Singular Manual: multiDegBasis

| #### D.15.11.31 multiDegBasis Procedure from library `multigrading.lib` (see multigrading_lib). Usage: multiDegBasis(d), multidegree: intvec 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 l[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
    multiDegBasis(v3);
    ==>    ? Sorry: cannot find 'hilbert' command from 4ti2. Please install 4ti2!
    ==>    ? leaving multigrading.lib::hilbert4ti2intmat (0)
    ==>    ? leaving multigrading.lib::multiDegBasis (3317)
    setBaseMultigrading(g1,l);
    multiDegBasis(v1);
    ==>    ? Sorry: cannot find 'hilbert' command from 4ti2. Please install 4ti2!
    ==>    ? leaving multigrading.lib::hilbert4ti2intmat (0)
    ==>    ? leaving multigrading.lib::multiDegBasis (3344)
    setBaseMultigrading(g2);
    multiDegBasis(v2);
    ==>    ? Sorry: cannot find 'hilbert' command from 4ti2. Please install 4ti2!
    ==>    ? leaving multigrading.lib::hilbert4ti2intmat (0)
    ==>    ? leaving multigrading.lib::multiDegBasis (3317)
    intmat M[2][2] = 1, -1, -1, 1;
    intvec d = -2, 2;
    setBaseMultigrading(M);
    multiDegBasis(d);
    ==>    ? Sorry: cannot find 'hilbert' command from 4ti2. Please install 4ti2!
    ==>    ? leaving multigrading.lib::hilbert4ti2intmat (0)
    ==>    ? leaving multigrading.lib::multiDegBasis (3317)
    attrib(_, "ZeroPart");
    ==>
    kill R, M, d;
    ring R = 0, (x, y, z), dp;
    intmat M[2][3] = 1, -2, 1,     1, 1, 0;
    intmat L[2][1] = 0, 2;
    intvec d = 4, 1;
    setBaseMultigrading(M, L);
    multiDegBasis(d);
    ==>    ? Sorry: cannot find 'hilbert' command from 4ti2. Please install 4ti2!
    ==>    ? leaving multigrading.lib::hilbert4ti2intmat (0)
    ==>    ? leaving multigrading.lib::multiDegBasis (3344)
    attrib(_, "ZeroPart");
    ==>
    kill R, M, d;
    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;
    //  intmat T[2][1] = 0, 2;
    setBaseMultigrading(M); // BUG????
    intvec d = 6, 6;
    multiDegBasis(d);
    ==>    ? Sorry: cannot find 'hilbert' command from 4ti2. Please install 4ti2!
    ==>    ? leaving multigrading.lib::hilbert4ti2intmat (0)
    ==>    ? leaving multigrading.lib::multiDegBasis (3317)
    attrib(_, "ZeroPart");
    ==>
    kill R, Q, M, d;
    ring R = 0, (x, y, z), dp;
    qring Q = std(ideal( x*z^3 - y *z^6, x*y*z  - x^4*y^2 ));
    intmat M[2][3] = 1, -2, 1,     1, 1, 0;
    intmat T[2][1] = 0, 2;
    intvec d = 4, 1;
    setBaseMultigrading(M, T); // BUG????
    multiDegBasis(d);
    ==>    ? Sorry: cannot find 'hilbert' command from 4ti2. Please install 4ti2!
    ==>    ? leaving multigrading.lib::hilbert4ti2intmat (0)
    ==>    ? leaving multigrading.lib::multiDegBasis (3344)
    attrib(_, "ZeroPart");
    ==>

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