2x;
ideal J = 3y,2x,xy;
ideal aJJ = quotient( a*J, J );
finishes now
LIB("primdec.lib");
ring rng = (integer),(xs,xp,xm),(lp(2),lp(1),C);
ideal I = 4*xm^2-8,14*xm^2+1;
ideal J = -5*xs-14;
ideal A = intersect(std(I),std(J)); //ok
ideal B= intersect(I,J); // takes long time or hangs
seems ok now
problem with parser?
LIB("ring.lib");
proc intersect_via_eliminate(def i, def j)
"USAGE: intersect_via_eliminate(i,j);
@* i,j = ideals
ASSUME: i,j = ideals over the integers or a field
RETURN: ideal, the intersection of i and j
EXAMPLE: example intersect_via_eliminate; shows an example"
{
i = std(i);
j = std(j);
int bIsQring = isQuotientRing( basering );
ideal q = ideal(basering);
def BAS = basering;
// add one new variable "t" to a copy of basering
int numVariables = nvars(basering);
int pos_t = numVariables + 1; // position of new variable 't' is numVariables + 1
// introduce new variable called "t"
// hardcoded, but does not hurt, since there are no parameters. and 'x' is not in conflict with 't'
string tempstr = "ring pr2=" + charstr(BAS) + ",(x(1.."+ string(numVariables) + "), t), dp;";
execute(tempstr);
if ( not bIsQring )
{
def r2 = pr2;
}
else
{
ideal q = imap(BAS,q);
qring r2 = q;
}
/*
list rl = ringlist(basering);
rl[2] = indexedVariables("x", numVariables) + list("t");;
dbprint(printlevel-voice, "rl[2] = ", rl[2] );
// change variable ordering to dp:
rl = changeRingListVarOrderTo_dp (rl);
dbprint(printlevel-voice, "rl[2] = ", rl[2] );
// difference to previous variant: if basering is a qring, then r2 is also a qring.
def r2 = ring(rl);
setring r2;
// */
//dbprint(printlevel-voice, "intersect_via_eliminate:: r2 = ", basering );
//dbprint(printlevel-voice, "intersect_via_eliminate:: var(pos_t)= ", var(pos_t) );
// for i=(f_1,...,f_s) and j=(g_1,...,g_t) compute the ideal
// J=(tf_1,...,tf_s,(1-t)g_1,...,(1-t)g_t)
// then we eliminate "t" from J and map the new J to our basering
ideal J = 0;
int k;
ideal ii = fetch(BAS,i);
ii = std(ii); //not necessary due to Anne
for(k=1; k <= ncols(ii); k++)
{
J = J,var(pos_t)*ii[k];
}
ideal jj = fetch(BAS,j);
jj = std(jj); //not necessary due to Anne
for(k=1; k <= ncols(jj); k++)
{
J = J,(1 - var(pos_t) )*jj[k];
}
ideal e = eliminate(J, var(pos_t) );
setring BAS;
ideal result1 = fetch(r2,e);
for(k=1; k <= ncols(result1); k++)
{
if(leadcoef(result1[k]) < 0)
{
//ERROR("intersect_via_eliminate::Warning: negative leadcoef occured");
result1[k] = -result1[k];
}
}
return(result1);
}
//system("random",1412595701);
ring rng = (integer),(xn,xl,xf),(lp(2),lp(1),C);
//int trial: =14;
// ** redefining I **
// ** redefining J **
ideal I = -9*xl-10*xf,-10*xl^2-xf;
ideal J = 15*xl*xf-10*xl,-4*xl*xf+9*xl;
intersect(I,J);
intersect(std(I),std(J) );
intersect_via_eliminate(std(I),std(J));
ASSUME(0, idealsEqual( intersect(I,J), intersect( std(I), std(J) ) ) );
ASSUME(0, idealsEqual( intersect(I,J), intersect_via_eliminate(I,J) ) );
ideal stdI = std(I);
ideal stdJ = std(J);
ASSUME(0, idealsEqual( intersect(stdI,stdJ), intersect_via_eliminate(stdI,stdJ) ) );
intersect(std(I),std(J));
intersect_via_eliminate(std(I),std(J)); // segfault
ok now
ring rng = (integer),(xm,xv,xa),(lp(2),lp(1),C);
//int trial: =2;
// ** redefining I **
// ** redefining J **
ideal I = 4*xm-4,-6*xm+11;
ideal J = -2*xv+11,-15*xm*xv;
intersect(I,J);
intersect(std(I),std(J) ); //segfault
intersect(I,J);
intersect(std(I),std(J) );
seems ok now
simple example for remaining segfaults
the following example leads to a segfault and
to omError_NullSizeAlloc: alloc of size 0 in debug mode:
ring rng = integer,x,ds;
short = 0 ;
ideal J = -7, -3-15*x^2, -6+18*x-x^2;
ideal gJ = std(J);
Make stb over integers for ideals, local and mixed orderings - Master Thesis
hilb
Make the slice Roune algorithm properly (a function, change the old hilb with this one)
Signature SB over rings
to be done...
