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Transcendental equations

by physics4ever
Tags: equations, transcendental
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Dec4-05, 06:09 AM
P: 21
I wanted to find out what transcendental equations actually are. Can the computer solve such equations?
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Dec4-05, 07:31 AM
P: 646
Elementary Operations :

If any equation can be described by these operations alone, then such an equation is called algebraic equation. If not, they are called transcendental equations.

Can computers solve such equations?
Approximate solutions ofcourse, exact solutions ofcourse not!

-- AI
matt grime
Dec4-05, 08:22 AM
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I think you're under a slight misapprehension: computers can't (even) solve (algebraic) equations generally, if you mean outputting a number in a recognizable form that is a/the precise answer. There are almost no equations algebraic or transcendental that have solutions that can be output as a finite binary expansion which is all a computer deals with (possibly up to base change). I am ignoring the few symbolic manipulations that can be done.

i'd like to add that algebraic things involve finitely many of those operations, so that

2=1+x+x^2/2! + x^3/3!+...

is not algebraic (its exact solution is of course x=log(2)...

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