Maple Basics. K. Cooper

Transkript

1 Basics K. Cooper 2012

2 History History 1982 Macsyma/MIT 1988 Mathematica/Wolfram 1988 /Waterloo Others later

3 History Why? Prevent silly mistakes Time Complexity Plots Generate LATEX This is the 21st century; we have vast power at our ngertips: why are we still using pencil and paper?!

4 History Why? Macsyma is too old, klunky, inferior plots Mathematica uses extremely quirky syntax, does not handle NFS well tries to use a mathematical syntax

5 History When? is for symbolic processing. Use it for nding derivatives, antiderivatives, doing algebraic operations, solving dierential equations Use Matlab for purely numerical calculations Engineers use Matlab a lot; is used mostly by mathematicians.

6 Semicolons statements end with a semicolon. 3+4; In the document format, a single expression in a single cell can neglect the semicolon. You can use semicolons to put multiple statements on a single line 3+4; 4+5;

7 Assignment The symbol := indicates assignment of the value of the expression on the right to the variable on the left. f:=x 2; # results in f equal to x 2. Note: the expression on the right is evaluated once before the assignment is made. x:=5; f:=x 2; # results in f equal to 25. The symbol = represents a substitution. It can be used in macros to substitute the expression on the right for the object on the left. subs(x=1,x 2); The symbol = can also be a test for equality. a:=5; if a = 5 then print(yes); else print(no); end if;

8 Expressions and Functions f:=x 2; denes f to be an expression If x has a value, then f could be a number, if not, f is just symbolic. The expression f(2) is almost meaningless. g:=x->x 2; denes g to be a function. The expression g(2) has meaning. It turns out that f=g(x) is true.

9 Functions and Expressions To convert a function to an expression, just evaluate it. g(x) is an expression. To convert an expression to a function, use unapply h:=unapply(f,x); converts the expression f into a function using argument x. f(x) is meaningless, but h(x) is useful.

10 Evaluation To evaluate an expression, use eval() eval(f,x=2); gives the same result for our example as g(2). Note that eval() is really about substitution subs(x=2,f); has more or less the same eect as eval

11 Lists The symbols [ ] are reserved to enclose ordered lists of objects in, or or refer to elements of those lists.

12 Lists The symbols [ ] are reserved to enclose ordered lists of objects in, or or refer to elements of those lists. List elements have integer indices starting with one.

13 Lists The symbols [ ] are reserved to enclose ordered lists of objects in, or or refer to elements of those lists. List elements have integer indices starting with one. li:=[11,12,13,13]; li[2] gives 12

14 Lists The symbols [ ] are reserved to enclose ordered lists of objects in, or or refer to elements of those lists. List elements have integer indices starting with one. li:=[11,12,13,13]; li[2] gives 12 You can make lists of lists: li:=[[1,11],[2,12]]; li[2] gives [2,12]

15 Parts of expressions uses complex linked lists to parse expressions Each part of an expression goes into some entry in a complicated data structure We can refer to parts of the expression by using op()

16 Parts of expressions uses complex linked lists to parse expressions Each part of an expression goes into some entry in a complicated data structure We can refer to parts of the expression by using op() ex:=x (a+1)+b*x a+c; op(1,ex) gives x a+1

17 Parts of expressions uses complex linked lists to parse expressions Each part of an expression goes into some entry in a complicated data structure We can refer to parts of the expression by using op() ex:=x (a+1)+b*x a+c; op(1,ex) gives x a+1 op(2,ex) gives b x a

18 Parts of expressions uses complex linked lists to parse expressions Each part of an expression goes into some entry in a complicated data structure We can refer to parts of the expression by using op() ex:=x (a+1)+b*x a+c; op(1,ex) gives x a+1 op(2,ex) gives b x a op([1,1],ex) gives x

19 Parts of expressions uses complex linked lists to parse expressions Each part of an expression goes into some entry in a complicated data structure We can refer to parts of the expression by using op() ex:=x (a+1)+b*x a+c; op(1,ex) gives x a+1 op(2,ex) gives b x a op([1,1],ex) gives x op([1,2],ex) gives a + 1

20 Parts of expressions uses complex linked lists to parse expressions Each part of an expression goes into some entry in a complicated data structure We can refer to parts of the expression by using op() ex:=x (a+1)+b*x a+c; op(1,ex) gives x a+1 op(2,ex) gives b x a op([1,1],ex) gives x op([1,2],ex) gives a + 1 op([1,2,2],ex) gives 1

21 Numbers is symbolic: no approximations are made until you ask for them. has a constant called Pi: its value is π knows that sin(2) is irrational, and will refuse to approximate it.

22 Floating point approximations When you need an approximation, use evalf() evalf(pi) gives You can give a second argument to evalf() to specify the number of digits you want, e.g. evalf(pi,30) gives If you want a proper machine hardware oating point number, use evalhf(), which takes only one argument. If you nd yourself using evalhf much, it is probably a signal that you should be using Matlab.

23 Ranges x=0..x species a range, with behavior depending on the context

24 Ranges x=0..x species a range, with behavior depending on the context Integral Denotes the limits of integration Summation Denotes the indices over which the sum applies Plot Denotes the axis limits List creation Denotes the subscripts over which the list will be made