Basic Symbolic Computation in Perl
0 likes893 views
This document discusses using symbolic computation in Perl to represent and manipulate mathematical objects like rational numbers, complex numbers, polynomials, and linear/quadratic equations. It presents examples of implementing rational numbers as ordered pairs of integers, complex numbers as ordered pairs of reals, and polynomials as ordered tuples. The key steps are to figure out the rules/properties of the mathematical objects, eliminate extraneous details, and find a representation to encode the objects as data structures that support defined arithmetic operations and algorithms. This allows performing symbolic rather than numeric computations natively in Perl.
More Related Content
Similar to Basic Symbolic Computation in Perl (20)
More from Mike Friedman (8)
Recently uploaded (20)
![[HIFLUX] Lok Fitting&Valve Catalog 2025 (Eng)](https://cdn.slidesharecdn.com/ss_thumbnails/lokfittingen-250528072439-8696f1c6-thumbnail.jpg?width=560&fit=bounds)
Basic Symbolic Computation in Perl
- 1. Symbolic Computation in Perl Mike Friedman (friedo) YAPC::NA 2015 Salt Lake City, UT @friedo
- 4. The Problem:
- 5. The Problem: We have computers.
- 6. The Problem: We have computers. But they don't really compute.
- 7. The Problem: We have computers. But they don't really compute.
- 8. The Problem: We have computers. But they don't really compute. ==
- 9. The Problem: Native number types in most programming languages (including Perl) are ints and floats.
- 10. The Problem: Native number types in most programming languages (including Perl) are ints and floats. Because that's what the microprocessor can do.
- 11. The Problem: What about rational numbers?
- 12. The Problem: What about rational numbers?
- 13. The Problem: What about rational numbers? These can only be approximated by floating point.
- 14. The Problem: What about irrational numbers?
- 15. The Problem: What about irrational numbers? Same problem.
- 16. The Problem: What about imaginary and complex numbers?
- 17. The Problem: What about imaginary and complex numbers? Floats can't even approximate these.
- 18. The Solution: We do not want to calculate with numbers.
- 19. The Solution: We do not want to calculate with numbers. We want to compute with symbols.
- 20. The Solution: We do not want to calculate with numbers. We want to compute with symbols. We do that in software.
- 21. The Solution: >
- 23. Example 1 Rational numbers We start with integers.
- 24. Example 1 Rational numbers We start with integers.
- 25. Example 1 For division, we must extend the integers.
- 26. Example 1 For division, we must extend the integers.
- 27. Example 1 We can think of them as ordered pairs.
- 28. Example 1 Rational object as an ordered pair: Divide by greatest common factor $f to put in lowest terms.
- 29. Example 1 Convenience subs for a, b, c, d terms:
- 32. Example 1 Let's try it!
- 34. Example 2 Rational numbers We start with the real numbers.
- 35. Example 2 Rational numbers We start with the real numbers.
- 36. Example 2 Rational numbers We start with the real numbers.
- 37. Example 2 To solve, we must extend the real numbers.
- 38. Example 2 We can think of them as ordered pairs.
- 39. Example 2 Complex object as an ordered pair:
- 40. Example 2 Convenience subs for a, b, c, d terms: Remember these?
- 43. Example 2 Let's try it!
- 45. Example 3 Linear equations standard form:
- 46. Example 3 Linear equations standard form: solution:
- 47. Example 3 We can think of them as ordered pairs.
- 48. Example 3 Linear object as an ordered pair:
- 50. Example 3 Let's try it!
- 51. Example 3 What about Rationals? Changed integer 0 to Rational 0/1. Overloading handles the rest.
- 52. Example 3 Let's try it!
- 54. Example 4 Quadratic equations standard form:
- 55. Example 4 Quadratic equations standard form: solution:
- 56. Example 4 We can think of them as ordered triplets.
- 57. Example 4 Quadratic object as an ordered triplet:
- 59. Example 4 Let's try it! Now make it work with Complex objects!
- 60. Example 4 Let's try it! Now make it work with Complex objects! (I'm too lazy.)
- 64. Example 5 We can think of them as ordered tuples of size n+1, where n is the degree of the polynomial.
- 65. Example 5 Polynomial object as an ordered tuple:
- 67. Example 5 Let's try it!
- 68. Example 5 How about derivatives?
- 70. Example 5 Let's try it!
- 71. Conclusions 1. Figure out the rules for your thing.
- 72. Conclusions Complex numbers extend the reals. They have self-consistent rules for arithmetic.
- 73. Conclusions 2. Eliminate extraneous information.
- 74. Conclusions Rationals are just pairs of integers. Complex are just pairs of reals. Fraction bars and i are just notation.
- 75. Conclusions 3. Find a representation for your thing.
- 76. Conclusions Ordered pairs, triplets, and tuples. For more interesting things, you'll use trees.
- 77. Thanks! Symbolic Computation in Perl Mike Friedman (@friedo) github.com/friedo/perl-symbolic