 mathematical independence - Maple Help

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type/freeof

check for mathematical independence Calling Sequence type(f, freeof(x)) Parameters

 f - expression or list or set of expressions x - name or list or set of names Description

 • Returns true if all of the expressions in f are mathematically independent of all the names contained in x.
 • The definition of mathematical dependence is that used by depends. For more information, see depends. Examples

 > $\mathrm{type}\left(x,\mathrm{freeof}\left(\left\{x,y\right\}\right)\right)$
 ${\mathrm{false}}$ (1)
 > $\mathrm{type}\left(\left[a,b\right],\mathrm{freeof}\left(\left[c,d\right]\right)\right)$
 ${\mathrm{true}}$ (2)
 > $\mathrm{type}\left({x}^{y},{\mathrm{identical}\left(x\right)}^{\mathrm{freeof}\left(x\right)}\right)$
 ${\mathrm{true}}$ (3)
 > $\mathrm{type}\left(\mathrm{int}\left(f\left(x\right),x=a..b\right),\mathrm{freeof}\left(x\right)\right)$
 ${\mathrm{true}}$ (4)
 > $\mathrm{type}\left(\mathrm{int}\left(f\left(x\right),x=a..b\right),\mathrm{freeof}\left(a\right)\right)$
 ${\mathrm{false}}$ (5)