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D.7.1.10 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 proc
gauss_rowfrom ’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 = i-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]=3z-8u+20 → _[3]=18y-6z+7u+14 → _[4]=13x+8y+6z-7u-1 → |