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Power

inert power function

 Calling Sequence Power(a, n)

Parameters

 a - multivariate polynomial n - non-negative integer

Description

 • The Power function is a placeholder for representing ${a}^{n}$. It is used in conjunction with either mod or modp1.
 • The call Power(a, n) mod p computes ${a}^{n}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{mod}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}p$. The multivariate polynomial a must have rational coefficients or coefficients from a finite field specified by RootOfs.
 • The call modp1(Power(a, n), p) also computes ${a}^{n}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathbf{mod}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}p$. The polynomial a must be in the modp1 representation and p must be a positive integer.
 • Power is also equivalent to the infix operator &^ as shown in the examples.

Examples

 > $\mathrm{Power}\left(x+1,3\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{mod}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}2$
 ${{x}}^{{3}}{+}{{x}}^{{2}}{+}{x}{+}{1}$ (1)
 > $\mathrm{Power}\left(x+1,4\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{mod}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}2$
 ${{x}}^{{4}}{+}{1}$ (2)
 > $\left(x+1\right)&^4\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{mod}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}2$
 $\left({x}{+}{1}\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{&ˆ}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}{4}$ (3)
 > $3&^781247\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}\mathbf{mod}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}99999617$
 ${67158091}$ (4)