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LREtools

 REcreate
 create an RESol from a recurrence equation

 Calling Sequence REcreate(eqns, fcns, inits)

Parameters

 eqns - single equation or a set of equations fcns - function name or set of function names inits - set of initial conditions

Description

 • The first argument should be a single recurrence relation or a set of recurrence relations.  Any expressions in eqns which are not equations will be understood to be equal to zero.
 • The second argument fcns indicates the functions from eqns over which they are considered to be recurrences.  The names must always be entered in the form function(var).
 • The third argument inits is a set of initial conditions on the functions fcns.
 • The result of an REcreate call is an RESol data-structure, which is much easier to handle than a raw recurrence equation.
 • In the rest of this package, a problem is synonymous with either valid input for REcreate or a valid RESol data structure.

Examples

 > $\mathrm{LREtools}\left[\mathrm{REcreate}\right]\left(\left(18+12n\right)t\left(n\right)+\left(-20-7n\right)t\left(n+1\right)+\left(4+n\right)t\left(n+2\right),t\left(n\right),\left\{t\left(0\right)=0,t\left(1\right)=2\right\}\right)$
 ${\mathrm{RESol}}{}\left(\left\{\left({18}{+}{12}{}{n}\right){}{t}{}\left({n}\right){+}\left({-}{20}{-}{7}{}{n}\right){}{t}{}\left({n}{+}{1}\right){+}\left({4}{+}{n}\right){}{t}{}\left({n}{+}{2}\right){=}{0}\right\}{,}\left\{{t}{}\left({n}\right)\right\}{,}\left\{{t}{}\left({0}\right){=}{0}{,}{t}{}\left({1}\right){=}{2}\right\}{,}{\mathrm{INFO}}\right)$ (1)
 > $\mathrm{rec}≔a\left(n+2\right)-\frac{\left(2n+1\right)a\left(n+1\right)}{n}+\frac{na\left(n\right)}{n-1}=n\left(n+1\right):$
 > $\mathrm{LREtools}\left[\mathrm{REcreate}\right]\left(\mathrm{rec},a\left(n\right),\varnothing \right)$
 ${\mathrm{RESol}}{}\left(\left\{{{n}}^{{2}}{}{a}{}\left({n}\right){+}\left({-}{2}{}{{n}}^{{2}}{+}{n}{+}{1}\right){}{a}{}\left({n}{+}{1}\right){+}\left({{n}}^{{2}}{-}{n}\right){}{a}{}\left({n}{+}{2}\right){=}{{n}}^{{2}}{}\left({n}{-}{1}\right){}\left({n}{+}{1}\right)\right\}{,}\left\{{a}{}\left({n}\right)\right\}{,}\left\{{a}{}\left({1}\right){=}{0}{,}{a}{}\left({2}\right){=}{a}{}\left({2}\right){,}{a}{}\left({3}\right){=}{a}{}\left({3}\right)\right\}{,}{\mathrm{INFO}}\right)$ (2)