i PowerBookG4 Maple 9 L A T E X Maple Maple 9 Waterloo Maple Inc. Macintosh, Power Macintosh Apple Computer, Inc. UNIX AT&T X Window System Microsoft

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1 Maple Copyright 005 Shigeto R. Nishitani Department of Informatics, Kwansei Gakuin University, Sanda, Japan [email protected] 7 5 3

2 i PowerBookG4 Maple 9 L A T E X Maple Maple 9 Waterloo Maple Inc. Macintosh, Power Macintosh Apple Computer, Inc. UNIX AT&T X Window System Microsoft Windoes Microsoft Corporation Maple Copyright c 005 v.0 ( ) ( ) Maple : Essentials and Applications on Numerical Recipe Copyright c 005 by Shigeto R. Nishitani. This material may be distributed only subject to the terms and conditions set forth in the Open Publication License, v.0 or later (the latest version is presently available at Distribution of the work or derivative of the work in any standard (paper) book form is prohibited unless prior permission is obtained from the copyright holder.

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4 iii Maple Maple proc Maple Maple

5 iv.6 Maple Maple linux

6 . Maple.. Maple PC user interface Java base OS linux xmaple GUI maple maple terminal character.. (">") [enter] enter return [shift+enter] shift enter > +;[ enter] > factor(x^-3*x+);[ shift+enter] > 3/+5/3;[ shift+enter] > 00!;[ enter] (x ) (x ) \ \ > plot(tanh(x),x=-5..5);[ enter]

7 x 0.5 > eq:=sin(x)*cos(y):[ shift+enter] > plot3d(eq,x=-pi..pi,y=-pi..pi);[ enter] y x 3 enter shift+enter enter shift+enter shift+enter ( ) enter enter [enter] [shift+enter]

8 .. 3 (">") [shift+enter]..3 enter π +π > plot(sin(x),x=-pi..pi); Error, (in plot) range values must be real constants ( (plot ) ) Maple pi Pi > plot(sin(x),x=-pi..pi); x Maple

9 4 >?plot; plot index help Help Calling Sequence: Parameters: Description: Examples: See Also: Windows Examples Maple

10 > mass:=0; mass := 0 > force:=-mass*accel; force := 0 accel % > exp:=%; exp := 0 accel > restart; > mass:= mass ; > force:=-mass*accel; mass := mass force := mass accel subs > subs(mass=0,accel=4,force); > force; 40 mass accel

11 6 > x:=;y:=3; > f:= x+y ;g:=x+y; x := y := 3 f := x + y g := 5 restart free.. (trigonometric functions) log ln > log[](5); ln(5) ln() evalf(evaluate float ) > evalf(%); Maple help index keywords? inifcns -? index[package] - (DETools), (linalg), (plots)? index[function] - Maple > with(plots): Warning, the name changecoords has been redefined

12 i) ii) unapply > f:=x->-x*ln(exp(-/x)/(-exp(-/x))); f := x x ln e ( x ) unapply eq x f > eq:=(+exp(-/t))/(-exp(-/t)): > f:=unapply(eq,t); e( x ) f := T + e( T ) e ( T ) T 3 > f(3); > f3:=t->eq; > f3(3); + e ( /3) e ( /3) f3 := T eq + e ( T ) e ( T )..4 Maple plot

13 8 > plot(f(x),x=0..0); 0 x > plot({f(x),f(x)},x=0..0); x plot3d > plot3d(sin(x)*exp(-y),x=-pi..pi,y=-pi..pi); y 0 0 x 3 3

14 .. 9 plotting plot ) > with(plots): > with(plottools): plots package plottools package.6..5 solve > eqset:={x+y=,y=+x^}; > solve(eqset,{x,y}); > x;y; eqset := {x + y =, y = + x } {y =, x = 0}, {x =, y = } x,y x,y assign > solset:=solve(eqset,{x,y}); > solset[]; > assign(solset[]); > x;y; x y solset := {y =, x = 0}, {x =, y = } {y =, x = 0} fsolve > restart; > f:=x->-x*ln(exp(-/x)/(-exp(-/x))); > fsolve(f(x)=0,x); 0