See Tests
LLL_Flint
Bug from Gerhard
ring q = (integer,2,3),(r,s,a,b,b_2,b_1,b_0),lp;
poly p0 = b -1_b_0 -2_b_1 -4_b_2;
poly p1 = r-a_b_0;
poly p2 = s_b_0;
poly p3 = s_b_1;
poly p4 = s_b_2;
ideal I = (p0,p1,p2,p3,p4);
poly goal = r- a_b;
poly p = 1 - s;
I = std(I);
I,p;
print("-------std(I,p)-------");
std(I,p); //Segmentation Fault
$;
tail not reduced example
LIB "primdec.lib";
LIB "wrappers.lib";
ring rng = (integer),(x,y,z),(lp(1),lp(2),C);
intvec op = 100663296,16787537;
option() ;
option(set, op) ;
ASSUME(0, optionIsSet("redTail"));
int trial = 5;
system("random", 226841520);
ideal I = -4*x*y*z+9*x*z^2+9*y,-4*x*y*z-3*y;
ideal J = 5*x*y*z+6,8*x*z^2-10*y;
ideal gI = std(I);
ideal ggI = std(gI);
ideal gJ = std(J);
ideal ggJ = std(gJ);
ASSUME(0, 0== size( std(reduce (I,gI ) )) );
ASSUME(0, 0== size( std(reduce (J,gJ ) )) );
ASSUME(0, size(gJ)== size(ggJ) );
ASSUME(0, size(gI)== size(ggI) );
ASSUME(0, idealsEqual(gI,ggI ));
ASSUME(0, idealsEqual(gJ,ggJ ));
ASSUME(0, idealsAreEqual(gI,ggI ));
ASSUME(0, idealsAreEqual(gJ,ggJ ));
ASSUME(0, idealRepresentationReducedTail(gI ));// fails
// idealRepresentationReducedTail : I[3]4xyz-9xz2-9y
// idealRepresentationReducedTail: lead(I[2])9xz2
ASSUME(0, idealRepresentationReducedTail(gJ ));
ASSUME(0, idealRepresentationReducedTail(ggI ));
ASSUME(0, idealRepresentationReducedTail(ggJ ));
observed a segfault on SignatureSB branch
// lipmanresolve-with-flint/infiniteTests/log/test.std.correct.04/bugs$ more id_1.4.bug
option(redSB);
LIB "primdec.lib";
LIB "wrappers.lib";
ring rng = (integer),(x,y,z),(ls(3),C);
int trial = 3;
system("random", 158291770);
ideal I = -10*x*y*z,12*z^2-8*y-14*x*z+14*x^2*y*z,-7*y^4+4*x^2+9*x^2*y;
ideal J = -1+7*y^3*z,-15+14*x+14*x*y*z,15*z+7*x-10*x*z+5*x*y^2;
ideal gI = std(I); // segfault
update: the example failed before commit
adipopescu/Sources@97ae278
detailed example for the intersect() bug in the SignatureSB branch
LIB("primdec.lib");
ring rng = (integer),(x,y,z),lp;
option(redSB);
option(redTail);
ideal I = -4*z+10;
ideal J = -7*x+4*z,-13;
ideal gI = std(I);
ideal gJ = std(J);
ideal IJ = intersect(I,J) ;
ideal gIJ = intersect( gI,gJ ); // falsch!
