symmfunc - Maple Help

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type/symmfunc

check for a symmetric function

 Calling Sequence type(f, symmfunc(x, y, ...))

Parameters

 f - function x, y, ... - name(s)

Description

 • This procedure tests the symmetry of the function f with respect to the argument(s) $\mathrm{x,y},...$.
 • It returns true if f is symmetric in all of the given variables, and false otherwise.

Examples

 > $\mathrm{type}\left(xy,\mathrm{symmfunc}\left(x,y\right)\right)$
 ${\mathrm{true}}$ (1)
 > $\mathrm{type}\left(x\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}&*\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}y,\mathrm{symmfunc}\left(x,y\right)\right)$
 ${\mathrm{false}}$ (2)
 > $f≔\mathrm{&*}\left(a,b,c\right)+\mathrm{&*}\left(b,c,a\right)+\mathrm{&*}\left(c,a,b\right)+\mathrm{&*}\left(b,a,c\right)+\mathrm{&*}\left(a,c,b\right)+\mathrm{&*}\left(c,b,a\right)$
 ${f}{≔}{\mathrm{&*}}{}\left({a}{,}{b}{,}{c}\right){+}{\mathrm{&*}}{}\left({b}{,}{c}{,}{a}\right){+}{\mathrm{&*}}{}\left({c}{,}{a}{,}{b}\right){+}{\mathrm{&*}}{}\left({b}{,}{a}{,}{c}\right){+}{\mathrm{&*}}{}\left({a}{,}{c}{,}{b}\right){+}{\mathrm{&*}}{}\left({c}{,}{b}{,}{a}\right)$ (3)
 > $\mathrm{type}\left(f,\mathrm{symmfunc}\left(a,b,c\right)\right)$
 ${\mathrm{true}}$ (4)

Note that any function of a single variable is symmetric in that variable:

 > $\mathrm{type}\left(g\left(x\right),\mathrm{symmfunc}\left(x\right)\right)$
 ${\mathrm{true}}$ (5)

 See Also