Download APL Programs for the Mathematics Classroom by Norman D. Thomson PDF
By Norman D. Thomson
The proposal for this booklet grew out of proposals on the APL86 con ference in Manchester which resulted in the initiation of the I-APL (International APL) undertaking, and during it to the provision of an interpreter which might carry some great benefits of APL in the technique of substantial numbers of college little ones and their academics. the inducement is that after tuition lecturers have glimpsed the chances, there'll be a spot for an "ideas" booklet of brief courses for you to permit beneficial algorithms to be introduced swiftly into school room use, and even perhaps to be written and constructed in entrance of the category. A test of the contents will exhibit how the conciseness of APL makes it attainable to deal with a major 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 valuable in genuine paintings, or that have stuck my mind's eye as applicants for demonstrating the worth 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 maths involved, and to estab lish that APL isn't really, as is usually meant, an unreadable lan guage written in a weird and wonderful personality set.
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Extra info for APL Programs for the Mathematics Classroom
2 that is, 3 yards 2 feet 6 inches is equivalent to 3m. 50 cm. 2mm. 2. 11. Problems involving Base 10 Digits Find the sum of the digits in a base 10 integer R, (or vector of base 10 integers) : DIGSUM +f10 BASE R Example: DIGSUM 23 199 5 19 I. The following program returns 1 if the two arguments Land R contain exactly the same digits (possibly in a different order). SAMEDIG:A/(TEU),(U+,10 BASE R)E T+,10 BASE L Use SAMEDIG to find all the pairs of 2-digit integers such as (21,87) whose product 1827 consists of the same 4 digits.
5)+2xR[lJ R : vector of coefficients in descending power order The expression -2 1 -2+. xRx~R is an APL version of b 2 -4ac. Where the roots are imaginary, the result is given as a 2-item vector a,b which is to be interpreted as (a + ib), (a-ib). Example: QUAD 1 2 1 1 1 QUAD 1 1 1 IMAG. 3. Matrix Operations Product of two (compatible) matrices Land R L+ • xR Inverse of square matrix R IiIR Quotient of two (compatible) matrices Land R LIiIR Solution of simultaneous linear equations LIiIR where the equations to be solved are Rx = L.
The result is the coefficients of the expansion in the order X2, xy, y2. +/xfO l¢R)[l 3 2J 29 3. 2. Roots of Quadratics This is written in the conditional direct definition form, with the 3 sections in order corresponding to (1) real roots, (2) b 2 -4ac > 0 test, (3) imaginary roots. xRx~R 'IMAG. 5)+2xR[lJ R : vector of coefficients in descending power order The expression -2 1 -2+. xRx~R is an APL version of b 2 -4ac. Where the roots are imaginary, the result is given as a 2-item vector a,b which is to be interpreted as (a + ib), (a-ib).