up previous next
PrintBettiNumbers

print the (multi-)graded Betti numbers

Syntax
PrintBettiNumbers(M: IDEAL|MODULE|Resolution)

Description
This function prints the Betti numbers for M .

Example
/**/ M := MakeTermOrd(matrix([[5,5,5,1,1], [1,1,1,0,0]]));
/**/ P := NewPolyRing(QQ, "t[1],t[2],t[3],x,y", M, 2); -- ZZ^2-grading
/**/ use P;
/**/ I := ideal(t[1]^6 -t[3]^6, t[2]^6 -t[1]^5*t[3], t[1]*t[3]*x^8 -t[2]^2*y^8);
/**/ RES := res(P/I);
/**/ PrintRes(RES);
0 --> R[-78,-14] --> R[-48,-8]^2(+)R[-60,-12] --> R[-18,-2](+)R[-30,-6]^2 --> R

/**/ PrintBettiNumbers(RES);  --> just prints in a readable way
----- 1 -----------
----- 2 -----------
  [18,  2]: 1
  [30,  6]: 2
----- 3 -----------
  [48,  8]: 2
  [60,  12]: 1
----- 4 -----------
  [78,  14]: 1
-------------------

/**/ BettiNumbers(RES);  --> returns the value for further computations
[[],  [[[18,  2],  1],  [[30,  6],  2]],  [[[48,  8],  2],
 [[60,  12],  1]],  [[[78,  14],  1]]]

See Also