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  1. denseform(n, coeff)={
  2.   local(f); f = vector(n);
  3.   for(i=1, matsize(coeff)[1], f[coeff[i,1]]+=coeff[i,2]);
  4.   f;
  5. }
  6.  
  7. \\ inequality t_{ij} > t_{ik}, that is, (k-j)v_i + (i-k) v_j + (j-i) v_k > 0
  8. \\ (for i < j < k)
  9. collideright(n, i,j,k)=denseform(n, [i, k-j; j, i-k; k, j-i]);
  10. collideleft(n, i,j,k) =-collideright(n, i,j,k);
  11. collide(n, i,j) = denseform(n, [i,1;j,-1]);
  12. notcollide(n, i,j) = -collide(n, i, j);
  13.  
  14. ineq(s)={
  15.   local(l, d, depth, match, R);
  16.   l=Vec(s); depth=vector(#l); d=0;
  17.   for(i=1, #l, depth[i]=d; d+=(l[i]=="(")-(l[i]==")"));
  18.   match=vector(#l);
  19.   for(i=1, #l, if(l[i]=="(", for(j=i+1, #l,
  20.     if(depth[j]==depth[i]+1 && l[j]==")", match[i]=j; match[j]=i; next (2)))));
  21.  
  22.   R=[];
  23.   for(i1=1,#l,
  24.     if (l[i1] == "(", j1=match[i1];
  25.       \\ (): v_i > v_j
  26.       R = concat(R, [collide(#l, i1, j1)]);
  27.       \\ (())
  28.       for (i2=i1+1, j1-1, if (l[i2] == "(", j2=match[i2];
  29.         R = concat (R,
  30.           [collideright (#l, i1, i2, j2), collideleft (#l, i2, j2, j1)])));
  31.       \\ ()()
  32.       for (i2=j1+1, #l, if (l[i2] == "(", j2=match[i2];
  33.         R = concat (R,
  34.           [collideleft (#l, i1, j1, i2), collideright (#l, j1, i2, j2)])))
  35.     , if (l[i1] != ")", \\ escaped bullet
  36.       \\ !! and !()
  37.       for (i2=i1+1, #l, if (l[i2]!=")",
  38.         R = concat (R, [notcollide (#l, i1, i2)])));
  39.       \\ ()!  (!! already done)
  40.       for (i2=1, i1-1, if (l[i2]==")",
  41.         R = concat (R, [notcollide (#l, i2, i1)])));
  42.     ))
  43.   );
  44.   R;
  45. }
  46. polytope(s)={
  47.   local(R); R=ineq(s);
  48.   concat([vector(#R, i, vector(#s+1,j,if(j<=#s, R[i][j]))),
  49.     vector(#s,i, vector(#s+1,j, j==i)),
  50.     vector(#s,i, vector(#s+1,j, (j>#s)-(j==i)))]);
  51. }
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