ASSUME(0, idealsEqual(IJ , gIJ ) ) ;
gI;
gJ;
IJ;
gIJ;
attrib(gI,"isSB",0);
attrib(gJ,"isSB",0);
ideal ngIJ = intersect(gI,gJ ); // wrong
ngIJ;
output
> ASSUME(0, idealsEqual(IJ , stdI_stdJ ) ) ;
? ASSUME failed:ASSUME(0, idealsEqual(IJ , stdI_stdJ ) ) ;
? error occurred in or before STDIN line 11: ` return(0);`
> stdI;
stdI[1]=4z-10
> stdJ;
stdJ[1]=13
stdJ[2]=x-8z
> IJ;
IJ[1]=52z-130
IJ[2]=4xz-10x-240z2+15992z-38480
> stdI_stdJ;
stdI_stdJ[1]=52z-130
segfault for 'sba' example
option(redSB);
LIB "primdec.lib";
ring rng = (integer),(x,y,z),(dp(3),C);
system("random", 1979129011);
ideal I = 40*y*z-35,-8,25*x^2+4*z;
ideal gI = std(I);
ideal ggI = std(gI);
ideal sI = sba(I); //segfault
more examples:
option(redSB);
LIB "primdec.lib";
LIB "wrappers.lib";
ring rng = (integer),(x,y,z),(dp(3),C);
int trial = 1;
system("random", 1923388056);
ideal I = -12,23*y+46,26*x*z-31*z;
ideal gI = std(I);
ideal ggI = std(gI);
ideal sI = sba(I);
option(redSB);
LIB "primdec.lib";
LIB "wrappers.lib";
ring rng = (integer),(x,y,z),(dp(3),C);
int trial = 0;
system("random", 784341798);
ideal I = -49*y^2+40*z^2+17,-34*z^2-3,-25*y*z-28*z;
ideal gI = std(I);
ideal ggI = std(gI);
ideal sI = sba(I);
Example in std over Z
example which in Singular take forever,
in M2 the result is immediate
64 Bits
QRings allows constant entry in ideal
interesting example for 'idealsEqual'
Assuming that the 'gI' and 'ggI' is ok (please check!)
this is an example for which 'Primdec::idealsEqual' does not work correctly. (Then the documentation
or the implementation of 'idealsEqual' should be updated)
otherwise it is a bug in std():
LIB "primdec.lib";
ring rng = (integer),(x,y,z),(ls(3),C);
//option("redTail");
option(redSB);
system("random", 1022116625);
ideal I = -14*y*z^2+7*x-11*x*y,-15*x*y,-8*y^2*z^2+5*x*y*z,5*y*z^2-15*y^2*z+8*x^2*z^2+3*x^2*y^2;
ideal gI = std(I);
ideal ggI = std(gI);
idealsEqual(gI,ggI ); //0
quit;
It seems ok after adding 'redTail' option:
LIB "primdec.lib";
ring rng = (integer),(x,y,z),(ls(3),C);
option(redTail);
system("random", 1022116625);
ideal I = -14*y*z^2+7*x-11*x*y,-15*x*y,-8*y^2*z^2+5*x*y*z,5*y*z^2-15*y^2*z+8*x^2*z^2+3*x^2*y^2;
ideal gI = std(I);
ideal ggI = std(gI);
idealsEqual(gI,ggI ); //1
quit;
more examples:
option(redSB);
LIB "primdec.lib";
LIB "wrappers.lib";
ring rng = (integer),(x,y,z),(ls(3),C);
int trial = 3;
system("random", 820791554);
ideal I = 1+7*y*z^3,-4*x+2*x*z+14*x^2,-9-10*z^2+8*x*z;
