Basic arithmeticLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRicvJSVzaXplR1EjMTJGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0YrRjdGOg==Arithmetic expressions can be typed into Maple using the regular operators: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
(type "3 * 7")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
(type "12 / 9")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(type "2 ^ 7")
Maple does know about the usual precedence of operations
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
We can use parentheses to alter this
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
Arithmetic expressions may contain variables, they remain unevaluated
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(in the document version of Maple we have a choice of typing "5 y" or "5 * y" - Maple accepts both. The command line version only accepts "5 * y". Be careful with the product of variables, however, since LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEifkYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTi1GLDYmUSJ5RidGL0YyRjUvJSVzaXplR1EjMTJGJ0YyRjw= (ie, "x [Space] y") and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEjeHlGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lJXNpemVHUSMxMkYnRjIvRjZRJ25vcm1hbEYn (ie "xy" with no space in between) refer to different things!)
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
Notice that Maple usually does not simplify the terms we enter
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(we will see later how we can bring Maple to expand terms like the above).
Maple knows many mathematical functions and constants
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1Ekc2luRicvJSdmYW1pbHlHUTBMaWJlcmF0aW9uflNhbnNGJy8lJXNpemVHUSMxMUYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiYtRiM2Jy1JI21uR0YkNiZRIjBGJ0YvRjJGOEYvRjIvJStleGVjdXRhYmxlR0Y3RjhGL0YyRjhGL0YyRkRGOA==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EkY29zRicvJSdmYW1pbHlHUTBMaWJlcmF0aW9uflNhbnNGJy8lJXNpemVHUSMxMUYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiYtRiM2Jy1JI21uR0YkNiZRIjFGJ0YvRjJGOEYvRjIvJStleGVjdXRhYmxlR0Y3RjhGL0YyRjhGL0YyRkRGOA==(Maple automatically simplifies "sin(0)" because the result is a simple number. On the other hand, there is no nicer representation for "cos(1)" than "cos(1)", and so Maple does not simplify it by default.)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(for the symbol LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEnJiM5NjA7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUrZXhlY3V0YWJsZUdGMS8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRidGMkY0 type "pi [Esc]" an select the corresponding entry from the menu).
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW5HRiQ2JlEiNUYnLyUnZmFtaWx5R1EwTGliZXJhdGlvbn5TYW5zRicvJSVzaXplR1EjMTFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYvUSIhRidGL0YyRjUvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj4vJSlzdHJldGNoeUdGPi8lKnN5bW1ldHJpY0dGPi8lKGxhcmdlb3BHRj4vJS5tb3ZhYmxlbGltaXRzR0Y+LyUnYWNjZW50R0Y+LyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdGTUYvRjIvJStleGVjdXRhYmxlR0Y+RjU=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EkZXhwRicvJSdmYW1pbHlHUTBMaWJlcmF0aW9uflNhbnNGJy8lJXNpemVHUSMxMUYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiYtRiM2Jy1JI21uR0YkNiZRIjJGJ0YvRjJGOEYvRjIvJStleGVjdXRhYmxlR0Y3RjhGL0YyRjhGL0YyRkRGOA==(we can also insert the exponential e with "e [Esc]").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(Maple accepts "i [Esc]" and "I" as the imaginary unit).
The help pages list the mathematical functions initially known to Maple
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW9HRiQ2L1EiP0YnLyUnZmFtaWx5R1EwTGliZXJhdGlvbn5TYW5zRicvJSVzaXplR1EjMTFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjovJSlzdHJldGNoeUdGOi8lKnN5bW1ldHJpY0dGOi8lKGxhcmdlb3BHRjovJS5tb3ZhYmxlbGltaXRzR0Y6LyUnYWNjZW50R0Y6LyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdGSS1JI21pR0YkNidRMWluaXRpYWxmdW5jdGlvbnNGJ0YvRjIvJSdpdGFsaWNHUSV0cnVlRicvRjZRJ2l0YWxpY0YnRi9GMi8lK2V4ZWN1dGFibGVHRjpGNQ==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2I1EhRictRiM2JUYrLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRisvJSdmYW1pbHlHUTBMaWJlcmF0aW9uflNhbnNGJy8lJXNpemVHUSMxMUYnRjFGNA==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW9HRiQ2L1EiP0YnLyUnZmFtaWx5R1EwTGliZXJhdGlvbn5TYW5zRicvJSVzaXplR1EjMTFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjovJSlzdHJldGNoeUdGOi8lKnN5bW1ldHJpY0dGOi8lKGxhcmdlb3BHRjovJS5tb3ZhYmxlbGltaXRzR0Y6LyUnYWNjZW50R0Y6LyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdGSS1JI21pR0YkNidRJGV4cEYnRi9GMi8lJ2l0YWxpY0dGOkY1Ri9GMi8lK2V4ZWN1dGFibGVHRjpGNQ==(You can use the syntax ?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 to obtain help on any special topic.)Expression manipulation (expand, collect, sort, (i)factor, combine)LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2I1EhRictRiM2J0YrLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRicvJSVzaXplR1EjMTJGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0YrLUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHUSYwLjBlbUYnLyUmZGVwdGhHRkIvJSpsaW5lYnJlYWtHUShuZXdsaW5lRidGL0YrRjdGOg==We have seen that Maple does not necessarily expand expressions:
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In order to expand this expression we can either use the context menu (click on Maple's output with the right mouse button) or the builtin "expand" function.
