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D.5.7.2 truncateFast

Procedure from library sheafcoh.lib (see sheafcoh_lib).

Usage:
truncateFast(M,d); M module, d int

Assume:
M is graded, and it comes assigned with an admissible degree vector as an attribute 'isHomog'

Return:
module

Note:
Output is a presentation matrix for the truncation of coker(M) at d.
Fast + experimental version. M shoud be a SB!

Display:
If printlevel>=1, step-by step timings will be printed. If printlevel>=2 we add progress debug messages if printlevel>=3, even all intermediate results...

Example:
 
LIB "sheafcoh.lib";
ring R=0,(x,y,z,u,v),dp;
module M=maxideal(3);
homog(M);
==> 1
// compute presentation matrix for truncated module (R/<x,y,z,u>^3)_(>=2)
int t=timer;
module M2t=truncate(M,2);
t = timer - t;
"// Simple truncate: ", t;
==> // Simple truncate:  0
t=timer;
module M2=truncateFast(std(M),2);
t = timer - t;
"// Fast truncate: ", t;
==> // Fast truncate:  0
print(M2);
==> v,0,0,0,0,0,0,0,0,0,0,0,0,0,0,u, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,z, 0, 0,\
    0, 0, 
==>   0, 0, 0, 0, 0,0,0,0,0,0,y, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0,x, 0,\
    0, 0, 
==>   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
==> 0,v,0,0,0,0,0,0,0,0,0,0,0,0,0,-v,u, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,0, z, 0,\
    0, 0, 
==>   0, 0, 0, 0, 0,0,0,0,0,0,0, y, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0,0, x,\
    0, 0, 
==>   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
==> 0,0,v,0,0,0,0,0,0,0,0,0,0,0,0,0, 0, u, 0, 0, 0,0,0,0,0,0,0,0,0,0,-v,0, z,\
    0, 0, 
==>   0, 0, 0, 0, 0,0,0,0,0,0,0, 0, y, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0,0, 0,\
    x, 0, 
==>   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
==> 0,0,0,v,0,0,0,0,0,0,0,0,0,0,0,0, 0, 0, u, 0, 0,0,0,0,0,0,0,0,0,0,0, 0, 0,\
    z, 0, 
==>   0, 0, 0, 0, 0,0,0,0,0,0,-v,0, 0, y, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,0,0, 0,\
    0, x, 
==>   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
==> 0,0,0,0,v,0,0,0,0,0,0,0,0,0,0,0, 0, 0, 0, u, 0,0,0,0,0,0,0,0,0,0,0, 0, 0,\
    0, z, 
==>   0, 0, 0, 0, 0,0,0,0,0,0,0, 0, 0, 0, y, 0, 0, 0, 0, 0, 0, 0, 0,0,0,-v,0,\
    0, 0, 
==>   x, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
==> 0,0,0,0,0,v,0,0,0,0,0,0,0,0,0,0, -v,0, 0, 0, u,0,0,0,0,0,0,0,0,0,0, 0, 0,\
    0, 0, 
==>   z, 0, 0, 0, 0,0,0,0,0,0,0, 0, 0, 0, 0, y, 0, 0, 0, 0, 0, 0, 0,0,0,0, 0,\
    0, 0, 
==>   0, x, 0, 0, 0, 0, 0, 0, 0, 0, 0,
==> 0,0,0,0,0,0,v,0,0,0,0,0,0,0,0,0, 0, -v,0, 0, 0,u,0,0,0,0,0,0,0,0,0, -v,0,\
    0, 0, 
==>   -u,z, 0, 0, 0,0,0,0,0,0,0, 0, 0, 0, 0, 0, y, 0, 0, 0, 0, 0, 0,0,0,0, 0,\
    0, 0, 
==>   0, 0, x, 0, 0, 0, 0, 0, 0, 0, 0,
==> 0,0,0,0,0,0,0,v,0,0,0,0,0,0,0,0, 0, 0, -v,0, 0,0,u,0,0,0,0,0,0,0,0, 0, 0,\
    0, 0, 
==>   0, 0, z, 0, 0,0,0,0,0,0,0, -v,0, 0, 0, -u,0, y, 0, 0, 0, 0, 0,0,0,0, 0,\
    0, 0, 
==>   0, 0, 0, x, 0, 0, 0, 0, 0, 0, 0,
