Singular Manual: solvelinearpart

| #### D.8.3.10 solvelinearpart Procedure from library `presolve.lib` (see presolve_lib). Usage: solvelinearpart(id [,n] ); id=ideal/module, n=integer (default: n=0) Return: (interreduced) generators of id of degree <=1 in reduced triangular form if n=0 [non-reduced triangular form if n!=0] Assume: monomial ordering is a global ordering (p-ordering) Note: may be used to solve a system of linear equations, see `gauss_row` from 'matrix.lib' for a different method Warning: the result is very likely to be false for 'real' coefficients, use char 0 instead! Example:
    LIB "presolve.lib";
    // Solve the system of linear equations:
    //         3x +   y +  z -  u = 2
    //         3x +  8y + 6z - 7u = 1
    //        14x + 10y + 6z - 7u = 0
    //         7x +  4y + 3z - 3u = 3
    ring r = 0,(x,y,z,u),lp;
    ideal i= 3x +   y +  z -  u,
    13x +  8y + 6z - 7u,
    14x + 10y + 6z - 7u,
    7x +  4y + 3z - 3u;
    ideal j= 2,1,0,3;
    j = matrix(i)-matrix(j);        // difference of 1x4 matrices
    // compute reduced triangular form, setting
    solvelinearpart(j);             // the RHS equal 0 gives the solutions!
    ==> _[1]=u-4
    ==> _[2]=z-4
    ==> _[3]=y+1
    ==> _[4]=x-1
    solvelinearpart(j,1); "";       // triangular form, not reduced
    ==> _[1]=u-4
    ==> _[2]=2z-u-4
    ==> _[3]=11y+5z-8u+23
    ==> _[4]=3x+y+z-u-2
    ==>

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