Galois Numbers: Solving Polynomial Equations

Generalizing the square root, we can try adjoining imaginary solutions to any kind of polynomial equation.

[Numeroscope Applet: displays the Galois fields with variable prime modulus, and variable extension degree up to 4. Can serve as a calculator for this number system, or display additive and multiplicative series, as well as function ranges.]

Lab Activities

Mode Oper. r c Activity
all r + 0 What are the possible sets of multiples and their sizes?

all z × 1 This shows sets of all r'th powers for varying r.

one z × p 1 This shows the p'th power of the number you click. What is the effect?

*Mode*	*Oper.*	r	c	*Activity*
all r	+		0	What are the possible sets of multiples and their sizes?
all z	×		1	This shows sets of all r'th powers for varying r.
one z	×	p	1	This shows the p'th power of the number you click. What is the effect?

Discussion Topics

[For now, see the discussion topics for the previous lab.]

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