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verify/sign

verify for sign differences

 Calling Sequence verify(expr1, expr2, sign)

Parameters

 expr1, expr2 - anything, assumed to be of type algebraic

Description

 • The verify(expr1, expr2, sign) calling sequence returns true if any of the following is true:
 1 The arguments are equal.
 2 Multiplying pairs of multiplicands by $-1$ results in equal arguments.
 3 Given ${a}^{n}$ and ${b}^{n}$ where $n$ is even, $a=b$ or $a=-b$.
 • This verification is more memory and computationally intensive than checking whether the normal of the difference is zero, but it ensures that the two arguments have similar forms.
 • This verification is symmetric.

Examples

 > $\mathrm{verify}\left(-\frac{x}{a-b},\frac{x}{b-a},\mathrm{sign}\right)$
 ${\mathrm{true}}$ (1)
 > $p≔\frac{3{\left(x-y\right)}^{2}\left(x-2y-xy\right)\left(x-y-4x\right)\left(x{y}^{2}+2x-2y\right)}{y-3x}$
 ${p}{:=}\frac{{3}{}{\left({x}{-}{y}\right)}^{{2}}{}\left({-}{x}{}{y}{+}{x}{-}{2}{}{y}\right){}\left({-}{3}{}{x}{-}{y}\right){}\left({x}{}{{y}}^{{2}}{+}{2}{}{x}{-}{2}{}{y}\right)}{{y}{-}{3}{}{x}}$ (2)
 > $q≔\frac{3{\left(y-x\right)}^{2}\left(xy+2y-x\right)\left(4x-y-x\right)\left(2y-x{y}^{2}-2x\right)}{3x-y}$
 ${q}{:=}{3}{}{\left({y}{-}{x}\right)}^{{2}}{}\left({x}{}{y}{-}{x}{+}{2}{}{y}\right){}\left({-}{x}{}{{y}}^{{2}}{-}{2}{}{x}{+}{2}{}{y}\right)$ (3)
 > $\mathrm{verify}\left(p,q,\mathrm{sign}\right)$
 ${\mathrm{false}}$ (4)