15 0 f := x x ln e( x ) e ( x )..6 diff > restart; > diff(x^,x); > diff(y^*x^,x,x); > c:=(x,t)->x(x)*t(t); > diff(c(x,t),x); > diff(c(x,t),x,t); x y c := (x, t) X(x) T(t) ( d X(x)) T(t) dx ( d dx X(x)) ( d dt T(t))..7 > int(ln(x),x); > int(sin(x),x=-pi..0); x ln(x) x int integrate > eq:=x^/sqrt(-x^); > int(eq,x); eq := x x

16 .. x x > eq:=exp(-x^); > int(eq,x=0..zz); + arcsin(x) eq := e ( x ) π erf(zz) Int. x, cos(x) x = f(x) = x cos(x) x = fsolve x cos(x) = 0 4. E(T ) = + exp( /T ) exp( /T ) (.) (T ) (C(T ) = de/dt )

17 .3 Maple Maple Maple Maple C.3. Maple C > i:=; > x:=3; > y:=.0; > z:=x+y; i := x := 3 y :=.0 z := 5.0 print printf C \t \n %d, %e, %f x,y,z %0.5f 0 5 Z > printf("%03d, %5.3e\t%0.5f\n",x,y,z); 003,.000e > printf("%0.5zf\n",z+y*i); I.3. +,-,*,/ > 3/4; > 3/4+/5; 3 4

18 .3. Maple irem( ) iquo( ) > irem(0,3); > iquo(0,3); evalf > evalf(0/3); > evalf(pi,30); Digits > Digits:=0; > evalf(exp()); Digits := trunc 0 round floor ceil floor trunc frac % C %%... > %; ^ >.^3.4;

19 4 round(x) x=-.6 round(x) x= ceil(x) floor(x) trunc(x) trunc(x) floor(x) ceil(x).: trunc, round, floor, ceil.3.3 if-else if-else if < > then < > elif < > then < > else < > end if ( ) > x:=-4; > if (x>0) then > y:=x; > else > y:=-x; > end if x := 4 y := 4 <, <=, >, >=, =, <> and, or, xor, implies, not evalb, type

20 .3. Maple 5 do-loop for-loop for < > from < > by < > < > end do; ( ) to < > do > total:=0; > for i from to 0 do > total:=total+i; > end: > total; total := 0 55 > for i from by - to -4 do > i; > end do; 0 4 loop loop end do; while-loop while < > do < > end do; next, break do-loop next do-loop break do-loop

21 6 > for i from to 5 do > if (i=3) then next; end if; > i; > end do; > for i from to 5 do > if (i=3) then break; end if; > i; > end do; [ ] > restart; > list:=[,,3,4]; list := [,, 3, 4] > list[3]; > list[-]; > list[..4]; 3 4 [, 3, 4] -,- C 0 > list[0]; Error, invalid subscript selector

22 .3. Maple 7 op > op(list); > list:=[op(list),5];,, 3, 4 list := [,, 3, 4, 5] > list[4]:=x; > list; list 4 := x [,, 3, x, 5] > list:=subsop(4=null,list); > list; nops > nops(list); list := [,, 3, 5] [,, 3, 5] 4 ( Maple ) > aa:=[];# > for i from to 3 do > aa:=[op(aa),i];# > end do: > print(aa); aa := [] [,, 3] > n:=nops(aa); # > total:=0; > for i from to n do #for-loop > total:=total+aa[i]; > end do: > print(total);

23 8 n := 3 total := 0 [ ] (listlist) > aa:=[[,],[3,4]]; > aa[,]; 6 aa := [[, ], [3, 4]] array array listlist OK > A:=array(..3,..3,diagonal); > print(a); A := array(diagonal,..3,..3, []) A, A, A 3, 3 > B:=array(0..,-..,[[,,3,4],[5,6,7,8]]): > B[,-]; convert array listlist > A:=convert(aa,array); > print(a); [ ] A := 3 4 [ ] 3 4 i j array 5