ideal J = -14*x*z^3+5*x^2*y*z,15*z-7*x*y+12*x*y*z^2-11*x*y^2;
ideal gI = std(I);
ideal ggI = std(gI);
ideal gJ = std(J);
ideal ggJ = std(gJ);
ASSUME(0, 0== size( std(reduce (I,gI ) )) );
ASSUME(0, 0== size( std(reduce (J,gJ ) )) );
ASSUME(0, idealsEqual(gI,ggI ));
ASSUME(0, idealsEqual(gJ,ggJ ));
// /lipmanresolve-with-flint/infiniteTests/log/test.std.correct.04/bugs$ more id_1.2.bug
option(redSB);
LIB "primdec.lib";
LIB "wrappers.lib";
ring rng = (integer),(x,y,z),(ls(3),C);
int trial = 8;
system("random", 774004311);
ideal I = -3+8*x+3*x*y^2*z-8*x^2*y,8-4*z+2*y;
ideal J = 9*x*z+10*x^2*y*z,-3*y*z^2-8*x-4*x*y*z-4*x^2*z,-9*y^2*z+4*x+5*x*y+x^2;
ideal gI = std(I);
ideal ggI = std(gI);
ideal gJ = std(J);
ideal ggJ = std(gJ);
ASSUME(0, 0== size( std(reduce (I,gI ) )) );
ASSUME(0, 0== size( std(reduce (J,gJ ) )) );
ASSUME(0, idealsEqual(gI,ggI ));
ASSUME(0, idealsEqual(gJ,ggJ ));
//lipmanresolve-with-flint/infiniteTests/log/test.std.correct.04/bugs$ more id_1.3.bug
option(redSB);
LIB "primdec.lib";
LIB "wrappers.lib";
ring rng = (integer),(x,y,z),(ls(3),C);
int trial = 4;
system("random", 1143393520);
ideal I = -13*z^2-3*y-13*y*z^2-3*x^2*y^2,-11*z+12*y+14*y^2*z-9*x*y*z^2,-12*x+4*x*y*z^2,-7*y*z^3+7*x^2*z+10*x^3*y;
ideal J = -11+9*x*y*z;
ideal gI = std(I);
ideal ggI = std(gI);
ideal gJ = std(J);
ideal ggJ = std(gJ);
ASSUME(0, 0== size( std(reduce (I,gI ) )) );
ASSUME(0, 0== size( std(reduce (J,gJ ) )) );
ASSUME(0, idealsEqual(gI,ggI ));
bug in std(), branch SignatureSB
reduce fails for example ; std(J)<> std( std(J) )
option(redSB);
LIB "primdec.lib";
ring rng = (integer),(x,y,z),dp;
ideal I = -25*x^3+104*x*y^3-23*y^2*z-128;
ideal J = -118*x*y^3*z+50*x*y^2*z^2-50*x*y*z-49*y,149*x*y^2*z^2-142*y^2-112;
ideal gI = std(I);
ideal gJ = std(J);
reduce (I,gI );
reduce (J,gJ );
ASSUME(0, 0== size( std(reduce (I,gI ) )) );
ASSUME(0, 0== size( std(reduce (J,gJ ) )) );
check in M2 says that J == gJ:
R = ZZ[x,y,z]
gJ = ideal(16756*y^4-7100*y^3*z+7301*y^2*z+20316*y^2-5600*y*z+5600,4172000*x*z^2+9383360*y^3*z-3976000*y^2*z^2+9383360*y^2+4088560*y*z^2+7400960*y*z-3136000*z^2+4088560*z+7400960,7450*x*y*z^2+16756*y^3-7100*y^2*z+7301*y*z+13216*y-5600*z,13216*x*y^2*z-5600*x*y*z^2+5600*x*z+5488,x*y^2*z^2-537600*x*y*z^3+537600*x*z^2+1209130*y^2+526848*z+953680,118*x*y^3*z-26880000*x*y*z^3+50*x*y*z+26880000*x*z^2+60456500*y^2+49*y+26342400*z+47684000)
J = ideal(-118*x*y^3*z+50*x*y^2*z^2-50*x*y*z-49*y,149*x*y^2*z^2-142*y^2-112)
J == gJ -- true !