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 can represent the expression as polynomial in "x" using the "collect" command: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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYtLUkjbWlHRiQ2I1EhRictRiM2JUYrLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRistSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuMGVtRicvJSZkZXB0aEdGPC8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GODYmRjpGPUZAL0ZDUSVhdXRvRidGL0YrLyUnZmFtaWx5R1EwTGliZXJhdGlvbn5TYW5zRicvJSVzaXplR1EjMTFGJ0YxRjQ=If we don't want to enter the complete expression again, we can refer to it by its label:
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(use the menu "InsertLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LlEoJnNyYXJyO0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGRUYvRjI=Label" or "Control+L" to insert the label). Labels and the references to labels are updated when additional expressions are inserted or old expressions are deleted.
If we want to refer to the last expression which was evaluated we can also use "%":
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(Be careful when reevaluating the document! The "%" always refers to the last expression which was evaluated and not necessarily to the expression right above the current line. For that reason the usage of labels or variables is preferable.)
We can also sort expressions using "sort"
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 is possible to sort the with respect to a monomial ordering. For instance, the following command sorts the expression with respect to the lexicographic order with 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.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See the help page of "sort" for further options.
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW9HRiQ2LlEiP0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4xMTExMTExZW1GJy8lJ3JzcGFjZUdGRS1JI21pR0YkNiZRJXNvcnRGJy8lJ2l0YWxpY0dRJXRydWVGJ0YvL0YzUSdpdGFsaWNGJy8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYnLyUlc2l6ZUdRIzEyRidGL0YyThe opposite of "expand" is "factor":
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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=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In fact, "factor" can be applied to any polynomial expression to find a factorisation.
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
By default, the factorisation has only rational numbers as coefficients. However, we can allow Maple to use non-rational numbers:
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(to obtain LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbXNxcnRHRiQ2Iy1GIzYoLUkjbW5HRiQ2JVEiMkYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZm9yZWdyb3VuZEdRLFsxMjgsMCwxMjhdRidGNC8lLHBsYWNlaG9sZGVyR0Y8L0Y4USdpdGFsaWNGJ0Y0Rjc= use "sqrt [Esc]").
The corresponding command for factoring integers is "ifactor":
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EoaWZhY3RvckYnLyUnZmFtaWx5R1EwTGliZXJhdGlvbn5TYW5zRicvJSVzaXplR1EjMTFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2Jy1JI21uR0YkNiZRIzg0RidGL0YyL0Y5USdub3JtYWxGJ0YvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJ0ZERi9GMkZERi9GMkZGRkQ=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYtLUkjbWlHRiQ2I1EhRictRiM2JUYrLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRistSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuMGVtRicvJSZkZXB0aEdGPC8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GODYmRjpGPUZAL0ZDUSVhdXRvRidGL0YrLyUnZmFtaWx5R1EwTGliZXJhdGlvbn5TYW5zRicvJSVzaXplR1EjMTFGJ0YxRjQ=
Sometimes expanding will not yield a sufficient simplification:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYvLUkjbWlHRiQ2I1EhRictRiM2JUYrLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRistSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuMGVtRicvJSZkZXB0aEdGPC8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1JI21vR0YkNi9RIn5GJy8lJ2ZhbWlseUdRMExpYmVyYXRpb25+U2Fuc0YnLyUlc2l6ZUdRIzExRidGNC8lJmZlbmNlR0YzLyUqc2VwYXJhdG9yR0YzLyUpc3RyZXRjaHlHRjMvJSpzeW1tZXRyaWNHRjMvJShsYXJnZW9wR0YzLyUubW92YWJsZWxpbWl0c0dGMy8lJ2FjY2VudEdGMy8lJ2xzcGFjZUdGPy8lJ3JzcGFjZUdGP0Y3RkUtRiw2J1EnZXhwYW5kRidGSUZMLyUnaXRhbGljR1EldHJ1ZUYnL0Y1USdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2Ji1GIzYoLUkmbWZyYWNHRiQ2KC1GIzYoLUYsNidRJGV4cEYnRklGTC9GX29GM0Y0LUZkbzYmLUYjNictRiw2J1EieEYnRklGTEZeb0Zhb0ZJRkxGMUY0RklGTEY0RklGTEYxRjQtRiM2KEZdcC1GZG82Ji1GIzYnLUYsNidRInlGJ0ZJRkxGXm9GYW9GSUZMRl5vRmFvRklGTEY0RklGTEZeb0Zhby8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGZnEvJSliZXZlbGxlZEdGM0ZFRklGTEYxRjRGSUZMRjRGSUZMRjFGNA==In