24 .3. Maple 9 > n:=: > i:=op(,op(,eval(b))[n])-op(,op(,eval(b))[n])+; > n:=: > j:=op(,op(,eval(b))[n])-op(,op(,eval(b))[n])+; i := j := 4 set {} set set > {x,y,z},{y,z,x},{x,x,y,z,z,x}; {x, z, y}, {x, z, y}, {x, z, y} (union) (intersect) (minus) > {x,y,z} union {u,v,z}; > {x,y,z} intersect {u,v,z}; > {x,y,z} minus {z}; {v, x, z, y, u} {z} {x, y} [ ] Maple > {x,y,z}[]; x.3.5 proc proc < >:=proc(< >); local < >;

25 0 global < >; < > end proc; global,local C local, global global,local Maple :=proc() end proc; proc ( ) a > total:=proc(a) > local S,n,i; > n:=nops(a); > S:=0; > for i from to n do > S:=S+a[i]; > end do; > eval(s); > end proc:# > aa:=[3,5,7]; > total(aa); aa := [3, 5, 7] 5. Maple script C Maple script scanf irem #include <stdio.h> int main(void){ int i,n;

26 .3. Maple } scanf("%d",&n); for (i=n-;i>;i--){ if (n%i==0){ break; } } if (i==){ printf("%d is a prime number.\n",n); } else { printf("%d is not a prime number.\n",n); } return 0;. Google e 0 Maple evalf floor isprime true, false evalf 00 exp() floor 0 ( ) 0 isprime > EE:=.78; > i:=; > AA[i]:=floor(EE); > EE:=0*(EE-AA[i]); EE :=.78 i := AA := EE := 7.80

27 ( ) 3 (3 ) 00.: ( ) [0] [0] p p Newton-Raphson Newton-Raphson x cos(x) = 0 f (x) = + sin x Newton-Raphson x 0 x = x0 f(x0) f (x0) (.) y = f(x) x for-loop 3 x0, x, f(x) (eps=.0e-0 ) ( )

28 .3. Maple 3 x x x0.: Newton-Raphson x[0]=(0.0, 0.0) x[]=(.0,.0) x[]=(.0, 0.0) x[3]=(0.0,.0) [0,,,3,0]

29 4.4 Maple array list LinearAlgebra.4. > with(linearalgebra): matrix, vector Vector > v:=vector([x,y,z]); v := Vector ( ) (column vector) ( ) (row vector) ( row, column ) > v:=vector[row]([x,y,z]); x y z v := [x, y, z] [ ] < > > v:=<x,y,z>; > v:=<x y z>; v := x y z v := [x, y, z] Matrix 3 listlist > A0:=Matrix(,3,[[,,3],[4,5,6]]);

30 .4. Maple 5 [ ] 3 A0 := < > > A:=<<,,3> <4,5,6> <7,8,9>>; A := (shape=identity) > E:=Matrix(3,3,shape=identity); E := listlist convert > A3:=[[,],[3,4]]; > A4:=convert(A3,Matrix); A3 := [[, ], [3, 4]] [ ] A4 := Maple > A5:=Matrix(,,[[3,-],[,]]); > a*a4+b*a5; [ ] 3 A5 := [ ] a + 3 b a b 3 a + b 4 a + b "."( ) > A4.A4; [ ] "."

31 6 > A.v; > v.v; x + 4 y + 7 z x + 5 y + 8 z 3 x + 6 y + 9 z x + y + z Error > v.a; Error, (in LinearAlgebra:-VectorMatrixMultiply) invalid input: LinearAlgebra:-VectorMatrixMultiply expects its st argument, v, to be of type Vector[row] but received Vector[column](3, [...], datatype = anything, storage = rectangular, order = Fortran_order, shape = []) (outer product) OuterProductMatrix > OuterProductMatrix(v,v); x x y x z x y y y z x z y z z.4.3 MatrixInverse > A3:=Matrix(3,3,[[,,],[4,5,6],[7,8,9]]): > MatrixInverse(A3); Determinant > Determinant(A3); 6 A MatrixInverse > MatrixInverse(A); Error, (in LinearAlgebra:-LA_Main:-MatrixInverse) singular matrix

