For example, the following is parsed as (x1)/2.x^1/212xSo in general, parentheses are needed when the exponent is an expression.x^(1/2)x1/251.2 DeningsymbolsAs we saw earlier, Eigenmath uses the same syntax as dear old Fortran.N=212^17No result is printed when a symbol is dened. Never mind the minus sign, what is the bindingof the caret symbol itself? The answer is, it binds to the rst symbol thatfollows it and nothing else. So Eigenmathrequiresx^(-1/2)which is unambiguous.Now a new question arises. For example, considerx^-1/2It is not clear whether the exponent should be 1 or 1/2. For example,10^(-3)instead of10^-3Thereasonforthisisthatthebindingofthenegativesignisnotalwaysobvious. To see the value of a symbol, just evaluate it by putting it on a lineby itself.NN= 352947114576027513230189734205586617139241.1 NegativeexponentsEigenmath requires parentheses around negative exponents. We can enter oat or click on the oatbutton to scale the number down to size.float3.52947 1039Now let us see if Eigenmath can nd the seventeenth root of this number,like the Hindu calculator could.N=212^17NN= 3529471145760275132301897342055866171392N^(1/17)212It is worth mentioning that when a symbol is assigned a value, no result isprinted. 418 Built-infunctions 429 Syntax 5431 IntroductionThe following is an excerpt from Vladimir Nabokovs autobiography Speak,Memory.A foolish tutor had explained logarithms to me much too early,andI hadread(inaBritishpublication, theBoysOwnPa-per,I believe) about a certain Hindu calculator who in exactlytwo seconds could nd the seventeenth root of, say, 3529471145760275132301897342055866171392 (I am not sure I have got thisright anyway the root was 212).We can check Nabokovs arithmetic by typing the following into Eigenmath.212^17After pressing the return key, Eigenmath displays the following result.3529471145760275132301897342055866171392So Nabokov did get it right after all. 52 Draw 83 Scripts 114 Complexnumbers 135 Linearalgebra 156 Calculus 176.1 Derivative. Restrictions and other terms apply.Eigenmath ManualJanuary1,200912Contents1 Introduction 31.1 Negative exponents. Plan is automatically renewed until cancelled.
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