Combine - Maple Help

SolveTools

 Combine
 perform various combining of the expressions

 Calling Sequence Combine(expr, options)

Parameters

 expr - expression options - (optional) one or more of 'ln', 'exp', or 'power'

Description

 • The Combine command combines expressions.
 • The Combine command performs the following transformations after calling SolveTools[CancelInverses] on the expr first.
 • If the option 'ln' is specified, the transformation is the following.

$aj\mathrm{ln}\left(x\right)+\dots +ai\mathrm{ln}\left(y\right)\to a\mathrm{ln}\left({x}^{j}{y}^{i}\right)+\dots$

 • If the option 'exp' is specified, the transformations are the following.

$\mathrm{exp}{\left(x\right)}^{i}\dots \mathrm{exp}{\left(y\right)}^{j}\to \mathrm{exp}\left(ix+jy\right)\dots$

$\mathrm{exp}{\left(x\right)}^{b}\to \mathrm{exp}\left(xb\right)$

 • If the option 'power' is specified, the transformations are the following.

${\left({x}^{b}\right)}^{i}\dots {\left({x}^{c}\right)}^{j}\to {x}^{ib+jc}\dots$

${\left({x}^{y}\right)}^{z}\to {x}^{yz}$

${a}^{b}\to \mathrm{exp}\left(b\mathrm{ln}\left(a\right)\right)$

 The last transformation is only done if ${ⅇ}^{b\mathrm{ln}\left(a\right)}$ is already present.
 • In all of the previous transformations, i and j denote integers.
 • If no options are specified, all combinations are performed.
 Note: Not all simplifications are valid everywhere. You should be aware of this when calling Combine.

Examples

 > $\mathrm{with}\left(\mathrm{SolveTools}\right):$
 > $\mathrm{Combine}\left(3x\mathrm{ln}\left(y\right)+4x\mathrm{ln}\left(z\right)+{\left(\mathrm{exp}\left(t\right)\right)}^{5}{\left(\mathrm{exp}\left(s\right)\right)}^{6}\right)$
 ${{ⅇ}}^{{5}{}{t}{+}{6}{}{s}}{+}{x}{}{\mathrm{ln}}{}\left({{y}}^{{3}}{}{{z}}^{{4}}\right)$ (1)
 > $\mathrm{Combine}\left(3x\mathrm{ln}\left(y\right)+4x\mathrm{ln}\left(z\right)+{\left(\mathrm{exp}\left(t\right)\right)}^{5}{\left(\mathrm{exp}\left(s\right)\right)}^{6},'\mathrm{ln}'\right)$
 ${\left({{ⅇ}}^{{t}}\right)}^{{5}}{}{\left({{ⅇ}}^{{s}}\right)}^{{6}}{+}{x}{}{\mathrm{ln}}{}\left({{y}}^{{3}}{}{{z}}^{{4}}\right)$ (2)
 > $\mathrm{Combine}\left(3x\mathrm{ln}\left(y\right)+4x\mathrm{ln}\left(z\right)+{\left(\mathrm{exp}\left(t\right)\right)}^{5}{\left(\mathrm{exp}\left(s\right)\right)}^{6},'\mathrm{exp}'\right)$
 ${3}{}{x}{}{\mathrm{ln}}{}\left({y}\right){+}{4}{}{x}{}{\mathrm{ln}}{}\left({z}\right){+}{{ⅇ}}^{{5}{}{t}{+}{6}{}{s}}$ (3)
 > $\mathrm{Combine}\left({\left({x}^{y}\right)}^{5}+{\left({x}^{z}\right)}^{6}+5t\mathrm{ln}\left(z\right)+6t\mathrm{ln}\left(x\right),'\mathrm{power}'\right)$
 ${{x}}^{{5}{}{y}}{+}{{x}}^{{6}{}{z}}{+}{5}{}{t}{}{\mathrm{ln}}{}\left({z}\right){+}{6}{}{t}{}{\mathrm{ln}}{}\left({x}\right)$ (4)
 > $\mathrm{Combine}\left({\left({x}^{y}\right)}^{5}+{\left({x}^{z}\right)}^{6}+5t\mathrm{ln}\left(z\right)+6t\mathrm{ln}\left(x\right),'\mathrm{power}','\mathrm{ln}'\right)$
 ${{x}}^{{5}{}{y}}{+}{{x}}^{{6}{}{z}}{+}{t}{}{\mathrm{ln}}{}\left({{x}}^{{6}}{}{{z}}^{{5}}\right)$ (5)
 > $\mathrm{Combine}\left({a}^{b}+2\mathrm{exp}\left(b\mathrm{ln}\left(a\right)\right)\right)$
 ${3}{}{{ⅇ}}^{{b}{}{\mathrm{ln}}{}\left({a}\right)}$ (6)