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solve/symbolic

expressions involving branch cuts

 Calling Sequence solve(eqns, vars, symbolic)

Parameters

 eqns - equations (as for solve) vars - variables (as for solve)

Description

 • The symbolic option to the solve command controls whether solve will attempt to account for branch cuts in the input equations and build piecewise expressions that are correct for substitution of parameters. Specifying $\mathrm{symbolic}$ or $\mathrm{symbolic}=\mathrm{true}$ will ignore branch cuts, while $\mathrm{symbolic}=\mathrm{false}$ will cause piecewise expressions to be constructed if necessary.
 • The symbolic option to solve currently defaults to true but the default is expected to change in a future version of Maple.  Applications that rely on the current branch cut behavior should add $\mathrm{symbolic}=\mathrm{true}$ to their calls to solve.

Examples

Only the output with symbolic=false is correct for substitutions on the parameters such as $a=1$.

 > $\mathrm{expr}≔a=\sqrt{a+y}+1$
 ${\mathrm{expr}}{≔}{a}{=}\sqrt{{a}{+}{y}}{+}{1}$ (1)
 > $\mathrm{solve}\left(\mathrm{expr},\left[y\right],\mathrm{symbolic}=\mathrm{true}\right)$
 $\left[\left[{y}{=}{{a}}^{{2}}{-}{3}{}{a}{+}{1}\right]\right]$ (2)
 > $\mathrm{solve}\left(\mathrm{expr},\left[y\right],\mathrm{symbolic}=\mathrm{false}\right)$
 $\left\{\begin{array}{cc}\left[\left[{y}{=}{{a}}^{{2}}{-}{3}{}{a}{+}{1}\right]\right]& {2}{}{\mathrm{arg}}{}\left({a}{-}{1}\right){\le }{\mathrm{\pi }}{\wedge }{-}{\mathrm{\pi }}{<}{2}{}{\mathrm{arg}}{}\left({a}{-}{1}\right)\\ \left[\right]& {\mathrm{otherwise}}\end{array}\right\$ (3)
 > $\mathrm{solve}\left(\genfrac{}{}{0}{}{\mathrm{expr}}{\phantom{a=-1}}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}|\phantom{\rule[-0.0ex]{0.1em}{0.0ex}}\genfrac{}{}{0}{}{\phantom{\mathrm{expr}}}{a=-1},\left[y\right]\right)$
 $\left[\right]$ (4)

Compatibility

 • The symbolic option was introduced in Maple 17.
 • For more information on Maple 17 changes, see Updates in Maple 17.