this case we can use the "combine" command: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYtLUkjbWlHRiQ2I1EhRictRiM2JUYrLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRistSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuMGVtRicvJSZkZXB0aEdGPC8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GODYmRjpGPUZAL0ZDUSVhdXRvRidGL0YrLyUnZmFtaWx5R1EwTGliZXJhdGlvbn5TYW5zRicvJSVzaXplR1EjMTFGJ0YxRjQ=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EoY29tYmluZUYnLyUnZmFtaWx5R1EwTGliZXJhdGlvbn5TYW5zRicvJSVzaXplR1EjMTFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2Jy1GLDYnUSIlRidGL0YyRjVGOEYvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GOVEnbm9ybWFsRidGL0YyRkZGL0YyRkNGRg=="combine" works also with other kinds of expressions:
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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EoY29tYmluZUYnLyUnZmFtaWx5R1EwTGliZXJhdGlvbn5TYW5zRicvJSVzaXplR1EjMTFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2Jy1GLDYnUSIlRidGL0YyRjVGOEYvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GOVEnbm9ybWFsRidGL0YyRkZGL0YyRkNGRg==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2I1EhRictRiM2JUYrLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRisvJSdmYW1pbHlHUTBMaWJlcmF0aW9uflNhbnNGJy8lJXNpemVHUSMxMUYnRjFGNA==Expression manipulation (subs, eval, evalf)LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2I1EhRictRiM2JUYrLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRisvJSdmYW1pbHlHUTBMaWJlcmF0aW9uflNhbnNGJy8lJXNpemVHUSMxMUYnRjFGNA==We can substitute variables in expressions by arbitrary values using the "subs" command:
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYlLUkobWZlbmNlZEdGJDYmLUYjNictSSNtaUdGJDYnUSJ4RicvJSdmYW1pbHlHUTBMaWJlcmF0aW9uflNhbnNGJy8lJXNpemVHUSMxMUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi9RIitGJ0Y3RjovRkFRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZLLyUpc3RyZXRjaHlHRksvJSpzeW1tZXRyaWNHRksvJShsYXJnZW9wR0ZLLyUubW92YWJsZWxpbWl0c0dGSy8lJ2FjY2VudEdGSy8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRlotRjQ2J1EieUYnRjdGOkY9RkAvJStleGVjdXRhYmxlR0ZLRkdGN0Y6RkctRiM2KS1JI21uR0YkNiZRIjVGJ0Y3RjpGR0Y3RjpGPUZqbi8lMGZvbnRfc3R5bGVfbmFtZUdRKDJEfk1hdGhGJ0ZALyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0ZqbkZHLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1Elc3Vic0YnLyUnZmFtaWx5R1EwTGliZXJhdGlvbn5TYW5zRicvJSVzaXplR1EjMTFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2Ly1GLDYnUSJ4RidGL0YyRjVGOC1JI21vR0YkNi9RIj1GJ0YvRjIvRjlRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZLLyUpc3RyZXRjaHlHRksvJSpzeW1tZXRyaWNHRksvJShsYXJnZW9wR0ZLLyUubW92YWJsZWxpbWl0c0dGSy8lJ2FjY2VudEdGSy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlotSSNtbkdGJDYmUSIxRidGL0YyRkctRkQ2L1EiLEYnRi9GMkZHRkkvRk1GN0ZORlBGUkZURlYvRllRJjAuMGVtRicvRmZuUSwwLjMzMzMzMzNlbUYnLUZENi9RIn5GJ0YvRjJGR0ZJRkxGTkZQRlJGVEZWRl9vL0ZmbkZgby1JKG1hY3Rpb25HRiQ2JS1JKm12ZXJiYXRpbUdGJDYjUT4qJCksJkkieEc2IiIiIkkieUc2IiIiIiIiJiIiIkYnLyUrYWN0aW9udHlwZUdROm1hcGxlc29mdC5jb206bGFiZWwoTDk1NilGJy8lJXZpZXdHUSZsYWJlbEYnLUYsNiNRIUYnLUYjNiVGZHAvJStleGVjdXRhYmxlR0ZLRkdGZHBGL0YyRmlwRkdGL0YyRkdGL0YyRmlwRkc=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1Elc3Vic0YnLyUnZmFtaWx5R1EwTGliZXJhdGlvbn5TYW5zRicvJSVzaXplR1EjMTFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2Li1GLDYnUSJ5RidGL0YyRjVGOC1JI21vR0YkNi9RIj1GJ0YvRjIvRjlRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZLLyUpc3RyZXRjaHlHRksvJSpzeW1tZXRyaWNHRksvJShsYXJnZW9wR0ZLLyUubW92YWJsZWxpbWl0c0dGSy8lJ2FjY2VudEdGSy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlotSSNtbkdGJDYmUSIyRidGL0YyRkctRkQ2L1EiLEYnRi9GMkZHRkkvRk1GN0ZORlBGUkZURlYvRllRJjAuMGVtRicvRmZuUSwwLjMzMzMzMzNlbUYnLUkobWFjdGlvbkdGJDYlLUkqbXZlcmJhdGltR0YkNiNRPiokKSwmSSJ4RzYiIiIiSSJ5RzYiIiIiIiImIiIiRicvJSthY3Rpb250eXBlR1E6bWFwbGVzb2Z0LmNvbTpsYWJlbChMOTU2KUYnLyUldmlld0dRJmxhYmVsRictRiw2I1EhRictRiM2JUZgcC8lK2V4ZWN1dGFibGVHRktGR0ZgcEYvRjJGZXBGR0YvRjJGR0YvRjJGZXBGRw==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1Elc3Vic0YnLyUnZmFtaWx5R1EwTGliZXJhdGlvbn5TYW5zRicvJSVzaXplR1EjMTFