User:KHiddemann/GeSHi

GeSHi example

An example taken from the CoCoA School 2007 to demonstrate syntax highlighting of CoCoAL code in the Wiki:

Define Reduce(Generators)
-- Generators: List of polynomials
-- returns a set of generators with pairwise different LTs
-- (hence K-linear independent)
  
Generators := NonZero(Generators); -- remove zero polynomials
LinIndGens := [];
 
While Len(Generators) > 0 Do
 
   -- find polynomial with largest LT 
   MaxPoly := Generators[1];
   MaxTerm := LT(MaxPoly);
   MaxPos  := 1;
   For Pos := 2 To Len(Generators) Do
      If LT(Generators[Pos]) > MaxTerm Then
         MaxPoly := Generators[Pos];
         MaxTerm := LT(MaxPoly);
         MaxPos  := Pos
      EndIf
   EndFor;

   MaxPoly := MaxPoly / LC(MaxPoly);
   Append( LinIndGens, MaxPoly);
   Remove( Generators, MaxPos);
 
   -- reduce other polynomials
   For Pos := 1 To Len(Generators) Do
      If LT(Generators[Pos]) = MaxTerm Then       
         Generators[Pos] := Generators[Pos] - LC(Generators[Pos]) * MaxPoly
      EndIf
   EndFor; 
  
   -- remove zero polynomials
   Generators := NonZero(Generators)
EndWhile;
 
Return LinIndGens
EndDefine;

Another example

Another example:

// Exercise: Make one-liners out of these functions...

Define IsVarPower(I,T)
  L := Log(T);
  Return (Len(NonZero(L))=0) Or (Len(NonZero(L))=1 And L[I]<>0);
EndDefine;

Define IsZeroDim(I)
  VP := [[ IsVarPower(N,G) | G In Gens(LT(I)) ] | N In 1..NumIndets() ];
  Return Not FALSE IsIn [ TRUE IsIn L | L In VP];
EndDefine;

// Exercise: Why DO you have to check if your poly is constant?

Define SqFree(F)
  If (F=0 Or Deg(F)=0) Then
    Return 1;
  Elsif (UnivariateIndetIndex(F)=0) Then
    Error("Non-univariate poly "+Sprint(F));
  Else
    Return F/GCD(F, Der(F, Indet(UnivariateIndetIndex(F))));
  EndIf;
EndDefine;

Define ZeroDimRadical(I)
  E := [ Head(Gens(Elim(Diff(Indets(), [X]), I))) | X In Indets() ];
  If 0 IsIn E Then
    Error("Infinite set "+Sprint(I));
  Else
    Return I+Ideal([SqFree(G) | G In E]);
  EndIf;
EndDefine;

Line numbering

Line numbering in action:

Define S_ij(G_i, G_j)
  Return LCM(LT(G_i), LT(G_j))/LT(G_i) * G_i/LC(G_i) - LCM(LT(G_i), LT(G_j))/LT(G_j) * G_j/LC(G_j);
EndDefine;

Define CheckGB(F)
  B := [I | I In (1..Len(F))><(1..Len(F)) And I[1] < I[2]];
  S := [NR(S_ij(F[I[1]], F[I[2]]), F) | I In B];
  Return EqSet(S, [0]);
EndDefine;

R_1 ::= Q[x,y], Lex;
R_2 ::= Q[x,y], DegRevLex;
R_3 ::= Q[x,y,z], Lex;
R_4 ::= Q[x,y,z], DegLex;
R_5 ::= Q[x[1..4]], DegRevLex;

Using R_1 Do
  CheckGB([x^2, xy+y^2, y^3]);
EndUsing;

Using R_2 Do
  CheckGB([x^2-1, xy^2-x]);
EndUsing;

Using R_3 Do
  CheckGB([xy^2-xz+y, xy-z^2, x-yz^4]);
EndUsing;

Using R_4 Do
  CheckGB([x^4y^2-z^5, x^3y^3-1, x^2y^4-2z]);
EndUsing;

Using R_5 Do
  CheckGB([x[1]x[3]-x[2]^2, x[1]x[4]-x[2]x[3], x[2]x[4]-x[3]^2]);
EndUsing;

Custom starting number:

Define CheckGB(F)
  B := [I | I In (1..Len(F))><(1..Len(F)) And I[1] < I[2]];
  S := [NR(S_ij(F[I[1]], F[I[2]]), F) | I In B];
  Return EqSet(S, [0]);
EndDefine;