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D.15.5.7 mDegBasis
Procedure from library multigrading.lib (see multigrading_lib).
- Usage:
- multidegree d
- Assume:
- current ring is multigraded, monomial ordering is global
- Purpose:
- compute all monomials of multidegree d
Example:
| LIB "multigrading.lib";
ring R = 0, (x, y), dp;
intmat g1[2][2]=1,0,0,1;
intmat t[2][1]=2,0;
intmat g2[2][2]=1,1,1,1;
intvec v1=4,0;
intvec v2=4,4;
intmat g3[1][2]=1,1;
setBaseMultigrading(g3);
intvec v3=4:1;
v3;
==> 4
mDegBasis(v3);
==> -------------------------------------------------
==> 4ti2 version 1.3.2, Copyright (C) 2006 4ti2 team.
==> 4ti2 comes with ABSOLUTELY NO WARRANTY.
==> This is free software, and you are welcome
==> to redistribute it under certain conditions.
==> For details, see the file COPYING.
==> -------------------------------------------------
==>
==>
==> Final basis has 1 inhomogeneous, 5 homogeneous and 0 free elements.
==>
==> 4ti2 Total Time: 0.00 secs
==> _[1]=x4
==> _[2]=y4
==> _[3]=xy3
==> _[4]=x2y2
==> _[5]=x3y
setBaseMultigrading(g1,t);
mDegBasis(v1);
==> // ** You are using coefficient rings which are not fields.
==> // ** Please note that only limited functionality is available
==> // ** for these coefficients.
==> // **
==> // ** The following commands are meant to work:
==> // ** - basic polynomial arithmetic
==> // ** - std
==> // ** - syz
==> // ** - lift
==> // ** - reduce
==> -------------------------------------------------
==> 4ti2 version 1.3.2, Copyright (C) 2006 4ti2 team.
==> 4ti2 comes with ABSOLUTELY NO WARRANTY.
==> This is free software, and you are welcome
==> to redistribute it under certain conditions.
==> For details, see the file COPYING.
==> -------------------------------------------------
==>
==>
==> Final basis has 1 inhomogeneous, 1 homogeneous and 0 free elements.
==>
==> 4ti2 Total Time: 0.00 secs
==> _[1]=0
setBaseMultigrading(g2);
mDegBasis(v2);
==> -------------------------------------------------
==> 4ti2 version 1.3.2, Copyright (C) 2006 4ti2 team.
==> 4ti2 comes with ABSOLUTELY NO WARRANTY.
==> This is free software, and you are welcome
==> to redistribute it under certain conditions.
==> For details, see the file COPYING.
==> -------------------------------------------------
==>
==>
==> Final basis has 1 inhomogeneous, 5 homogeneous and 0 free elements.
==>
==> 4ti2 Total Time: 0.00 secs
==> _[1]=y4
==> _[2]=x4
==> _[3]=x3y
==> _[4]=x2y2
==> _[5]=xy3
intmat M[2][2] = 1, -1, -1, 1;
intvec d = -2, 2;
setBaseMultigrading(M);
mDegBasis(d);
==> -------------------------------------------------
==> 4ti2 version 1.3.2, Copyright (C) 2006 4ti2 team.
==> 4ti2 comes with ABSOLUTELY NO WARRANTY.
==> This is free software, and you are welcome
==> to redistribute it under certain conditions.
==> For details, see the file COPYING.
==> -------------------------------------------------
==>
==>
==> Final basis has 1 inhomogeneous, 2 homogeneous and 0 free elements.
==>
==> 4ti2 Total Time: 0.00 secs
==> _[1]=y2
attrib(_, "ZeroPart");
==> _[1]=xy
kill R;
ring R = 0, (x, y, z), dp;
intmat M[2][3] = 1, -2, 1, 1, 1, 0;
==> // ** redefining M **
intmat T[2][1] = 0, 2;
intvec d = 4, 1;
==> // ** redefining d **
setBaseMultigrading(M, T);
mDegBasis(d);
==> -------------------------------------------------
==> 4ti2 version 1.3.2, Copyright (C) 2006 4ti2 team.
==> 4ti2 comes with ABSOLUTELY NO WARRANTY.
==> This is free software, and you are welcome
==> to redistribute it under certain conditions.
==> For details, see the file COPYING.
==> -------------------------------------------------
==>
==>
==> Final basis has 1 inhomogeneous, 9 homogeneous and 0 free elements.
==>
==> 4ti2 Total Time: 0.00 secs
==> _[1]=xz3
==> _[2]=yz6
==> _[3]=x6y
==> _[4]=x3z
attrib(_, "ZeroPart");
==> _[1]=y2z4
==> _[2]=xyz
==> _[3]=x4y2
kill R;
ring R = 0, (x, y, z), dp;
qring Q = std(ideal( y^6+ x*y^3*z-x^2*z^2 ));
intmat M[2][3] = 1, 1, 2, 2, 1, 1;
==> // ** redefining M **
// intmat T[2][1] = 0, 2;
setBaseMultigrading(M);
intvec d = 6, 6;
==> // ** redefining d **
mDegBasis(d);
==> ? Sorry no torsion matrix!
==> ? leaving multigrading.lib::getTorsion
==> ? leaving multigrading.lib::isFreeRepresented
==> ? leaving multigrading.lib::mDegBasis
attrib(_, "ZeroPart");
==>
kill R;
ring R = 0, (x, y, z), dp;
qring Q = std(ideal( x*z^3 - y *z^6, x*y*z - x^4*y^2 ));
==> // ** redefining Q **
intmat M[2][3] = 1, -2, 1, 1, 1, 0;
==> // ** redefining M **
intmat T[2][1] = 0, 2;
==> // ** redefining T **
intvec d = 4, 1;
==> // ** redefining d **
setBaseMultigrading(M, T);
mDegBasis(d);
==> ? Sorry no torsion matrix!
==> ? leaving multigrading.lib::getTorsion
==> ? leaving multigrading.lib::isFreeRepresented
==> ? leaving multigrading.lib::mDegBasis
attrib(_, "ZeroPart");
==>
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