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2Ni1GLDYnUSJ4RidGL0YyRjVGOC1JI21vR0YkNi9RIj1GJ0YvRjIvRjlRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZLLyUpc3RyZXRjaHlHRksvJSpzeW1tZXRyaWNHRksvJShsYXJnZW9wR0ZLLyUubW92YWJsZWxpbWl0c0dGSy8lJ2FjY2VudEdGSy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlotSSNtbkdGJDYmUSIxRidGL0YyRkctRkQ2L1EiLEYnRi9GMkZHRkkvRk1GN0ZORlBGUkZURlYvRllRJjAuMGVtRicvRmZuUSwwLjMzMzMzMzNlbUYnLUZENi9RIn5GJ0YvRjJGR0ZJRkxGTkZQRlJGVEZWRl9vL0ZmbkZgby1GLDYnUSJ5RidGL0YyRjVGOEZDLUYsNidRImFGJ0YvRjJGNUY4LUZENi9RIitGJ0YvRjJGR0ZJRkxGTkZQRlJGVEZWL0ZZUSwwLjIyMjIyMjJlbUYnL0ZmbkZhcEZnbkZbb0Zjby1JKG1hY3Rpb25HRiQ2JS1JKm12ZXJiYXRpbUdGJDYjUT4qJCksJkkieEc2IiIiIkkieUc2IiIiIiIiJiIiIkYnLyUrYWN0aW9udHlwZUdROm1hcGxlc29mdC5jb206bGFiZWwoTDk1NilGJy8lJXZpZXdHUSZsYWJlbEYnLUYsNiNRIUYnLUYjNiVGYHEvJStleGVjdXRhYmxlR0ZLRkdGYHFGL0YyRmVxRkdGL0YyRkdGL0YyRmVxRkc=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYtLUkjbWlHRiQ2I1EhRictRiM2JUYrLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRistSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuMGVtRicvJSZkZXB0aEdGPC8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GODYmRjpGPUZAL0ZDUSVhdXRvRidGL0YrLyUnZmFtaWx5R1EwTGliZXJhdGlvbn5TYW5zRicvJSVzaXplR1EjMTFGJ0YxRjQ=The substitutions are carried out in the order in which they are given.
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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYtLUkjbWlHRiQ2I1EhRictRiM2JUYrLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRistSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuMGVtRicvJSZkZXB0aEdGPC8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GODYmRjpGPUZAL0ZDUSVhdXRvRidGL0YrLyUnZmFtaWx5R1EwTGliZXJhdGlvbn5TYW5zRicvJSVzaXplR1EjMTFGJ0YxRjQ=A similar command is "eval":
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
The difference is, that "eval" performs a simplification on the result while "subs" does only a substitution: Compare
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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2J0YrLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRicvJSVzaXplR1EjMTJGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0YrRjdGOg==Related to "eval" is the command "evalf" ("evaluate to a floating point number:)
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Now, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn will evaluate to 7:
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We can tell Maple to forget about this definition by using either the menu or the "unassign" command (note the single quotes!):
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Now LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn again evaluates to itself:
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2J1EidkYnLyUnZmFtaWx5R1EwTGliZXJhdGlvbn5TYW5zRicvJSVzaXplR1EjMTFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjlRJ25vcm1hbEYn
We have already seen that Maple does usually not alter the input apart from trivial simplifications:
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
Here, we can use the "simplify" command in order to tell Maple to make the expression as simple as possible:
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1Epc2ltcGxpZnlGJy8lJ2ZhbWlseUdRMExpYmVyYXRpb25+U2Fuc0YnLyUlc2l6ZUdRIzExRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYmLUYjNictRiw2J1ElZXhwckYnRi9GMkY1RjhGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjlRJ25vcm1hbEYnRi9GMkZGRi9GMkZDRkY=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2I1EhRictRiM2JUYrLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRisvJSdmYW1pbHlHUTBMaWJlcmF0aW9uflNhbnNGJy8lJXNpemVHUSMxMUYnRjFGNA==
Sometimes, expressions don't get fully simplified:
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
Maple can't do any simplification here, because it does not have enough information on the variables. We can supply more information using the "assuming" statement:
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We can also put global assumptions on variables using the "assume" command:
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(Maple marks the presence of assumptions by a tilde - this can be changed using the "ToolsLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LlEoJnNyYXJyO0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGRUYvRjI=Options" menu.)
