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45 lines
1.5 KiB
45 lines
1.5 KiB
2 years ago
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Exercise 2.97:
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Implement this algorithm as a procedure reduce-terms that takes two term
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lists n and d as arguments and returns a list nn,
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dd, which are n and d reduced to lowest terms via the
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algorithm given above. Also write a procedure reduce-poly, analogous to
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add-poly, that checks to see if the two polys have the same variable.
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If so, reduce-poly strips off the variable and passes the problem to
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reduce-terms, then reattaches the variable to the two term lists
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supplied by reduce-terms.
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Define a procedure analogous to reduce-terms that does what the original
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make-rat did for integers:
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(define (reduce-integers n d)
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(let ((g (gcd n d)))
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(list (/ n g) (/ d g))))
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and define reduce as a generic operation that calls apply-generic
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to dispatch to either reduce-poly (for polynomial arguments) or
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reduce-integers (for scheme-number arguments). You can now
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easily make the rational-arithmetic package reduce fractions to lowest terms by
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having make-rat call reduce before combining the given numerator
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and denominator to form a rational number. The system now handles rational
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expressions in either integers or polynomials. To test your program, try the
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example at the beginning of this extended exercise:
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(define p1
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(make-polynomial 'x '((1 1) (0 1))))
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(define p2
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(make-polynomial 'x '((3 1) (0 -1))))
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(define p3
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(make-polynomial 'x '((1 1))))
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(define p4
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(make-polynomial 'x '((2 1) (0 -1))))
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(define rf1 (make-rational p1 p2))
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(define rf2 (make-rational p3 p4))
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(add rf1 rf2)
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See if you get the correct answer, correctly reduced to lowest terms.
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