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VectorCalculus

 Wronskian
 computes the Wronskian of a function f : R -> R^n

 Calling Sequence Wronskian(f, t, det)

Parameters

 f - list(algebraic); a list of expressions defining a function from $ℝ$ to ${ℝ}^{n}$ t - name; the variable of differentiation det - (optional) equation of the form determinant = true or false; specify whether to return the determinant (default: determinant = false)

Description

 • The Wronskian(f, t) command computes the Wronskian Matrix of the function f with respect to the variable t.  This is an $n×n$ Matrix A such that ${A}_{\mathrm{ij}}=\frac{{ⅆ}^{j-1}}{ⅆ{t}^{j-1}}{f}_{i}\left(t\right)$ where $n=\mathrm{nops}\left(f\right)$.
 • The det option specifies whether the determinant of the Wronskian matrix is also returned.  If given as determinant = true, or just determinant, then an expression sequence containing the Wronskian matrix and its determinant is returned.

Examples

 > $\mathrm{with}\left(\mathrm{VectorCalculus}\right):$
 > $\mathrm{Wronskian}\left(\left[\mathrm{exp}\left(t\right),\mathrm{sin}\left(t\right),\mathrm{cos}\left(t\right)\right],t\right)$
 $\left[\begin{array}{ccc}{{ⅇ}}^{{t}}& {\mathrm{sin}}{}\left({t}\right)& {\mathrm{cos}}{}\left({t}\right)\\ {{ⅇ}}^{{t}}& {\mathrm{cos}}{}\left({t}\right)& {-}{\mathrm{sin}}{}\left({t}\right)\\ {{ⅇ}}^{{t}}& {-}{\mathrm{sin}}{}\left({t}\right)& {-}{\mathrm{cos}}{}\left({t}\right)\end{array}\right]$ (1)
 > $\mathrm{Wronskian}\left(\left[{t}^{3},{t}^{4}\right],t\right)$
 $\left[\begin{array}{cc}{{t}}^{{3}}& {{t}}^{{4}}\\ {3}{}{{t}}^{{2}}& {4}{}{{t}}^{{3}}\end{array}\right]$ (2)
 > $\mathrm{Wronskian}\left(\left[{t}^{3},{t}^{4}\right],t,'\mathrm{determinant}'\right)$
 $\left[\begin{array}{cc}{{t}}^{{3}}& {{t}}^{{4}}\\ {3}{}{{t}}^{{2}}& {4}{}{{t}}^{{3}}\end{array}\right]{,}{{t}}^{{6}}$ (3)

Compatibility

 • The determinant option was introduced in Maple 15.