This routine is used to return a new problem of reduced order from a problem and one or many partial solutions.  The result is an RESol data structure of the new problem.  No attempt is made to solve the reduced problem.

partsol may be a single partial solution, or a list of partial solutions.  Note that it is assumed all given partial solutions are correct and valid.  When a reduced problem is returned, the order of the resulting problem will be equal to the order of the original less the number of partial solutions given.

If multiple partial solutions are given, the problem is reduced recursively starting with the first solution in the list.  The other solutions are then also 'reduced' to solutions of the new problem, and reducing is then called on the rest.

The command with(LREtools,REreduceorder) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{LREtools}\right)\:$

$\mathrm{REreduceorder}\left(2na\left(n+2\right)+\left(n^2+1\right)a\left(n+1\right)-{\left(n+1\right)}^{2}a\left(n\right)=0\,a\left(n\right)\,\varnothing \,\mathrm{C1}\right)$

$\mathrm{RESol}\left(\left\{\left(-n^2-2n-1\right)a\left(n\right)-2na\left(n+1\right)=0\right\}\,\left\{a\left(n\right)\right\}\,\left\{a\left(0\right)=0\,a\left(1\right)=a\left(1\right)\right\}\,\mathrm{INFO}\right)$

$\mathrm{REreduceorder}\left(a\left(n+2\right)-2a\left(n+1\right)+a\left(n\right)=0\,a\left(n\right)\,\varnothing \,\mathrm{C1}n\right)$

$\mathrm{RESol}\left(\left\{na\left(n\right)+\left(-n-2\right)a\left(n+1\right)=0\right\}\,\left\{a\left(n\right)\right\}\,\left\{a\left(0\right)=a\left(0\right)\right\}\,\mathrm{INFO}\right)$