LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= If you are self-learning, then you should go right now to the "Help" menu and go through the "Getting Started" material. It will give you the basic ideas of the program. To begin with, you can erase all definitions in Maple by running the command restart. It's a good thing to do. To run a command, put your cursor on the command and press enter. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJStleGVjdXRhYmxlR0Y9Rjk= Hooray! You can use Maple just like a graphing calculator. Type in an expression you want to work out, then press enter. You must do "*" for multiplicatio and "^" for exponents. 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 You can access your previously computed value using the symbol "%". LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEiJUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYjLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYtUSI7RidGPi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0ZJLyUqc3ltbWV0cmljR0ZJLyUobGFyZ2VvcEdGSS8lLm1vdmFibGVsaW1pdHNHRkkvJSdhY2NlbnRHRkkvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4yNzc3Nzc4ZW1GJw== Click on the arrow below to get your various tutorials.

To mod in Maple, you use the mod command. You can type it in in various ways: 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 The mod command in Maple returns the remainder. This is a bit different from what we do in the book/notes. If you are doing a power mod in Maple, you want to use "&^" instead of "^". The "&^" tells Maple to work out the mod and the exponent at the same time (using our power mod algoirthm). The "^" says to compute the exponent first, then work out the mod.Compare the times of these two commands: (Note: you need to type in & \134 ^ to get the "&^".) 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 We can work out inverses also: 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 Let's check: 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 We can assign values to letters if we so desire. The assign command is := 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 This will give a list of g raised to various powers mod p. Then we'll plot them in a graph, like the graph of the discrete log that I gave you. 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

We have several built-in commands to find prime numbers: isprime(n) - tells you if n is a prime number or not. ithprime(i) - returns the i-th prime nextprime(n) - gives the first prime that occurs after n prevprime(n) - gives the first prime that occurs before n LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEoaXNwcmltZUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYjLUkjbW5HRiQ2JFEjMTNGJy9GM1Enbm9ybWFsRidGPi1JI21vR0YkNi1RIjtGJ0Y+LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkYvJSpzeW1tZXRyaWNHRkYvJShsYXJnZW9wR0ZGLyUubW92YWJsZWxpbWl0c0dGRi8lJ2FjY2VudEdGRi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjI3Nzc3NzhlbUYn LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEoaXNwcmltZUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYjLUkjbW5HRiQ2JFEjMTRGJy9GM1Enbm9ybWFsRidGPi1JI21vR0YkNi1RIjtGJ0Y+LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkYvJSpzeW1tZXRyaWNHRkYvJShsYXJnZW9wR0ZGLyUubW92YWJsZWxpbWl0c0dGRi8lJ2FjY2VudEdGRi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjI3Nzc3NzhlbUYn 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEqcHJldnByaW1lRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtSSVtc3VwR0YkNiUtSSNtbkdGJDYkUSIyRicvRjNRJ25vcm1hbEYnLUYjNiMtRj42JFEkMTI4RidGQS8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYtUSIrRidGQS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGUS8lKXN0cmV0Y2h5R0ZRLyUqc3ltbWV0cmljR0ZRLyUobGFyZ2VvcEdGUS8lLm1vdmFibGVsaW1pdHNHRlEvJSdhY2NlbnRHRlEvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0Zqbi1GPjYkUSIxRidGQUZBLUZMNi1RIjtGJ0ZBRk8vRlNGMUZURlZGWEZaRmZuL0ZpblEmMC4wZW1GJy9GXG9RLDAuMjc3Nzc3OGVtRic= The following command will produce a random prime number with n digits. You must first load the code (by pressing enter while the cursor is on it), then you can use it. 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEqZmluZHByaW1lRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiMtSSNtbkdGJDYkUSIzRicvRjNRJ25vcm1hbEYnRj4tSSNtb0dGJDYtUSI7RidGPi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZGLyUqc3ltbWV0cmljR0ZGLyUobGFyZ2VvcEdGRi8lLm1vdmFibGVsaW1pdHNHRkYvJSdhY2NlbnRHRkYvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4yNzc3Nzc4ZW1GJw== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEqZmluZHByaW1lRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiMtSSNtbkdGJDYkUSI0RicvRjNRJ25vcm1hbEYnRj4tSSNtb0dGJDYtUSI7RidGPi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZGLyUqc3ltbWV0cmljR0ZGLyUobGFyZ2VvcEdGRi8lLm1vdmFibGVsaW1pdHNHRkYvJSdhY2NlbnRHRkYvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4yNzc3Nzc4ZW1GJw== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEqZmluZHByaW1lRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiMtSSNtbkdGJDYkUSQyMDBGJy9GM1Enbm9ybWFsRidGPi1JI21vR0YkNi1RIjtGJ0Y+LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkYvJSpzeW1tZXRyaWNHRkYvJShsYXJnZW9wR0ZGLyUubW92YWJsZWxpbWl0c0dGRi8lJ2FjY2VudEdGRi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjI3Nzc3NzhlbUYn LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEoaXNwcmltZUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYjLUYsNiVRIiVGJ0YvRjIvRjNRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiO0YnRj0vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGRS8lKnN5bW1ldHJpY0dGRS8lKGxhcmdlb3BHRkUvJS5tb3ZhYmxlbGltaXRzR0ZFLyUnYWNjZW50R0ZFLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRic=

