APL Programs for the Mathematics Classroom by Norman D. Thomson

By Norman D. Thomson

The thought for this booklet grew out of proposals on the APL86 con­ ference in Manchester which ended in the initiation of the I-APL (International APL) venture, and during it to the provision of an interpreter which might carry the benefits of APL in the technique of significant numbers of college kids and their lecturers. the inducement is that when university academics have glimpsed the probabilities, there'll be a spot for an "ideas" ebook of brief courses as a way to permit valuable algorithms to be introduced speedily into lecture room use, and even perhaps to be written and built in entrance of the category. A experiment of the contents will convey how the conciseness of APL makes it attainable to deal with a big variety of themes in a small variety of pages. there's obviously a level of idiosyncrasy within the collection of themes - the choice i've got made displays algo­ rithms that have both proved beneficial in genuine paintings, or that have stuck my mind's eye as applicants for demonstrating the price of APL as a mathematical notation. the place acceptable, notes at the courses are meant to teach the naturalness with which APL offers with the math involved, and to estab­ lish that APL isn't, as is usually intended, an unreadable lan­ guage written in a strange personality set.

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Example text

N Table Velocity at time T : Formula U+AxT UO. +Ao. 1. Compound Interest In the following, A stands for Amount, R for Rate, and N for Number of years. The problem is to compute the value of A following investment for N years at rate R. 12 N+5 10 15 20 5.

This technique is known as Neville's algorithm. The best estimate at any stage is that for which the the tabular x-values are closest to and on either side of the x-value for interpolation. L is the polynomial degree and R is a table such as T with (O,x) appended as first column. APL Programs for the Mathematics Classroom 54 NEV : (-f(e1 OFF(L-1)NEV R)xT-R[2;1J) +-fT+L OFF 1~R[2;J : L=O : 1~R[1;J OFF : (0 ,-LH (LR) , [. 5JR Example : Find the 2nd degree polynomial interpolation for x = n/6 in the table T above.

T~ODDS L These can be compared with the values of 20L and 10L. 11. Continued Fractions Evaluate the continued fraction corresponding to vector R CONFRAC: R[1]++R[2] : 2

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