also weird is that std(J) differs from std(std(J)) (look at the second generator):
> gJ;
gJ[1]=7450*x*y*z^2+16756*y^3-7100*y^2*z+7301*y*z+13216*y-5600*z
gJ[2]=4172000*x^2*z^2+4088560*x*y*z^2+9383360*x*y^2+3424960*x*y*z-3136000*x*z^2+4088560*x*z+7400960*x-3896480*y
gJ[3]=9383360*y^3*z-3976000*y^2*z^2+4172000*x*z^2+4088560*y*z^2+9383360*y^2+7400960*y*z-3136000*z^2+4088560*z+7400960
gJ[4]=13216*x*y^2*z-5600*x*y*z^2+5600*x*z+5488
gJ[5]=16756*y^4-404235155900*y^3*z+171286080000*y^2*z^2+7301*y^2*z-179729760000*x*z^2-176135164800*y*z^2-404235128484*y^2-318833362400*y*z+135098880000*z^2-176135164800*z-318833351200
gJ[6]=x*y^2*z^2-537600*x*y*z^3+537600*x*z^2+1209130*y^2+526848*z+953680
gJ[7]=118*x*y^3*z-26880000*x*y*z^3+50*x*y*z+26880000*x*z^2+60456500*y^2+49*y+26342400*z+47684000
> std(gJ);
_[1]=7450*x*y*z^2+16756*y^3-7100*y^2*z+7301*y*z+13216*y-5600*z
_[2]=834400*x^2*z^2+817712*x*y*z^2+1876672*x*y^2+684992*x*y*z-627200*x*z^2+817712*x*z+1480192*x-779296*y
_[3]=1876672*y^3*z-795200*y^2*z^2+834400*x*z^2+817712*y*z^2+1876672*y^2+1480192*y*z-627200*z^2+817712*z+1480192
_[4]=13216*x*y^2*z-5600*x*y*z^2+5600*x*z+5488
_[5]=16756*y^4-404235155900*y^3*z+171286080000*y^2*z^2+7301*y^2*z-179729760000*x*z^2-176135164800*y*z^2-404235128484*y^2-318833362400*y*z+135098880000*z^2-176135164800*z-318833351200
_[6]=x*y^2*z^2-537600*x*y*z^3+537600*x*z^2+1209130*y^2+526848*z+953680
_[7]=118*x*y^3*z-26880000*x*y*z^3+50*x*y*z+26880000*x*z^2+60456500*y^2+49*y+26342400*z+47684000
another failing example:
option(redSB);
LIB "primdec.lib";
LIB "wrappers.lib";
ring rng = (integer),(x,y,z),(dp(3),C);
int trial = 0;
system("random", 912758297);
ideal I = -27*x+25*z,-46*x*z+35*x,21*x-42;
ideal gI = std(I);
ideal ggI = std(gI);
ideal sI = sba(I);
reduce (I,gI );
ASSUME(0, 0== size( std(reduce (I,gI ) )) );
new: std(I)<>std(std(I)) in SignatureSB branch
input:
LIB "primdec.lib";
ring rng = (integer),(x,y,z),dp;
option(redSB);
option(redTail);
ideal I = -5*z^2-y*z^2, x^3*y*z-z^2+1, y^2*z^2+5*x^2*y*z;
ideal gI = std(I);
ideal ggI = std(gI);
gI;
ggI;
ASSUME(0, size(gI)==size(ggI));
output:
> ring rng = (integer),(x,y,z),dp;
> option(redSB);
> option(redTail);
> ideal I = -5*z^2-y*z^2, x^3*y*z-z^2+1, y^2*z^2+5*x^2*y*z;
> ideal gI = std(I);
> ideal ggI = std(gI);
> gI;
gI[1]=5y+25
gI[2]=25x2-25z
gI[3]=125z3-5z2-25x+5
gI[4]=yz2+5z2
gI[5]=5xz2+25z3-5x
gI[6]=x3yz-z2+1
> ggI;
ggI[1]=y+5
ggI[2]=25x2-25z
ggI[3]=125z3-5z2-25x+5
ggI[4]=5xz2+25z3-5x
ggI[5]=25z4-5x3-z3+z
ggI[6]=5x3z+z2-1
ggI[7]=5x4+xz3+5z4-xz-5z2
ggI[8]=xz4+5z5-2xz2-5z3+x