We can remove the assumptions with "unassign"
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Now, again
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
Alternatively, we can also restart the Maple session. This will remove all assigments which we have made. To restart either type
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2J1EocmVzdGFydEYnLyUnZmFtaWx5R1EwTGliZXJhdGlvbn5TYW5zRicvJSVzaXplR1EjMTFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GOVEnbm9ybWFsRic=
or use the corresponding icon.JSFHFunctionsWe can assign (mathematical) functions in Maple using an "arrow notation" (type "-" and ">"):
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
We can now compute different values of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn by using the normal function notation:
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EiZkYnLyUnZmFtaWx5R1EwTGliZXJhdGlvbn5TYW5zRicvJSVzaXplR1EjMTFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2Jy1JI21uR0YkNiZRIjBGJ0YvRjIvRjlRJ25vcm1hbEYnRi9GMi8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRkRGL0YyRkRGL0YyRkZGRA==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EiZkYnLyUnZmFtaWx5R1EwTGliZXJhdGlvbn5TYW5zRicvJSVzaXplR1EjMTFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2Jy1JI21uR0YkNiZRIjFGJ0YvRjIvRjlRJ25vcm1hbEYnRi9GMi8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRkRGL0YyRkRGL0YyRkZGRA==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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EiZkYnLyUnZmFtaWx5R1EwTGliZXJhdGlvbn5TYW5zRicvJSVzaXplR1EjMTFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2Jy1GLDYnUSJhRidGL0YyRjVGOEYvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GOVEnbm9ybWFsRidGL0YyRkZGL0YyRkNGRg==
For functions of more than one argument, we have to enclose the arguments in brackets:
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 application of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiZ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn uses again the normal mathematical notation:
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, that the following statement does not define a function in older versions of Maple (or the command line version of Maple):
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(Modern versions will define a function here and some versions of Maple will ask us whether we actually meant to define a function.)
If we choose "remember table assigment" (the default in older versions), then this will not make LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEiaEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn a function.
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EiaEYnLyUnZmFtaWx5R1EwTGliZXJhdGlvbn5TYW5zRicvJSVzaXplR1EjMTFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2Jy1JI21uR0YkNiZRIjFGJ0YvRjIvRjlRJ25vcm1hbEYnRi9GMi8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnRkRGL0YyRkRGL0YyRkZGRA==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EiaEYnLyUnZmFtaWx5R1EwTGliZXJhdGlvbn5TYW5zRicvJSVzaXplR1EjMTFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2Jy1GLDYnUSJ0RidGL0YyRjVGOEYvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GOVEnbm9ybWFsRidGL0YyRkZGL0YyRkNGRg==
Only when applied to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn will we see the definitionLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EiaEYnLyUnZmFtaWx5R1EwTGliZXJhdGlvbn5TYW5zRicvJSVzaXplR1EjMTFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2Jy1GLDYnUSJ4RidGL0YyRjVGOEYvRjIvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GOVEnbm9ybWFsRidGL0YyRkZGL0YyRkNGRg==
Another way of obtaining a function is to start from an expression and then to declare some of the variables as parameters using the "unapply" command:
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
We can define piecewise functions using either the "piecewise" command
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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2I1EhRictRiM2JUYrLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRisvJSVzaXplR1EjMTFGJ0YxRjQ=See also the plot of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEicUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYnLyUlc2l6ZUdRIzEyRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GM1Enbm9ybWFsRic= (open the context menu by right clicking and then choose "PlotsLUkjbW9HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2L1EnJnJhcnI7RicvJSdmYW1pbHlHUTBMaWJlcmF0aW9uflNhbnNGJy8lJXNpemVHUSMxMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZG2-D Plot"):SSJxRzYiLUkjbW9HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2LlEnJnJhcnI7RicvJTBmb250X3N0eWxlX25hbWVHUSgyRH5NYXRoRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHUSV0cnVlRicvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkQ=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
Or we can use the expressions palette
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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkjbWlHRiQ2I1EhRictRiM2J0YrLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRicvJSVzaXplR1EjMTJGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0YrLUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHUSYwLjBlbUYnLyUmZGVwdGhHRkIvJSpsaW5lYnJlYWtHUShuZXdsaW5lRictRj42JkZARkNGRi9GSVElYXV0b0YnRi9GK0YxRjdGOg==JSFH
See also the plot for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEicUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRidGMi9GNlEnbm9ybWFsRic=:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEicUYnLyUlc2l6ZUdRIzExRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRi8vJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GNlEnbm9ybWFsRic=LUkjbW9HNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2LlEnJnJhcnI7RicvJTBmb250X3N0eWxlX25hbWVHUSgyRH5NYXRoRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHUSV0cnVlRicvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkQ=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SetsMaple can compute with (finite) sets.
We can define sets by enclosing the objects in curly braces:
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
As expected, sets contain each element only once:
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
Maple does know the usual set operations: Intersection
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(use the palette for the last input or type "cap [Esc]").