The following two programs can be used to encode and decode messages. They transform text to numbers, and then numbers to text. Again, you need to load the programs before running them. 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEpbWVzczJudW1GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JS1GLDYjUSFGJy1JI21zR0YkNiNRLEl0fndvcmtlZCEhRidGOi9GM1Enbm9ybWFsRictSSNtb0dGJDYtUSI7RidGQS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZJLyUqc3ltbWV0cmljR0ZJLyUobGFyZ2VvcEdGSS8lLm1vdmFibGVsaW1pdHNHRkkvJSdhY2NlbnRHRkkvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4yNzc3Nzc4ZW1GJw== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEpbnVtMm1lc3NGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2Iy1JI21uR0YkNiRRODM5MjcxMTU3ODUyNzc3OTAyMjU4NzYxRicvRjNRJ25vcm1hbEYnRj4tSSNtb0dGJDYtUSI7RidGPi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZGLyUqc3ltbWV0cmljR0ZGLyUobGFyZ2VvcEdGRi8lLm1vdmFibGVsaW1pdHNHRkYvJSdhY2NlbnRHRkYvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4yNzc3Nzc4ZW1GJw== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

Some commands are not loaded automatically in Maple. They are put into program libraries, and you call them up with the with command. For instance, I needed to load the plots library so I could use the pointplot command up above. A useful package for us is the number theory package, numtheory. Let's load it: QyQtSSV3aXRoRzYiNiNJKm51bXRoZW9yeUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJSIiIg== In this list, you will see order, primroot, safeprime, and mlog. We can use these. The command order(g, p) returns the order of g mod p. QyQtSSZvcmRlckclKnByb3RlY3RlZEc2JCIiJCIiKCIiIg== QyQtSSZvcmRlckclKnByb3RlY3RlZEc2JCIiIyIiKCIiIg== The command primroot(p) returns the smallest primitive root mod p. If you do primroot(g, p), it will return the smallest primitive root mod p that is bigger than g. QyQtSSlwcmltcm9vdEc2IjYjIiIoIiIi QyQtSSlwcmltcm9vdEc2IjYkIiImIiIoIiIi The command safeprime(x) returns the smallest prime p larger than x such that (p-1)/2 is also prime. See? Even Maple thinks these primes are useful. QyQtSSpzYWZlcHJpbWVHNiI2IyIiJCIiIg== LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEqc2FmZXByaW1lRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtSSNtbkdGJDYkUSMxMkYnL0YzUSdub3JtYWxGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRj5GPi1JI21vR0YkNi1RIjtGJ0Y+LyUmZmVuY2VHRkIvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGQi8lKnN5bW1ldHJpY0dGQi8lKGxhcmdlb3BHRkIvJS5tb3ZhYmxlbGltaXRzR0ZCLyUnYWNjZW50R0ZCLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRidGQEY+ QyQtSSpzYWZlcHJpbWVHNiI2Iy1JIl5HJSpwcm90ZWN0ZWRHNiQiIiMiJEciIiIi QyQtSShpc3ByaW1lRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMtSSIqR0YmNiQsJkkiJUdGKCIiIiEiIkYvI0YvIiIjRi8= Finally, mlog(h, g, p) gives the discrete log of h with base g mod p. QyQtSSVtbG9nRzYiNiUiIiQiIiYiI0IiIiI= QyQtSSRtb2RHNiI2JC1JIyZeR0YlNiQiIiYiIzsiI0IiIiI= We can make mlog weep. I expect you will get bored before Maple finishes evaluating the mlog below. QyQ+SSJwRzYiLUkqc2FmZXByaW1lR0YlNiMtSSJeRyUqcHJvdGVjdGVkRzYkIiIjIiRHIiIiIg== QyQ+SSJnRzYiLUkpcHJpbXJvb3RHRiU2I0kicEdGJSIiIg== QyQtSSVtbG9nRzYiNiUiJCsiSSJnR0YlSSJwR0YlIiIi JSFH