more variants:
LIB "primdec.lib";
ring rng = (integer),(x,y,z),(dp(3),C);
option(redSB);
option(redTail);
ideal I = -5*x*z^2-73*y*z^2, 68*x^3*y*z-129*x*z^2+98, 11*y^3*z^2+85*x^2*y*z;
ideal gI = std(I);
ideal ggI = std(gI);
size(gI)==size(ggI);
ASSUME( size(gI)==size(ggI) );
///////////////////////////////////////
LIB "primdec.lib";
ring rng = (integer),(x,y,z),(dp(3),C);
option(redSB);
option(redTail);
ideal I = -5*x*z^2-73*y*z^2, 2*x^3*y*z-129*x*z^2+8, 11*y^3*z^2+85*x^2*y*z;
ideal gI = std(I);
ideal ggI = std(gI);
size(gI)==size(ggI);
///////////////////////////////////////
LIB "primdec.lib";
ring rng = (integer),(x,y,z),(dp(3),C);
option(redSB);
option(redTail);
ideal I = -5*x*z^2-73*y*z^2, 2*x^3*y*z-129*x*z^2+8, y^3*z^2+85*x^2*y*z;
ideal gI = std(I);
ideal ggI = std(gI);
size(gI)==size(ggI);
///////////////////////////////////////
LIB "primdec.lib";
ring rng = (integer),(x,y,z),(dp(3),C);
option(redSB);
option(redTail);
ideal I = -5*x*z^2-73*y*z^2, 2*x^3*y*z-129*x*z^2+8, y^3*z^2+5*x^2*y*z;
ideal gI = std(I);
ideal ggI = std(gI);
size(gI)==size(ggI);
///////////////////////////////////////
LIB "primdec.lib";
ring rng = (integer),(x,y,z),(dp(3),C);
option(redSB);
option(redTail);
ideal I = -5*x*z^2-73*y*z^2, 2*x^3*y*z-9*x*z^2+8, y^3*z^2+5*x^2*y*z;
ideal gI = std(I);
ideal ggI = std(gI);
size(gI)==size(ggI);
///////////////////////////////////////
LIB "primdec.lib";
ring rng = (integer),(x,y,z),(dp(3),C);
option(redSB);
option(redTail);
ideal I = -5*x*z^2-11*y*z^2, 2*x^3*y*z-3*x*z^2+8, y^3*z^2+5*x^2*y*z;
ideal gI = std(I);
ideal ggI = std(gI);
size(gI)==size(ggI);
///////////////////////////////////////
LIB "primdec.lib";
ring rng = (integer),(x,y,z),(dp(3),C);
option(redSB);
option(redTail);
ideal I = -5*x*z^2-y*z^2, 2*x^3*y*z-3*x*z^2+8, y^3*z^2+5*x^2*y*z;
ideal gI = std(I);
ideal ggI = std(gI);
size(gI)==size(ggI);
///////////////////////////////////////
LIB "primdec.lib";
ring rng = (integer),(x,y,z),(dp(3),C);
option(noredSB);
option(noredTail);
ideal I = -5*x*z^2-y*z^2, 2*x^3*y*z-3*x*z^2+8, y^3*z^2+5*x^2*y*z;
ideal gI = std(I);
ideal ggI = std(gI);
size(gI)==size(ggI);
///////////////////////////////////////
LIB "primdec.lib";
ring rng = (integer),(x,y,z),(dp(3),C);
option(noredSB);
option(noredTail);
ideal I = -5*x*z^2-y*z^2, 2*x^3*y*z-3*x*z^2+1, y^3*z^2+5*x^2*y*z;
ideal gI = std(I);
ideal ggI = std(gI);
size(gI)==size(ggI);
///////////////////////////////////////
LIB "primdec.lib";
ring rng = (integer),(x,y,z),(dp(3),C);
option(noredSB);
option(noredTail);
