(1) -> V := OVAR [x,y,z]
(1) OrderedVariableList [x,y,z]
Type: Domain
(2) -> P := NSMP(Integer, V)
(2) NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z])
Type: Domain
(3) -> T := RegularChain(Integer, [x,y,z])
(3) RegularChain(Integer,[x,y,z])
Type: Domain
(4) -> lp: List P := [x^2 + y + z -1, x + y^2 +z -1, x + y +z^2 -1]
2 2 2
(4) [x + y + z - 1,x + y + z - 1,x + y + z - 1]
Type: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z])
(5) -> zeroSetSplit(lp)$T
2
(5) [{z + 2z - 1,y - z,x - z},{z,y - 1,x},{z,y,x - 1},{z - 1,y,x}]
Type: List RegularChain(Integer,[x,y,z])
(6) -> )set message time on
(7) -> lp: List P := [x^3 + y + z -1, x + y^3 +z -1, x + y +z^3 -1]
3 3 3
(7) [x + y + z - 1,x + y + z - 1,x + y + z - 1]
Type: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z])
Time: 0.01 (IN) = 0.01 sec
(8) -> zeroSetSplit(lp,true,true)$T
[1 <3,0> -> |3|; {0}]W[2 <4,0>,<2,1> -> |6|; {0}][2 <3,1>,<2,1> -> |5|; {0}]
G[2 <2,1>,<2,1> -> |4|; {0}]WW[3 <2,1>,<2,1>,<1,2> -> |5|; {0}]
Gwwww[5 <3,1>,<3,1>,<3,1>,<2,1>,<1,2> -> |12|; {0}]
GI[5 <2,2>,<3,1>,<3,1>,<2,1>,<1,2> -> |11|; {0}]
GG[5 <1,2>,<3,1>,<3,1>,<2,1>,<1,2> -> |10|; {0}]
[5 <0,3>,<3,1>,<3,1>,<2,1>,<1,2> -> |9|; {0}]
[4 <3,1>,<3,1>,<2,1>,<1,2> -> |9|; {1}]
WW[5 <2,2>,<2,2>,<3,1>,<2,1>,<1,2> -> |10|; {1}]
[5 <1,2>,<2,2>,<3,1>,<2,1>,<1,2> -> |9|; {1}]
W[5 <0,3>,<2,2>,<3,1>,<2,1>,<1,2> -> |8|; {1}]
[4 <2,2>,<3,1>,<2,1>,<1,2> -> |8|; {2}]
[4 <1,2>,<3,1>,<2,1>,<1,2> -> |7|; {2}]
WW[4 <0,3>,<3,1>,<2,1>,<1,2> -> |6|; {2}]
[3 <3,1>,<2,1>,<1,2> -> |6|; {3}]
GIWWW[3 <2,2>,<2,1>,<1,2> -> |5|; {3}]
[3 <1,2>,<2,1>,<1,2> -> |4|; {3}]
WWW[3 <0,3>,<2,1>,<1,2> -> |3|; {3}]
[2 <2,1>,<1,2> -> |3|; {4}]
WWWW[2 <1,2>,<1,2> -> |2|; {4}]
WWWW[2 <0,3>,<1,2> -> |1|; {4}][1 <1,2> -> |1|; {5}]
WWWWW[1 <0,3> -> |0|; {5}]
WwwWwWwWWwwWwWwWwWwWwWwWwwwWwWwwwwWwwwwwwwwww
*** QCMPACK Statistics ***
Table size: 42
Entries reused: 34
*** REGSETGCD: Gcd Statistics ***
Table size: 6
Entries reused: 0
*** REGSETGCD: Inv Set Statistics ***
Table size: 2
Entries reused: 0
(8)
[
7 6 5 4 3 2
{z + z + z - 2z - 2z - 2z - z - 1,
2 2 5 4 3 2 2 3
(z + z + 1)y + (z + z + z - z - z - 1)y + z + z, x + y + z - 1}
,
8 7 6 5 4 3 2 3 3
{z + z + z - 2z - 2z - 2z + 5z + 5z - 3,2y + z - 1,2x + z - 1},
2
{z - 1,y - 1,x + y}, {z,y - 1,x}, {z - 1,y,x}, {z,y,x - 1}]
Type: List RegularChain(Integer,[x,y,z])
Time: 0.09 (EV) + 0.01 (OT) = 0.10 sec
Now we show how to call the AXIOM implementation of lextriangular
V := OVAR [x,y,z]
(1) OrderedVariableList [x,y,z]
Type: Domain
Time: 0.02 (OT) = 0.02 sec
P := NSMP(Integer, V)
(2) NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z])
Type: Domain
Time: 0.01 (IN) = 0.01 sec
pack := LexTriangularPackage(Integer,[x,y,z])
(3) LexTriangularPackage(Integer,[x,y,z])
Type: Domain
Time: 0 sec
lp: List P := [x^2 + y + z -1, x + y^2 +z -1, x + y +z^2 -1]
2 2 2
(4) [x + y + z - 1,x + y + z - 1,x + y + z - 1]
Type: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z])
Time: 0.07 (IN) + 0.05 (OT) + 0.03 (GC) = 0.15 sec
lg := groebner(lp)$pack
2 2 2 2 4 2 6 4 3 2
(5) [x + y + z - 1,y - y - z + z,2z y + z - z ,z - 4z + 4z - z ]
Type: List NewSparseMultivariatePolynomial(Integer,OrderedVariableList [x,y,z])
Time: 0.08 (EV) + 0.01 (OT) + 0.01 (GC) = 0.10 sec
lexTriangular(lg,false)$pack
(6)
2
[{z + 2z - 1,(2z - 1)y + 5z - 2,x + y - 2z}, {z,y,x - 1}, {z - 1,y,x},
{z,y - 1,x}]
Type: List RegularChain(Integer,[x,y,z])
Time: 0.08 (EV) + 0.01 (OT) + 0.01 (GC) = 0.10 sec
lexTriangular(lg,true)$pack
(7)
4 2 2 2 2 2
[{z - 4z + 4z - 1,2y + z - 1,2x + z - 1},{z ,y - y + z,x + y - 1}]
Type: List RegularChain(Integer,[x,y,z])
Time: 0.02 (EV) = 0.02 sec