We can do unions:
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbWlHRiQ2J1EiU0YnLyUnZmFtaWx5R1EwTGliZXJhdGlvbn5TYW5zRicvJSVzaXplR1EjMTFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYvUSJ+RidGL0YyL0Y5USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQy8lKXN0cmV0Y2h5R0ZDLyUqc3ltbWV0cmljR0ZDLyUobGFyZ2VvcEdGQy8lLm1vdmFibGVsaW1pdHNHRkMvJSdhY2NlbnRHRkMvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZSLUY8NjFRJnVuaW9uRidGL0YyLyUlYm9sZEdGNy9GOVElYm9sZEYnLyUrZm9udHdlaWdodEdGZW5GQUZERkZGSEZKRkxGTkZQRlNGOy1GLDYnUSJURidGL0YyRjVGOEYvRjIvJStleGVjdXRhYmxlR0ZDRj8=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbWlHRiQ2J1EiU0YnLyUnZmFtaWx5R1EwTGliZXJhdGlvbn5TYW5zRicvJSVzaXplR1EjMTFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYvUSJ+RidGL0YyL0Y5USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQy8lKXN0cmV0Y2h5R0ZDLyUqc3ltbWV0cmljR0ZDLyUobGFyZ2VvcEdGQy8lLm1vdmFibGVsaW1pdHNHRkMvJSdhY2NlbnRHRkMvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZSLUY8Ni9RJiZjdXA7RidGL0YyRj9GQUZERkZGSEZKRkxGTkZQRlNGOy1GLDYnUSJURidGL0YyRjVGOEYvRjIvJStleGVjdXRhYmxlR0ZDRj8=
(use the palette or type "cup [Esc]").
And differences
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
(use the palette or type "bsol [Esc]").
We can compute the cardinality of a set with the "numelems" function:
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EpbnVtZWxlbXNGJy8lJ2ZhbWlseUdRMExpYmVyYXRpb25+U2Fuc0YnLyUlc2l6ZUdRIzExRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYmLUYjNictRiw2J1EiVEYnRi9GMkY1RjhGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjlRJ25vcm1hbEYnRi9GMkZGRi9GMkZDRkY=
We can also compute relations between sets:
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
Finally, we can also test for membership:
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
Here, Maple does not evaluate the statement to a truth value. We have to use the "evalb" command ("evaluate to a boolean value"):
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EmZXZhbGJGJy8lJ2ZhbWlseUdRMExpYmVyYXRpb25+U2Fuc0YnLyUlc2l6ZUdRIzExRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYmLUYjNictRiw2J1EiJUYnRi9GMkY1RjhGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjlRJ25vcm1hbEYnRi9GMkZGRi9GMkZDRkY=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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2I1EhRictRiM2JUYrLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRisvJSdmYW1pbHlHUTBMaWJlcmF0aW9uflNhbnNGJy8lJXNpemVHUSMxMUYnRjFGNA==Derivation and integration
Maple can compute derivatives of symbolic expressions using the "diff" command:
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
Recent versions of Maple also recognise the "prime" notation to mean derivation with respect to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRicvJSVzaXplR1EjMTJGJ0YyL0Y2USdub3JtYWxGJw==:
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
(also the right click context menu can be used.)
Here, the first argument is the expression and the second argument is the variable with respect to which we derive.
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1ElZGlmZkYnLyUnZmFtaWx5R1EwTGliZXJhdGlvbn5TYW5zRicvJSVzaXplR1EjMTFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2LC1GLDYnUSJ4RidGL0YyRjVGOC1JI21vR0YkNi9RJyZzZG90O0YnRi9GMi9GOVEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRksvJSlzdHJldGNoeUdGSy8lKnN5bW1ldHJpY0dGSy8lKGxhcmdlb3BHRksvJS5tb3ZhYmxlbGltaXRzR0ZLLyUnYWNjZW50R0ZLLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGWi1GLDYnUSJ5RidGL0YyRjVGOC1GRDYvUSIsRidGL0YyRkdGSS9GTUY3Rk5GUEZSRlRGVkZYL0ZmblEsMC4zMzMzMzMzZW1GJy1GRDYvUSJ+RidGL0YyRkdGSUZMRk5GUEZSRlRGVkZYRmVuRmduRi9GMi8lK2V4ZWN1dGFibGVHRktGR0YvRjJGR0YvRjJGY29GRw==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1ElZGlmZkYnLyUnZmFtaWx5R1EwTGliZXJhdGlvbn5TYW5zRicvJSVzaXplR1EjMTFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiYtRiM2Ky1GLDYnUSJ4RidGL0YyRjVGOC1JI21vR0YkNi9RJyZzZG90O0YnRi9GMi9GOVEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRksvJSlzdHJldGNoeUdGSy8lKnN5bW1ldHJpY0dGSy8lKGxhcmdlb3BHRksvJS5tb3ZhYmxlbGltaXRzR0ZLLyUnYWNjZW50R0ZLLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGWi1GLDYnUSJ5RidGL0YyRjVGOC1GRDYvUSIsRidGL0YyRkdGSS9GTUY3Rk5GUEZSRlRGVkZYL0ZmblEsMC4zMzMzMzMzZW1GJy1GLDYnUSJ6RidGL0YyRjVGOEYvRjIvJStleGVjdXRhYmxlR0ZLRkdGL0YyRkdGL0YyRmNvRkc=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2I1EhRictRiM2JUYrLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnRisvJSdmYW1pbHlHUTBMaWJlcmF0aW9uflNhbnNGJy8lJXNpemVHUSMxMUYnRjFGNA==We can compute partial and higher order derviatives by adding more variables as arguments:
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There is a short hand notation for multiple repetitions of the same variable using "$": The expression "x$n" refers to "n" repetitions of "x". For instance, in order to compute the 99-th derivative of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYoLUkjbW5HRiQ2JFEkMTAwRicvRjZRJ25vcm1hbEYnLyUnZmFtaWx5R1EwVGltZXN+TmV3flJvbWFuRidGMi8lK2ZvcmVncm91bmRHUSxbMjAwLDAsMjAwXUYnLyUscGxhY2Vob2xkZXJHRjRGNS8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGQEY+, we can use: 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For functions, the "D" operator is used instead of "diff":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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EiREYnLyUnZmFtaWx5R1EwTGliZXJhdGlvbn5TYW5zRicvJSVzaXplR1EjMTFGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkobWZlbmNlZEdGJDYmLUYjNictRiw2J1EiZkYnRi9GMi9GNlEldHJ1ZUYnL0Y5USdpdGFsaWNGJ0YvRjIvJStleGVjdXRhYmxlR0Y3RjhGL0YyRjhGL0YyRkdGOA==As you can see, the result of "LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEiREYnLyUnaXRhbGljR1EmZmFsc2VGJy8lK2V4ZWN1dGFibGVHRjEvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkobWZlbmNlZEdGJDYlLUYjNiUtRiw2JlEiZkYnL0YwUSV0cnVlRidGMi9GNVEnaXRhbGljRidGMkY0RjJGNEYyRjQ=" is again a function.