ideal I = -5*x*z^2-y*z^2, 2*x^3*y*z-x*z^2+1, y^3*z^2+5*x^2*y*z;
ideal gI = std(I);
ideal ggI = std(gI);
size(gI)==size(ggI);
///////////////////////////////////////
LIB "primdec.lib";
ring rng = (integer),(x,y,z),(dp(3),C);
option(noredSB);
option(noredTail);
ideal I = -5*x*z^2-y*z^2, x^3*y*z-x*z^2+1, y^3*z^2+5*x^2*y*z;
ideal gI = std(I);
ideal ggI = std(gI);
size(gI)==size(ggI);
///////////////////////////////////////
LIB "primdec.lib";
ring rng = (integer),(x,y,z),(dp(3),C);
option(redSB);
option(redTail);
ideal I = -5*x*z^2-y*z^2, x^3*y*z-x*z^2+1, y^3*z^2+5*x^2*y*z;
ideal gI = std(I);
ideal ggI = std(gI);
size(gI)==size(ggI);
///////////////////////////////////////
LIB "primdec.lib";
ring rng = (integer),(x,y,z),(dp(3),C);
option(redSB);
option(redTail);
ideal I = -5*x*z^2-y*z^2, x^3*y*z-z^2+1, y^3*z^2+5*x^2*y*z;
ideal gI = std(I);
ideal ggI = std(gI);
size(gI)==size(ggI);
///////////////////////////////////////
LIB "primdec.lib";
ring rng = (integer),(x,y,z),(dp(3),C);
option(redSB);
option(redTail);
ideal I = -5*z^2-y*z^2, x^3*y*z-z^2+1, y^3*z^2+5*x^2*y*z;
ideal gI = std(I);
ideal ggI = std(gI);
size(gI)==size(ggI);
///////////////////////////////////////
LIB "primdec.lib";
ring rng = (integer),(x,y,z),(dp(3),C);
option(redSB);
option(redTail);
ideal I = -5*z^2-y*z^2, x^3*y*z-z^2+1, y^2*z^2+5*x^2*y*z;
ideal gI = std(I);
ideal ggI = std(gI);
size(gI)==size(ggI);
new segfault examples
ring rng = (integer),(x,y),(lp(1),lp(1),C);
short = 0 ;
ideal I = 19*x^2*y+2*x^2+14*x*y^2-33*x*y,-3*x^4-34*x^2*y^2,18*x^3-32*x^2*y^2-9*y-29;
ideal gI = std(I);
//////////////////////////////////////////////////////////////////////////////////////////////////
ring rng = (integer),(x,y,z),(Wp(4,2,2),C);
short = 0 ;
ideal J = -42*x^2+25*x*y-3*z^3+10*x,29*z^4+18,-14*x^3*y+25*x*y*z^2+5*z;
ideal gJ = std(J);
//////////////////////////////////////////////////////////////////////////////////////////////////
ring rng = (integer),(x,y,z),(lp(3),C);
short = 0 ;
ideal I = 29*x^2*z-27*x*y*z^2-16*x*y*z-7*y*z,-19*x*z+30*y*z^2-31*y*z+39,28*x^3*z-32*x*y*z^2-41*x*y;
ideal gI = std(I);
//////////////////////////////////////////////////////////////////////////////////////////////////
// segfault
ring rng = (integer),(x,y,z),(lp(1),lp(1),lp(1),C);
short = 0 ;
intvec op = 100663296,16787537;
option(set, op) ;
option() ;
system("random", 2146987388);
ideal J = -17*x*y*z+18*z^2,-44*x*y^2*z-33*x*y*z+25*y+7,-x^3*z+31*x+19;
ideal gJ = std(J);
quit;
// no segfault
ring rng = (integer),(x,y,z),(lp(1),lp(1),lp(1),C);
short = 0 ;
