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CallOnGroebnerFanIdeals

apply a function to Groebner fan ideals

Syntax
CallOnGroebnerFanIdeals(I: IDEAL, FUN: FUNCTION)

Description
Storing all the possible different (reduced) GBases in a Groebner fan is practicable only for a small example; larger ideals may have thousands or even millions of different Groebner bases. Typically we are interested only in those bases satisfying a certain property.

This function calls a given function on each Groebner bases (stored in an ideal in a suitable ring) successively, without having to store them all in a big list.

Verbosity: see GroebnerFanIdeals .

Note: using this needs a little technical ability, but might make the difference between getting an answer or fill up the computer's memory.

Example
-- print ord and GBasis if ideal I has GBases of length 3:
/**/ define PrintIfGBHasLen3(I)
/**/   if len(GBasis(I))=3 then
/**/     println OrdMat(RingOf(I));
/**/     indent(ReducedGBasis(I));
/**/   endif;
/**/ enddefine;

/**/ use R ::= QQ[a,b,c];
/**/ I := ideal(a^5+b^3+c^2-1, b^2+a^2+c-1, c^3+a^6+b^5-1);
/**/ SetVerbosityLevel(10);
/**/ CallOnGroebnerFanIdeals(I, PrintIfGBHasLen3);
******************************************************(....)
matrix(ZZ,
 [[3, 7, 7],
  [3, 6, 8],
  [0, 0, -1]])
[b^2+c+a^2-1,
 a^5+c^2-b*c-a^2*b+b-1,
 c^3+b*c^2+2*a^2*b*c+a^4*b-a*c^2+a*b*c+a^3*b-2*b*c-2*a^2*b-a*b+b+a-1]
*
matrix(ZZ,
 [[6, 7, 14],
  [6, 5, 15],
  [0, 0, -1]])
[c+b^2+a^2-1,
 -b^6-3*a^2*b^4-3*a^4*b^2+b^5+3*b^4+6*a^2*b^2+3*a^4-3*b^2-3*a^2,
 a^5+b^4+2*a^2*b^2+a^4+b^3-2*b^2-2*a^2]
******************************************************(....)

See Also