32 .4. Maple 7 0 > Determinant(A); Transpose > Transpose(A0); > Transpose(v); > Transpose(v).v; [x, y, z] x + y + z.4.4 Eigenvectors > Eigenvectors(A); ( ) 4 ( ( ) ( ) 33 ) 3 ( 3 33 ) ( ) 33, ( ) ( 3 33 ) l(lambda) V > l,v:=evalf(eigenvectors(a)); 0. l, V := , V Column A.V = λ V (.3)

33 8 > l[].column(v,); > A.Column(V,); Row. x + 3y -z = -3 x + y -z = x + 3y +z = -6 (a) A (b) A (c) A A = E (d) b. H:=Matrix(,,[[,],[,3]]); Ax = b A Ax = A b Ex = A b (.4)

34 .4. Maple 9 Eigenvalues H:= H - x * Matrix(,,shape=identity); H solve

35 30.5 Maple exp Maple.5. solve( ), diff( ), int( ).: simplify: lhs, rhs: subs: expand: numer, denom: assume: factor: coeff: assuming: normal: nops, op assign: combine: about: collect: anames( user ): sort: restart,a:= a : convert: expand: expand(exp )

36 .5. Maple 3 factor: factor(exp ) normal: normal(exp ) combine: combine(exp ) collect: collect(exp,x) convert: convert(exp,opt ) > restart; > convert(sin(x),exp); I (e(x I) e > convert(sinh(x),exp); ex e x > convert(exp(i*x),trig); (x I) ) cos(x) + sin(x) I > convert(/(x-)/(x+3),parfrac); 4 (x + 3) + 4 (x ).3: convert opt polynom trig sincos exp parfrac rational tan sin, cos simplify: simplify(exp ), simplify(exp, ) > exp:=3*sin(x)^3-sin(x)*cos(x)^; exp := 3 sin(x) 3 sin(x) cos(x) > simplify(exp); (4 cos(x) 3) sin(x) > simplify(exp,{cos(x)^=-sin(x)^}); 4 sin(x) 3 sin(x)

37 3 sort: sort(exp ), sort(exp,[x,y]), sort(exp, [x],opts);opts=tdeg,plex,ascending,or descending (,, ) > exp:=x^3+4*x-3*x^+: > sort(exp); x 3 3 x + 4 x + > sort(exp,[x],ascending); + 4 x 3 x + x 3 > exp:=x^3-3*x*y+4*x^+y^: > sort(exp); > sort(exp,[x]); x x 3 x y + y x x 3 y x + y > sort(exp,[y],descending); y 3 x y + x x lhs, rhs: lhs(exp =exp ) numer, denom: numer(exp /exp ) coeff: coeff(exp,x^) op,nops:, op(exp ), nops(exp ) subs: subs(,exp ) > exp:=x^-4*x+4; > subs(x=a+,exp); assume: assume( ) exp := x 4 x + 4 (a + ) 4 a 4 assuming: exp assuming > sqrt(exp); ( + x) ascending, descending Maple9.5

38 .5. Maple 33 > sqrt(exp) assuming x>; + x additionally: assume assign: solve about: assume restart,a= a : anames( user ): > anames( user ); exp, exp series: series(exp,x,4) > series(exp(x),x); + x + x + 6 x3 + 4 x4 + 0 x5 + O(x 6 ) > series(sin(x),x=pi/3,); 3 + (x π 3 ) + O((x π 3 ) ) > convert(%,polynom); 3 + x π 6 : > a ; > a b; seq: for-loop > seq(i,i=0..3); a ab 0,,, 3 map: > map(sin,[seq(a i,i=0..3)]);

39 34 add, mul: [sin(a0 ), sin(a ), sin(a ), sin(a3 )] sum, product: > add(x^i,i=..3); > add(x^i,i=..n); x + x + x 3 Error, unable to execute add > sum(x^i,i=..n); x (n+) x x x > mul(x^i,i=..3); > mul(x^i,i=..n); x 6 Error, unable to execute mul limit: > product(x^i,i=..n); n x i i= > limit(exp(-x),x=infinity); > limit(tan(x),x=pi/,left); 0 > limit(tan(x),x=pi/,complex); + I.5. Maple