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2J1EiREYnLyUnZmFtaWx5R1EwTGliZXJhdGlvbn5TYW5zRicvJSVzaXplR1EjMTFGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkobWZlbmNlZEdGJDYmLUYjNictRiw2J1EiZkYnRi9GMi9GNlEldHJ1ZUYnL0Y5USdpdGFsaWNGJ0YvRjIvJStleGVjdXRhYmxlR0Y3RjhGL0YyRjgtRjw2Ji1GIzYnLUkjbW5HRiQ2JlEiMUYnRi9GMkY4Ri9GMkZHRjhGL0YyRjhGL0YyRkdGOA==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2J1EiREYnLyUnZmFtaWx5R1EwTGliZXJhdGlvbn5TYW5zRicvJSVzaXplR1EjMTFGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkobWZlbmNlZEdGJDYmLUYjNictRiw2J1EiZkYnRi9GMi9GNlEldHJ1ZUYnL0Y5USdpdGFsaWNGJ0YvRjIvJStleGVjdXRhYmxlR0Y3RjhGL0YyRjgtRjw2Ji1GIzYnLUYsNidRJyYjOTYwO0YnRi9GMkY1RjhGL0YyRkdGOEYvRjJGOEYvRjJGR0Y4
Note, that we did not have to specify the parameter for the derivation here. It will always be the parameter of the function.
We can compute partial and iterated derivates by adding the position of the argument with respect to which we want to derive in square brackets just after the D:
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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2J1EiREYnLyUnZmFtaWx5R1EwTGliZXJhdGlvbn5TYW5zRicvJSVzaXplR1EjMTFGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkobWZlbmNlZEdGJDYoLUYjNiUtSSNtbkdGJDYmUSIyRidGL0YyRjgvJStleGVjdXRhYmxlR0Y3RjhGL0YyRjgvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRictRjw2Ji1GIzYlLUYsNidRImdGJ0YvRjIvRjZRJXRydWVGJy9GOVEnaXRhbGljRidGREY4Ri9GMkY4RkRGOA==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
(The examples compute 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, 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, 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 and 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, respectively).
It is also possible to compute higher derivatives with the "function exponentiation" operator "@@". We will discuss it in more detail later.
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1JKG1mZW5jZWRHRiQ2Ji1GIzYmLUYsNidRIkRGJy8lJ2ZhbWlseUdRMExpYmVyYXRpb25+U2Fuc0YnLyUlc2l6ZUdRIzExRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi9RI0BARidGOUY8RkIvJSZmZW5jZUdGQS8lKnNlcGFyYXRvckdGQS8lKXN0cmV0Y2h5R0ZBLyUqc3ltbWV0cmljR0ZBLyUobGFyZ2VvcEdGQS8lLm1vdmFibGVsaW1pdHNHRkEvJSdhY2NlbnRHRkEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZZLUkjbW5HRiQ2JlEiMkYnRjlGPEZCRkJGOUY8RkItRjI2Ji1GIzYkLUYsNidRImZGJ0Y5RjwvRkBRJXRydWVGJy9GQ1EnaXRhbGljRidGQkY5RjxGQkZCRisvJStleGVjdXRhYmxlR0ZBRkI=Antiderivatives ("indefinite integrals") can be computed using "int":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
We can also use "int [Esc]" or the palettes to enter integrals:
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 can compute definite integrals with the following syntax:
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Maple uses the two-dot ".." notation to denotes ranges of numbers.This also works with multiple integrals.
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If we do not give a range for the summation variable, then Maple computes an "antidifference":
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(We will (probably) discuss antidifferences in the third part of the lecture when we learn how Maple actually finds these expressions.)
