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Roaders

Help With maple - _Z and label = _Li

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Roaders    122
Hi Guys I am am new to Maple and I am trying to use it to re-arrange a long trigonometry equation. the equation is: > equ := Offset = 4*cos(angle)*length + 4*cos(2*angle)*length + 4*cos(3*angle)*length + 2*cos(4*angle)*length + length; I want to re-arrange this to calculate the angle I need to produce a given offset with a given length. I try to do this: > solve(equ2, {angle}); and the answer I get back has references to _Z in and has "Label = _Li" in it. What do these mean? Thanks a lot.

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Guest Anonymous Poster   
Guest Anonymous Poster
You can throw an allvalues() at it, but the equation you''ll get will be ~10 pages long.

> equ := Offset = 4*cos(angle)*length + 4*cos(2*angle)*length + 4*cos(3*angle)*length + 2*cos(4*angle)*length + length;

> allvalues(solve(equ, angle));

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According to this page (search for _Z), when you get a _Z in your answer, it means maple can''t find the solution explicitly. It seems that (at least with maple 6) 3rd or higher order polynomials under radical signs tend to cause this problem. When you add cos(k*x) with differeing k''s and solve for x, the result seems to involve a polynomial with degree equal to the one less than the number of cos terms.

Basically, you''re trying to solve something that can''t easily be solved. The solution is too complicated or cannot be written explicitly.

http://www.google.ca/search?q=cache:1sT5-e25Hs8J:www-math.math.rwth-aachen.de/MapleAnswers/1149.html+maple+_Z&hl=en&ie=UTF-8

suggests that the label=_Li business is "to distinguish several unspecified roots of the same equation". The author doesn''t quite know what that means, nor do I, though I suspect it just means that your problem is really complicated.

You''ll need to find another way to solve this problem. For fun, here''s the first (presumably the simplest) solution provided by allvalues

arccos(-1/4+1/12*sqrt(3)*sqrt((7*length*((5*length-63*offset+3*sqrt(-(111*length^3-186*length^2*offset-249*length*offset^2-48*offset^3)/length))*length^2)^(1/3)+2^(1/3)*((5*length-63*offset+3*sqrt(-(111*length^3-186*length^2*offset-249*length*offset^2-48*offset^3)/length))*length^2)^(2/3)+8*2^(2/3)*length^2-6*2^(2/3)*length*offset)/(length*((5*length-63*offset+3*sqrt(-(111*length^3-186*length^2*offset-249*length*offset^2-48*offset^3)/length))*length^2)^(1/3)))+1/12*sqrt(-(-42*length*((5*length-63*offset+3*sqrt(-(111*length^3-186*length^2*offset-249*length*offset^2-48*offset^3)/length))*length^2)^(1/3)*sqrt((7*length*((5*length-63*offset+3*sqrt(-(111*length^3-186*length^2*offset-249*length*offset^2-48*offset^3)/length))*length^2)^(1/3)+2^(1/3)*((5*length-63*offset+3*sqrt(-(111*length^3-186*length^2*offset-249*length*offset^2-48*offset^3)/length))*length^2)^(2/3)+8*2^(2/3)*length^2-6*2^(2/3)*length*offset)/(length*((5*length-63*offset+3*sqrt(-(111*length^3-186*length^2*offset-249*length*offset^2-48*offset^3)/length))*length^2)^(1/3)))+3*sqrt((7*length*((5*length-63*offset+3*sqrt(-(111*length^3-186*length^2*offset-249*length*offset^2-48*offset^3)/length))*length^2)^(1/3)+2^(1/3)*((5*length-63*offset+3*sqrt(-(111*length^3-186*length^2*offset-249*length*offset^2-48*offset^3)/length))*length^2)^(2/3)+8*2^(2/3)*length^2-6*2^(2/3)*length*offset)/(length*((5*length-63*offset+3*sqrt(-(111*length^3-186*length^2*offset-249*length*offset^2-48*offset^3)/length))*length^2)^(1/3)))*2^(1/3)*((5*length-63*offset+3*sqrt(-(111*length^3-186*length^2*offset-249*length*offset^2-48*offset^3)/length))*length^2)^(2/3)+24*sqrt((7*length*((5*length-63*offset+3*sqrt(-(111*length^3-186*length^2*offset-249*length*offset^2-48*offset^3)/length))*length^2)^(1/3)+2^(1/3)*((5*length-63*offset+3*sqrt(-(111*length^3-186*length^2*offset-249*length*offset^2-48*offset^3)/length))*length^2)^(2/3)+8*2^(2/3)*length^2-6*2^(2/3)*length*offset)/(length*((5*length-63*offset+3*sqrt(-(111*length^3-186*length^2*offset-249*length*offset^2-48*offset^3)/length))*length^2)^(1/3)))*2^(2/3)*length^2-18*sqrt((7*length*((5*length-63*offset+3*sqrt(-(111*length^3-186*length^2*offset-249*length*offset^2-48*offset^3)/length))*length^2)^(1/3)+2^(1/3)*((5*length-63*offset+3*sqrt(-(111*length^3-186*length^2*offset-249*length*offset^2-48*offset^3)/length))*length^2)^(2/3)+8*2^(2/3)*length^2-6*2^(2/3)*length*offset)/(length*((5*length-63*offset+3*sqrt(-(111*length^3-186*length^2*offset-249*length*offset^2-48*offset^3)/length))*length^2)^(1/3)))*2^(2/3)*length*offset-18*sqrt(3)*length*((5*length-63*offset+3*sqrt(-(111*length^3-186*length^2*offset-249*length*offset^2-48*offset^3)/length))*length^2)^(1/3))/(length*((5*length-63*offset+3*sqrt(-(111*length^3-186*length^2*offset-249*length*offset^2-48*offset^3)/length))*length^2)^(1/3)*sqrt((7*length*((5*length-63*offset+3*sqrt(-(111*length^3-186*length^2*offset-249*length*offset^2-48*offset^3)/length))*length^2)^(1/3)+2^(1/3)*((5*length-63*offset+3*sqrt(-(111*length^3-186*length^2*offset-249*length*offset^2-48*offset^3)/length))*length^2)^(2/3)+8*2^(2/3)*length^2-6*2^(2/3)*length*offset)/(length*((5*length-63*offset+3*sqrt(-(111*length^3-186*length^2*offset-249*length*offset^2-48*offset^3)/length))*length^2)^(1/3))))))

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