40 .5. Maple 35 restart restart; plot Plotting error,empty plot xe ( β cx + β gx 3) dx (.5) Maple > f:=unapply(x*exp(-beta*c*x^)*(+beta*g*x^3),x); f := x x e ( β c x) ( + β g x 3 ) > int(f(x),x=-infinity..infinity); 3 g π 4 β c csgn(β c) = β c otherwise βc (csgn(βc)=) (otherwise) Maple restart > restart; > f:=unapply(x*exp(-beta*c*x^)*(+beta*g*x^3),x); f := x x e ( β c x) ( + β g x 3 ) plot

41 36 > plot(f(x),x=-0..0); Warning, unable to evaluate the function to numeric values in the region; see the plotting command s help page to ensure the calling sequence is correct Plotting error, empty plot > f(0); 0 e ( 00 β c) ( β g) beta,c,g > c:=; g:=0.0; beta:=0.; c := g := 0.0 β := 0. > plot(f(x),x=-0..0); x > c:= c ; g:= g ; beta:= beta ; c := c g := g β := β

42 .5. Maple 37 > int(f(x),x); e (β c x ) β c + β g x 3 e ( β c x ) β c + 3 x e ( β c x ) β c + π erf( β c x) 4 β c β c β c x=-alpha..alpha > int(f(x),x=-alpha..alpha); g (4 α 3 e ( β c α) β c β c + 6 α e ( β c α ) β c 3 π erf( β c α)) 4 β c β c alpha > limit(int(f(x),x=-alpha..alpha),alpha=infinity); lim g (4 α 3 e ( β c α) β c β c + 6 α e ( β c α ) β c 3 π erf( β c α)) α 4 β c β c beta*c>0 (assume) > assume(beta*c>0); > limit(int(f(x),x=-alpha..alpha),alpha=infinity); 3 π g 4 β c β c.5.3 ( ) ( )

43 38 Maple () () > ex:=(x-3)^4; ex := (x 3) 4 > ex:=x^4-*x^3+54*x^-08*x+8; > expand(ex-ex); ex := x 4 x x 08 x expand (thermal expansion) 3 x U(x) = cx gx 3 (.6) x 3 x x = x exp ( βu(x)) dx exp ( βu(x)) dx (.7)

44 .5. Maple 39 β /(k B T ) x = 3g 4βc (.8) Taylor 3 Maple > restart; > U:=c*x^-g*x^3; > eu:=expand(exp(-beta*u)); U := c x g x 3 eu := e(β g x3 ) e (β c x ) > ex:=convert(series(numer(eu),x,4),polynom); > f:=ex/denom(eu); ex := + β g x 3 f := + β g x3 e (β c x ) > den:=int(f,x=-infinity..infinity); π den := csgn(β c) = β c otherwise > num:=int(x*f,x=-infinity..infinity); 3 g π num := 4 β c csgn(β c) = β c otherwise beta c >0 beta c >0 (assume) > assume(beta*c>0):

45 40 > num/den; 3 g 4 β c 古典論 量子論 3 V (x) = 0 h d ϕ(x) = εϕ(x) (.9) m dx x 0 ϕ(x) = A exp(ikx) + B exp( ikx) (.0) x a ϕ(x) = C exp(ikx). k = mε/ h ε V 0 ε V 0 κ = m(ε V 0 )/ h 0 x a ϕ(x) = F exp(iκx) + G exp( iκx) (.) A 969

46 .5. Maple 4 x = 0 x = a x = 0 ϕ(x) A + B = F + G (.) x = 0 ϕ (x) k(a B) = κ(f G) x = a x = a ϕ(x) F exp(iκa) + G exp( iκa) = C exp(ika) ϕ (x) κf exp(iκa) κg exp( iκa) = kc exp(ika) 5 4 F, G B/A C/A B A C A = = [ 4k κ ] [ + (k κ ) sin = + 4ε(ε V ] 0) κa V0 sin (.3) κa [ + (k κ ) sin ] [ κa = + V 0 sin ] κa 4k κ 4ε(ε V 0 ) 0 < ε < V 0 α = m(v 0 ε)/ h 0 x a ϕ(x) = F exp(αx) + G exp( αx) (.4) [ C = + V 0 sinh ] αa (.5) A 4ε(ε V 0 ) mv 0 a / h = 8 E/V 0 < C/A C/A > restart; > psi:=x->a*exp(i*k*x)+b*exp(-i*k*x); ψ := x A e (k x I) ( I k x) + B e > psi:=x->e*exp(i*kappa*x)+f*exp(-i*kappa*x); ψ := x E e (κ x I) ( I κ x) + F e