There is a related command "add", which also performs a summation. However, it can only be applied to finite sums.
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We will revisit "add" when we discuss programming in Maple.
EquationsWe can input equations as symbolic values in Maple
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Without further instruction, Maple does not try to simplify or solve the equations.
Equations may be assigned to a variable:
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We can add equations together or multiply them by values:
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We can access the left hand side of an equations or the right hand side of an equation with "lhs" or "rhs", respectively.
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We will discuss how Maple can solve equations automatically later in this lecture.
It is also possible to enter and compute with inequalities:
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbW5HRiQ2JlEiN0YnLyUnZmFtaWx5R1EwTGliZXJhdGlvbn5TYW5zRicvJSVzaXplR1EjMTFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSNtb0dGJDYvUSJ+RidGL0YyRjUvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj4vJSlzdHJldGNoeUdGPi8lKnN5bW1ldHJpY0dGPi8lKGxhcmdlb3BHRj4vJS5tb3ZhYmxlbGltaXRzR0Y+LyUnYWNjZW50R0Y+LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTS1JI21pR0YkNidRInhGJ0YvRjIvJSdpdGFsaWNHUSV0cnVlRicvRjZRJ2l0YWxpY0YnLUY5Ni9RJiZsZXE7RidGL0YyRjVGPEY/RkFGQ0ZFRkdGSS9GTFEsMC4yNzc3Nzc4ZW1GJy9GT0Znbi1GLDYmUSIwRidGL0YyRjUvJStleGVjdXRhYmxlR0Y+RjU=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2J1EieUYnLyUnZmFtaWx5R1EwTGliZXJhdGlvbn5TYW5zRicvJSVzaXplR1EjMTFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYvUS8mR3JlYXRlckVxdWFsO0YnRi9GMi9GOVEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkMvJSlzdHJldGNoeUdGQy8lKnN5bW1ldHJpY0dGQy8lKGxhcmdlb3BHRkMvJS5tb3ZhYmxlbGltaXRzR0ZDLyUnYWNjZW50R0ZDLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUi1JI21uR0YkNiZRIjBGJ0YvRjJGPy8lK2V4ZWN1dGFibGVHRkNGPw==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2J1EiJUYnLyUnZmFtaWx5R1EwTGliZXJhdGlvbn5TYW5zRicvJSVzaXplR1EjMTFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYvUSIrRidGL0YyL0Y5USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQy8lKXN0cmV0Y2h5R0ZDLyUqc3ltbWV0cmljR0ZDLyUobGFyZ2VvcEdGQy8lLm1vdmFibGVsaW1pdHNHRkMvJSdhY2NlbnRHRkMvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZSLUYsNidRIyUlRidGL0YyRjVGOC8lK2V4ZWN1dGFibGVHRkNGPw==(Here, the "%%" symbol refers to the second-last expression which was evaluated. There is also "%%%" for the third last expression. Use them with the same care as "%"!)
To enter LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2LlEmJmxlcTtGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkUvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lJXNpemVHUSMxMkYnRi9GMg==and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2LlEvJkdyZWF0ZXJFcXVhbDtGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkUvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lJXNpemVHUSMxMkYnRi9GMg==type "< =" and "> =". For LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2LlErJk5vdEVxdWFsO0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGRS8lJ2ZhbWlseUdRMFRpbWVzfk5ld35Sb21hbkYnLyUlc2l6ZUdRIzEyRidGL0Yytype "! =".printing, quoting, LaTeX, inert formsMaple has a builtin command "print" which can be used to print any Maple expression:
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
This is not extremely useful right now, but we can make use of it later, when we write our own procedures in Maple.
Sometimes, we would like to stop Maple from evaluating a variable before printing.
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
For this, we can use "quotes": If we enter single quotation marks around a variable, this tells Maple not to evaluate it:
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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EpdW5hc3NpZ25GJy8lJ2ZhbWlseUdRMExpYmVyYXRpb25+U2Fuc0YnLyUlc2l6ZUdRIzExRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYmLUYjNictRiw2J1EieEYnRi9GMkY1RjhGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjlRJ25vcm1hbEYnRi9GMkZGRi9GMkZDRkY=
then Maple first evaluates LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn to 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 before applying the "unassign" command. The result is an error. If we use quotes,
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
then Maple does not evaluate LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn and "unassign" is passed the just the variable LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn.)
We can ask Maple to print an expression using LaTeX syntax: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(Maple's LaTeX output is not necessarily the most pretty one, and Maple's insistence on evaluating expressions can be annoying...)
Actually, we can enter inert (meaning unevaluated) integral using the "Int" command (notice the capitalisation!). Still Maple will not leave our expression completely untouched:
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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EmbGF0ZXhGJy8lJ2ZhbWlseUdRMExpYmVyYXRpb25+U2Fuc0YnLyUlc2l6ZUdRIzExRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYmLUYjNictRiw2J1EiJUYnRi9GMkY1RjhGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjlRJ25vcm1hbEYnRi9GMkZGRi9GMkZDRkY=JSFHAlso the derivation and sum have an inert form: Use "Diff" and "Sum" (notice the capitalisation).
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