The Usage Comparison of Mathematica and Maxima

The Comparison how to use Maxima and Mathematica ================================================ Keys ---- | Action | Maxima | Mathematica | | ------------- |:-------------:| :-----:| | Input the last input | `Alt` + `↑` | `Ctrl` + `l` | Syntax ------ | Function | Maxima | Mathematica | | ------------- |:-------------:| :-----:| | logarithm | `log(5)` | `Log[5]` | | plot 2D | `plot2d[log(x), [x, 0, 5]]` | `Plot[Log[x], {x, 0, 5}]` | <!-- http://beige.ucs.indiana.edu/P573/node35.html -->

Fibonacci Number Graph with Maxima

Let's make the graph of Fibonacci number (series). However if you plot fib(x) as usually as functions, e.g. sin(x), ``` wxplot2d (fib(x),[x, 0, 5])$ ``` then you got an error. ``` plot2d: expression evaluates to non-numeric value everywhere in plotting range. plot2d: nothing to plot. ``` Because the x of fib(x) doesn't allow a decimal value. In proof if you execute `fib(1.5)` your PC will be frozen... So works the following. ``` plot2d ([discrete, makelist(fib(i), i, 0, 64),[x, 0, 64]])$ wxplot2d ([discrete, makelist(fib(i), i, 0, 64),[x, 0, 64]])$ wxplot2d ([discrete, makelist(1/fib(i), i, 0, 64),[x, 0, 64]])$ ```

Fibonacci Number and their Factors

Here are Fibonacci numbers and their factors I calculated with Scala. ``` fib(1) = 0 = 0 fib(2) = 1 = 1 fib(3) = 1 = 1 fib(4) = 2 = 2 fib(5) = 3 = 3 fib(6) = 5 = 5 fib(7) = 8 = 2 * 2 * 2 fib(8) = 13 = 13 fib(9) = 21 = 7 * 3 fib(10) = 34 = 17 * 2 fib(11) = 55 = 11 * 5 fib(12) = 89 = 89 fib(13) = 144 = 3 * 3 * 2 * 2 * 2 * 2 fib(14) = 233 = 233 fib(15) = 377 = 29 * 13 fib(16) = 610 = 61 * 5 * 2 fib(17) = 987 = 47 * 7 * 3 fib(18) = 1597 = 1597 fib(19) = 2584 = 19 * 17 * 2 * 2 * 2 fib(20) = 4181 = 113 * 37 fib(21) = 6765 = 41 * 11 * 5 * 3 fib(22) = 10946 = 421 * 13 * 2 fib(23) = 17711 = 199 * 89 fib(24) = 28657 = 28657 fib(25) = 46368 = 23 * 7 * 3 * 3 * 2 * 2 * 2 * 2 * 2 fib(26) = 75025 = 3001 * 5 * 5 fib(27) = 121393 = 521 * 233 fib(28) = 196418 = 109 * 53 * 17 * 2 fib(29) = 317811 = 281 * 29 * 13 * 3 fib(30) = 514229 = 514229 fib(31) = 832040 = 61 * 31 * 11 * 5 * 2 * 2 * 2 fib(32) = 1346269 = 2417 * 557 fib(33) = 2178309 = 2207 * 47 * 7 * 3 fib(34) = 3524578 = 19801 * 89 * 2 fib(35) = 5702887 = 3571 * 1597 fib(36) = 9227465 = 141961 * 13 * 5 fib(37) = 14930352 = 107 * 19 * 17 * 3 * 3 * 3 * 2 * 2 * 2 * 2 fib(38) = 24157817 = 2221 * 149 * 73 fib(39) = 39088169 = 9349 * 113 * 37 fib(40) = 63245986 = 135721 * 233 * 2 fib(41) = 102334155 = 2161 * 41 * 11 * 7 * 5 * 3 fib(42) = 165580141 = 59369 * 2789 fib(43) = 267914296 = 421 * 211 * 29 * 13 * 2 * 2 * 2 fib(44) = 433494437 = 433494437 fib(45) = 701408733 = 307 * 199 * 89 * 43 * 3 fib(46) = 1134903170 = 109441 * 61 * 17 * 5 * 2 fib(47) = 1836311903 = 28657 * 461 * 139 fib(48) = 2971215073 = 2971215073 fib(49) = 4807526976 = 1103 * 47 * 23 * 7 * 3 * 3 * 2 * 2 * 2 * 2 * 2 * 2 fib(50) = 7778742049 = 6168709 * 97 * 13 fib(51) = 12586269025 = 3001 * 151 * 101 * 11 * 5 * 5 fib(52) = 20365011074 = 6376021 * 1597 * 2 fib(53) = 32951280099 = 90481 * 521 * 233 * 3 fib(54) = 53316291173 = 55945741 * 953 fib(55) = 86267571272 = 5779 * 109 * 53 * 19 * 17 * 2 * 2 * 2 fib(56) = 139583862445 = 474541 * 661 * 89 * 5 fib(57) = 225851433717 = 14503 * 281 * 29 * 13 * 7 * 7 * 3 fib(58) = 365435296162 = 54833 * 797 * 113 * 37 * 2 fib(59) = 591286729879 = 514229 * 19489 * 59 fib(60) = 956722026041 = 2710260697 * 353 fib(61) = 1548008755920 = 2521 * 61 * 41 * 31 * 11 * 5 * 3 * 3 * 2 * 2 * 2 * 2 fib(62) = 2504730781961 = 555003497 * 4513 fib(63) = 4052739537881 = 3010349 * 2417 * 557 fib(64) = 6557470319842 = 35239681 * 421 * 17 * 13 * 2 ```