One can cotrol a Groebner basis computation by setting various parameters.
These parameters can be set and examined by a built-in function
dp_gr_flags()
. Without argument it returns the current settings.
[100] dp_gr_flags(); [Demand,0,NoSugar,0,NoCriB,0,NoGC,0,NoMC,0,NoRA,0,NoGCD,0,Top,0,ShowMag,1, Print,1,Stat,0,Reverse,0,InterReduce,0,Multiple,0] [101]
The return value is a list which contains the names of parameters and their values. The meaning of the parameters are as follows. `on' means that the parameter is not zero.
NoSugar
NoCriB
NoGC
NoMC
NoRA
NoGCD
Top
Reverse
Print
Stat
Print
is `on'.
ShowMag
Print
is `on', the sum of bit length of
coefficients of a generated basis element, which we call magnitude,
is shown after every normal computation. After comleting the
computation the maximal value among the sums is shown.
Multiple
Multiple
times
larger than a registered value, which is set to the magnitude of the
input polynomial. After each content removal the registered value is
set to the magnitude of the resulting polynomial. Multiple
is
equal to 1, the simiplification is done after every normal form computation.
It is empirically known that it is often efficient to set Multiple
to 2
for the case where large integers appear during the computation.
Demand
If Print
is `on', the following informations are shown.
[93] gr(cyclic(4),[c0,c1,c2,c3],0)$ mod= 99999989, eval = [] (0)(0)<<0,2,0,0>>(2,3),nb=2,nab=5,rp=2,sugar=2,mag=4 (0)(0)<<0,1,2,0>>(1,2),nb=3,nab=6,rp=2,sugar=3,mag=4 (0)(0)<<0,1,1,2>>(0,1),nb=4,nab=7,rp=3,sugar=4,mag=6 . (0)(0)<<0,0,3,2>>(5,6),nb=5,nab=8,rp=2,sugar=5,mag=4 (0)(0)<<0,1,0,4>>(4,6),nb=6,nab=9,rp=3,sugar=5,mag=4 (0)(0)<<0,0,2,4>>(6,8),nb=7,nab=10,rp=4,sugar=6,mag=6 ....gb done reduceall ....... membercheck (0,0)(0,0)(0,0)(0,0) gbcheck total 8 pairs ........ UP=(0,0)SP=(0,0)SPM=(0,0)NF=(0,0)NFM=(0.010002,0)ZNFM=(0.010002,0)PZ=(0,0) NP=(0,0)MP=(0,0)RA=(0,0)MC=(0,0)GC=(0,0)T=40,B=0 M=8 F=6 D=12 ZR=5 NZR=6 Max_mag=6 [94]
In this example mod
and eval
indicate moduli used in
trace-lifting. mod
is a prime and eval
is a list of integers
used for evaluation when the ground field is a field of rational functions.
The following information is shown after every normal form computation.
(TNF)(TCONT)HT(INDEX),nb=NB,nab=NAB,rp=RP,sugar=S,mag=M
Meaning of each component is as follows.
TNF
TCONT
HT
INDEX
NB
NAB
RP
S
M
ShowMag
is `on'.)
The summary of the informations shown after a Groebner basis computation is as follows. If a component shows timings and it contains two numbers, they are a pair of time for computation and time for garbage colection.
UP
SP
SPM
NF
NFM
ZNFM
NFM
PZ
NP
MP
RA
MC
GC
T
B, M, F, D
ZR
NZR
Max_mag
Go to the first, previous, next, last section, table of contents.