==> 0,0,0,0,0,0,0,0,v,0,0,0,0,0,0,0, 0, 0, 0, -v,0,0,0,u,0,0,0,0,0,0,0, 0, 0,\
    0, 0, 
==>   0, 0, 0, z, 0,0,0,0,0,0,0, 0, 0, 0, 0, 0, 0, 0, y, 0, 0, 0, 0,0,0,0, -v\
   ,0, 0, 
==>   0, -u,0, 0, x, 0, 0, 0, 0, 0, 0,
==> 0,0,0,0,0,0,0,0,0,v,0,0,0,0,0,0, 0, 0, 0, 0, 0,0,0,0,u,0,0,0,0,0,0, 0, -v\
   ,0, 0, 
==>   0, -u,0, 0, z,0,0,0,0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, y, 0, 0, 0,0,0,0, 0,\
    0, 0, 
==>   0, 0, 0, 0, 0, x, 0, 0, 0, 0, 0,
==> 0,0,0,0,0,0,0,0,0,0,v,0,0,0,0,0, 0, 0, 0, 0, 0,0,0,0,0,u,0,0,0,0,0, 0, 0,\
    -v,0, 
==>   0, 0, -u,0, 0,z,0,0,0,0,0, 0, -v,0, 0, 0, -u,0, 0, -z,y, 0, 0,0,0,0, 0,\
    0, 0, 
==>   0, 0, 0, 0, 0, 0, x, 0, 0, 0, 0,
==> 0,0,0,0,0,0,0,0,0,0,0,v,0,0,0,0, 0, 0, 0, 0, 0,0,0,0,0,0,u,0,0,0,0, 0, 0,\
    0, -v,
==>   0, 0, 0, -u,0,0,z,0,0,0,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, y, 0,0,0,0, 0,\
    -v,0, 
==>   0, 0, -u,0, 0, -z,0, x, 0, 0, 0,
==> 0,0,0,0,0,0,0,0,0,0,0,0,v,0,0,0, 0, 0, 0, 0, 0,0,0,0,0,0,0,u,0,0,0, 0, 0,\
    0, 0, 
==>   0, 0, 0, 0, 0,0,0,z,0,0,0, 0, 0, -v,0, 0, 0, -u,0, 0, -z,0, y,0,0,0, 0,\
    0, 0, 
==>   0, 0, 0, 0, 0, 0, 0, 0, x, 0, 0,
==> 0,0,0,0,0,0,0,0,0,0,0,0,0,v,0,0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,u,0,0, 0, 0,\
    0, 0, 
==>   0, 0, 0, 0, 0,0,0,0,z,0,0, 0, 0, 0, -v,0, 0, 0, -u,0, 0, -z,0,y,0,0, 0,\
    0, -v,
==>   0, 0, 0, -u,0, 0, -z,0, -y,x, 0,
==> 0,0,0,0,0,0,0,0,0,0,0,0,0,0,v,0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,u,0, 0, 0,\
    0, 0, 
==>   0, 0, 0, 0, 0,0,0,0,0,z,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0,y,0, 0,\
    0, 0, 
==>   -v,0, 0, 0, -u,0, 0, -z,0, -y,x 
"// Check: M2t == M2?: ", size(NF(M2, std(M2t))) + size(NF(M2t, std(M2)));
==> // Check: M2t == M2?:  0
dimGradedPart(M2,1);
==> 0
dimGradedPart(M2,2);
==> 15
// this should coincide with:
dimGradedPart(M,2);
==> 15
// shift grading by 1:
intvec v=1;
attrib(M,"isHomog",v);
t=timer;
M2t=truncate(M,2);
t = timer - t;
"// Simple truncate: ", t;
==> // Simple truncate:  0
t=timer;
M2=truncateFast(std(M),2);
t = timer - t;
"// Fast truncate: ", t;
==> // Fast truncate:  0
print(M2);
==> u, z, 0, y, 0, 0, x, 0, 0, 0, v2,0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0\
   , 0, 
==>   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
==> -v,0, z, 0, y, 0, 0, x, 0, 0, 0, v2,0, 0, 0, uv,0, 0, 0, 0, 0, 0, 0, 0, 0\
   , u2,
==>   0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
==> 0, -v,-u,0, 0, y, 0, 0, x, 0, 0, 0, v2,0, 0, 0, uv,0, 0, zv,0, 0, 0, 0, 0\
   , 0, 
==>   u2,0, 0, zu,0, 0, 0, 0, 0, z2,0, 0, 0, 0, 0, 0, 0, 0, 0,
==> 0, 0, 0, -v,-u,-z,0, 0, 0, x, 0, 0, 0, v2,0, 0, 0, uv,0, 0, zv,0, yv,0, 0\
   , 0, 
==>   0, u2,0, 0, zu,0, yu,0, 0, 0, z2,0, yz,0, 0, y2,0, 0, 0,
==> 0, 0, 0, 0, 0, 0, -v,-u,-z,-y,0, 0, 0, 0, v2,0, 0, 0, uv,0, 0, zv,0, yv,x\
   v,0, 
==>   0, 0, u2,0, 0, zu,0, yu,xu,0, 0, z2,0, yz,xz,0, y2,xy,x2
"// Check: M2t == M2?: ", size(NF(M2, std(M2t))) + size(NF(M2t, std(M2))); //?
==> // Check: M2t == M2?:  20
dimGradedPart(M2,3);
==> 15