mathematical dependence - Maple Help

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type/dependent

check for mathematical dependence

 Calling Sequence type(f, dependent(x))

Parameters

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

Description

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

Examples

 > $\mathrm{type}\left(x,\mathrm{dependent}\left(\left\{x,y\right\}\right)\right)$
 ${\mathrm{true}}$ (1)
 > $\mathrm{type}\left(\left[a,b\right],\mathrm{dependent}\left(\left[c,d\right]\right)\right)$
 ${\mathrm{false}}$ (2)
 > $\mathrm{type}\left({x}^{y},{\mathrm{identical}\left(x\right)}^{\mathrm{dependent}\left(x\right)}\right)$
 ${\mathrm{false}}$ (3)
 > $\mathrm{type}\left({∫}_{a}^{b}f\left(x\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}ⅆx,\mathrm{dependent}\left(x\right)\right)$
 ${\mathrm{false}}$ (4)
 > $\mathrm{type}\left({∫}_{a}^{b}f\left(x\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}ⅆx,\mathrm{dependent}\left(a\right)\right)$
 ${\mathrm{true}}$ (5)