47 4 mv 0 a /h =8 0.8 C / A E/V 0 A = 4 > psi3:=x->c*exp(i*k*x); (k x I) ψ3 := x C e x = 0, x = a 0 > eq:=psi(0)=psi(0); eq := A + B = E + F > eq:=simplify(subs(x=0,diff(psi(x),x))=subs(x=0,diff(psi(x),x))); > eq3:=psi(a)=psi3(a); eq := A k I B k I = E κ I F κ I eq3 := E e (κ a I) + F e ( I κ a) (k a I) = C e > eq4:=simplify(subs(x=a,diff(psi(x),x))=subs(x=a,diff(psi3(x),x))); eq4 := κ (E e (κ a I) F e ( I κ a) ) I = C k e (k a I) I 4 A,B,C,E,F > solve({eq,eq,eq3,eq4},{a,b,c,e,f}); e (k a I) ( k e ( I κ a) + k e (κ a I) κ e ( I κ a) + κ e (κ a I) k κ e ( I κ a) k κ e (κ a I) ) C k κ e (κ a I) e ( I κ a), C = C, B = (k κ) e (k a I) (k + κ) ( e ( I κ a) + e (κ a I) ) C, F = 4 k κ e (κ a I) e ( I κ a) E = e (k a I) (k + κ) C κ e (κ a I) > assign(%); e (k a I) (k κ) C κ e ( I κ a), assign A/C (conjugate)

48 .5. Maple 43 kappa, k,a Maple > assume(kappa,real);assume(k,real),assume(a,real); conjugate (trig) convert > CC:=convert(A/C,trig): > CC:=combine(conjugate(CC)*CC); CC := κ k cos( κ a) + 6 κ k k 4 cos( κ a) κ 4 cos( κ a) + k 4 + κ 4 8 κ k > C_num:=simplify(expand(numer(CC)), > {cos(kappa*a)^=-sin(kappa*a)^, > cos(k*a)^=-sin(k*a)^}); C num := 8 κ k + ( 4 κ k + k 4 + κ 4 ) sin(κ a) > C_den:=denom(CC); > saa:=sin(kappa*a); C den := 8 κ k saa := sin(κ a) > CC:=collect(C_num/C_den,saa); CC := + ( 4 κ k + k 4 + κ 4 ) sin(κ a) 8 κ k k,kappa,a > NN:=8; > a:= a ; > a:=solve(m*v0*a/h=nn,a); > kappa:=*m*(epsilon-v0)/h; > k:=*m*epsilon/h; NN := 8 a := a a := 8 h m V0 κ := m (ε V0 ) h k := m ε h > CC3:=simplify( > subs({k=sqrt(k),kappa=sqrt(kappa)},coeff(cc,saa^)));

49 44 V0 CC3 := 4 (ε V0 ) ε > CC4:=simplify(subs(epsilon=x*V0,CC3)); CC4 := 4 (x ) x > aa:=simplify(subs(epsilon=x*v0,sqrt(kappa*a))); > CC5:=+CC4*sin(aa)^; aa := 4 x CC5 := + sin(4 x ) 4 (x ) x > f:=unapply(cc5,x); f := x + 4 > plot(/f(x),x=0..0); sin(4 x ) (x ) x. ( ) (i) (ii). 0 < ε < V 0 sinh sin cosh (α a) = + sinh (α a) (.6)

50 .6. Maple 45.6 Maple.6. plot > plot(sin(x),x); x 0.5 ({}) ([]) plot > plot({sin(x),cos(x),tan(x)},x=-pi..pi,y=-..); y x?plot[options]; plots[interactive]();