intvec op = 100663296,16787537;
option(set, op) ;
// option() ;
system("random", 2146987388);
ideal J = -17*x*y*z+18*z^2,-44*x*y^2*z-33*x*y*z+25*y+7,-x^3*z+31*x+19;
ideal gJ = std(J);
quit;
//////////////////////////////////////////////////////////////////////////////////////////////////
// segfault
ring rng = (integer),(x,y,z),(lp(1),dp(2),C);
short = 0 ;
intvec op = 100663298,16787537;
option(set, op) ;
option() ;
system("random", 1117796194);
ideal I = -2*x^2*y*z+41*y^2*z^2-16*y^2+40*z,20*x*y*z^2+43*x*z^2-19*z,-30*x^2*y^2-20*x^2*z^2-44;
ideal J = 21*x*y^2*z-2*x*y+24*y^2,34*x-26*y^3*z-5*y^2*z;
ideal gI = std(I);
//no segfault
ring rng = (integer),(x,y,z),(lp(1),dp(2),C);
short = 0 ;
intvec op = 100663298,16787537;
//option(set, op) ;
// option() ;
system("random", 1117796194);
ideal I = -2*x^2*y*z+41*y^2*z^2-16*y^2+40*z,20*x*y*z^2+43*x*z^2-19*z,-30*x^2*y^2-20*x^2*z^2-44;
ideal J = 21*x*y^2*z-2*x*y+24*y^2,34*x-26*y^3*z-5*y^2*z;
ideal gI = std(I);
//////////////////////////////////////////////////////////////////////////////////////////////////
// segfault
ring rng = (integer),(x,y,z),(lp(1),dp(2),C);
short = 0 ;
intvec op = 100663296,16787537;
option(set, op) ;
// option() ;
ideal I = 13*x^2*z^2-22*x*y+20,27*x^2+26*x*y*z^2+45*x*z^2,5*x^2*z+4*x*y^2*z+2*x*y*z-13*x*z^2;
ideal gI = std(I);
OK
// no segfault
ring rng = (integer),(x,y,z),(lp(1),dp(2),C);
short = 0 ;
intvec op = 100663296,16787537;
// option(set, op) ;
// option() ;
ideal I = 13*x^2*z^2-22*x*y+20,27*x^2+26*x*y*z^2+45*x*z^2,5*x^2*z+4*x*y^2*z+2*x*y*z-13*x*z^2;
ideal gI = std(I);
//////////////////////////////////////////////////////////////////////////////////////////////////
LIB "primdec.lib";
ring rng = (integer),(x,y,z),(dp(3),C);
short = 0 ;
ideal I = 9*x*y-1;
ideal J = 13*x^2*y-11*x*y-10*z,12*x^2*z+15*x*z^2-2*y+6,-6*x^2*z-z^3+4*x*y+4;
ideal gI = std(I);
ideal ggI = std(gI);
ideal gJ = std(J);
OK
Make test with
//ring rng = (integer),(x,y,z),dp;
//ideal i = -5*z^2-y*z^2, x^3*y*z-z^2+1, y^2*z^2+5*x^2*y*z;
//ideal gI = std(i);
//ideal ggI = std(gI);
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Open source projects and samples from Microsoft.
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Google
Google ❤️ Open Source for everyone.
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Alibaba
Alibaba Open Source for everyone
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D3
Data-Driven Documents codes.
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Tencent
China tencent open source team.