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 Topics FrontPage OldWishList finite field expressions <-- You are here. Here are some notes I took when I tried to allow expressions ove finite fields. when making ZMOD an OrderedSet in the obvious way, I can have EXPR ZMOD 5 and EXPR PF 5. However, not all things work that should:  a:EXPR PF 5 := 2 a < 3$EXPR PF 5  gives false, as does 3$EXPR PF 5 < a The reason for this is that in polycat.spad/POLYCAT, the following definition is used. It should be OrderedStructure, maybe:  if R has OrderedSet then p:% < q:% == (dp:= degree p) < (dq := degree q) => (leadingCoefficient q) > 0 dq < dp => (leadingCoefficient p) < 0 -- leadingCoefficient(p - q) < 0 -- the last test works only if < is compatible with - -- the following works, but is slower, of course leadingCoefficient(p) < leadingCoefficient(q)  Furthermore, saying:  a:EXPR PF 3 := 2 eval(a^x,x=5)  gives 2^2 unevaluated. Here we have two problems at once: it should be 2^5=32=2 rather than 2^2=4=1 (that is, it treats x as an element of EXPR PF 3 rather than an integer. Question: is a^(b::EXPR PF 3) meaningful? Rather not, since the power laws do not hold: 2=2*1=2^1*2^2=2^3=2^0=1 (3) What is required so that a^b is well defined? it should evaluate the expression. This happens in COMBF, since... Hmmm, I didn't take notes here anymore. I probably didn't find out.

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