51 46 plots display > with(plots): > p:=plot(arctan(x),x,color=black): > p:=plot(diff(arctan(x),x),x,color=blue): > display(p,p); x p p display listplot listplot > with(plots): > T:=[seq(exp(-i),i=0..5)]; > listplot(t); T := [, e ( ), e ( ), e ( 3), e ( 4), e ( 5) ] listplot list y i x i

52 .6. Maple 47 > listplot(t,style=point); point x i,, 3, > T:=[seq([i/,exp(-i/)],i=0..0)]: > pointplot(t); listlist [x i, y i ] pointplot listplot > pointplot(t,connect=true); plot3d 3 plot3d > plot3d(sin(x)*cos(y),x=-pi..pi,y=-pi..pi);

53 y 0 0 x 3 3 > contourplot(sin(x)*cos(y),x=-pi..pi,y=-pi..pi); 3 y 3 3 x 3 plots with(plots); parameteric plot > plot([sin(t),cos(t),t=0..*pi]);

54 .6. Maple Maple Maple plot[structure] PLOT,PLOT3D CURVES, POINTS, POLYGONS, TEXT plots pointplot point animate, listplot, logplot, polarplot,contourplot plottools PLOT arc, arrow, circle, curve, line, point, sphere PLOT plots[display].6.3 ( ) plots animate [] t > with(plottools):with(plots): > animate(plot, [sin(x-t),x=0..5*pi], t=0..0): display insequence=true ([]) > tmp:=[]; > n:=0; > for i from 0 to n do > t:=i; > tmp:=[op(tmp), plot(sin(x-t),x=0..5*pi)]; > end do: > display(tmp,insequence=true); tmp := [] n := 0

55 x

56 animation gif.7. Java Maplet GetFile > with(maplets[examples]): > file:=getfile(); Warning, the protected name LinearAlgebra has been redefined and unprotected Initializing Java runtime environment. file := /Users/bob/Desktop/data.txt GetFile file Windows > with(stringtools): > file:=substituteall(file,"\\","/"); \ / Substitute > with(stringtools): > file:=substitute(file,"data","data"); Warning, the assigned name Group now has a global binding file := /Users/bob/Desktop/data.txt.7. writedata,readdata > f:=t->subs({a=0,b=40000,c=380,d=8},a+b/(c+(t-d)^) ): > T:=[seq(f(i)*( *evalf(rand()/0^)),i=..56)]: > writedata(file,t);

57 5 T file > T:=readdata(file,): > with(plots): > listplot(t); Warning, the name changecoords has been redefined writeto > interface(quiet=true); > writeto(file); > for i from to 0 do > s:=data i; > printf("%0.5f %s\n",evalf(f(i)),s); > end do: > writeto(terminal): > interface(quiet=false); false true C fopen, readline, sscanf, fclose > fd:=fopen(file,read); > for i from to do > l:=readline(fd); > d:=sscanf(l,"%f %s"); > end do; > fclose(fd): fd :=

58 l :=.49 data d := [.49, data ] l := data d := [.46063, data ] fd (file descripter) readline sscanf format l l > d[]; > whattype(d[]); > d[]; > whattype(d[]); float data string animation gif plot > plotsetup(gif,plotoutput=file): > display(tmp,insequence=true); > plotsetup(default): quicktime Maple 3 vrml (?vrml; ).7.4 linux linux maple filter [bob@asura0 ~/test]$ cat test.txt T:=readdata("./data0"); interface(quiet=true); writeto("./result"); print(t[]); writeto(terminal); interface(quiet=false);

59 54 data0 result interface(quiet=true) maple ~/test]$ /usr/local/maple9.5/bin/maple < test.txt \^/ Maple 9.5 (IBM INTEL LINUX)._ \ / _. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 004 \ MAPLE / All rights reserved. Maple is a trademark of < > Waterloo Maple Inc. Type? for help. > T:=readdata("./data0"); T := [.3,.35] > interface(quiet=true); false true > quit bytes used=000, alloc=6096, time=0.00 [bob@asura0 ~/test]$ cat result.3