|[ << ]||[ < ]||[ Up ]||[ > ]||[ >> ]||[Top]||[Contents]||[Index]||[ ? ]|
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.
 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] 
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.
If ‘on’, Buchberger’s normal strategy is used instead of sugar strategy.
If ‘on’, criterion B among the Gebauer-Moeller’s criteria is not applied.
If ‘on’, the check that a Groebner basis candidate is indeed a Groebner basis, is not executed.
If ‘on’, the check that the resulting polynomials generates the same ideal as the ideal generated by the input, is not executed.
If ‘on’, the interreduction, which makes the Groebner basis reduced, is not executed.
If ‘on’, content removals are not executed during a Groebner basis computation over a rational function field.
If ‘on’, Only the head term of the polynomial being reduced is reduced.
If ‘on’, the selection strategy of reducer in a normal form computation is such that a newer reducer is used first.
If ‘on’, various informations during a Groebner basis computation is displayed.
If ‘on’ and Print is ‘off’, short information during a Groebner basis computation is displayed.
If ‘on’, a summary of informations is shown after a Groebner basis
computation. Note that the summary is always shown if
If ‘on’ and
If a non-zero rational number, in a normal form computation
over the rationals, the integer content of the polynomial being
reduced is removed when its magnitude becomes
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.
equal to 1, the simiplification is done after every normal form computation.
It is empirically known that it is often efficient to set
Content to 2
for the case where large integers appear during the computation.
An integer value can be set by the keyword
If the value (a character string) is a valid directory name, then generated basis elements are put in the directory and are loaded on demand during normal form computations. Each elements is saved in the binary form and its name coincides with the index internally used in the computation. These binary files are not removed automatically and one should remove them by hand.
 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 
In this example
eval indicate moduli used in
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.
Meaning of each component is as follows.
CPU time for normal form computation (second)
CPU time for content removal(second)
Head term of the generated basis element
Pair of indices which corresponds to the reduced S-polynomial
Number of basis elements after removing redundancy
Number of all the basis elements
Number of remaining pairs
Sugar of the generated basis element
Magnitude of the genrated basis element (shown if
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.
Time to manipulate the list of critical pairs
Time to compute S-polynomials over the rationals
Time to compute S-polynomials over a finite field
Time to compute normal forms over the rationals
Time to compute normal forms over a finite field
Time for zero reductions in
Time to remove integer contets
Time to compute remainders for coefficients of polynomials with coeffieints in the rationals
Time to select pairs from which S-polynomials are computed
Time to interreduce the Groebner basis candidate
Time to check that each input polynomial is a member of the ideal generated by the Groebner basis candidate.
Time to check that the Groebner basis candidate is a Groebner basis
Number of critical pairs generated
B, M, F, D
Number of critical pairs removed by using each criterion
Number of S-polynomials reduced to 0
Number of S-polynomials reduced to non-zero results
Maximal magnitude among all the generated polynomials
|[ << ]||[ < ]||[ Up ]||[ > ]||[ >> ]|
This document was generated on April 22, 2021 using texi2html 5.0.