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D.8.2.10 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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