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SolveTools

 GreaterComplexity
 compare the complexities of two expressions

 Calling Sequence GreaterComplexity(expr1, expr2)

Parameters

 expr1, expr2 - expressions

Description

 • The GreaterComplexity command returns true if the expression $\mathrm{expr1}$ is more complex than $\mathrm{expr2}$; otherwise, false is returned.
 GreaterComplexity uses SolveTools[Complexity] in polynomial mode to compute the relative complexities of the expressions. If the expressions have the same complexity according to the Complexity function, then GreaterComplexity determines that the more complex expression is the one that has the higher lexicographical order of its indeterminates.
 • This function is part of the SolveTools package, and so it can be used in the form GreaterComplexity(..) only after executing the command with(SolveTools). However, it can always be accessed through the long form of the command by using SolveTools[GreaterComplexity](..).

Examples

 > $\mathrm{with}\left(\mathrm{SolveTools}\right):$
 > $\mathrm{GreaterComplexity}\left(x,2x\right)$
 ${\mathrm{false}}$ (1)
 > $\mathrm{GreaterComplexity}\left(\mathrm{sin}\left(x\right),3x\right)$
 ${\mathrm{true}}$ (2)
 > $\mathrm{GreaterComplexity}\left(x,y\right)$
 ${\mathrm{true}}$ (3)
 > $\mathrm{GreaterComplexity}\left(y,x\right)$
 ${\mathrm{false}}$ (4)