種々の数学ソフトウェア

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ねんたろうねごろ
5 years ago
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1 January 17, 2013

2 Maple, Maxima, GeoGebra,,, Knoppix/Math

3 Maple,, : Student[Calculus1] : 30 ( 2 )

4 Maple Doc Maple ( ) cfep, ; ab a*b, x n xˆn x n + x m, xˆn, x n+xm

5 Maple ( ) =, <, <=, >, >=!= f(x):=xˆ3-3*x+1; function definition, :=, Enter

6 4 f x 2 y 2 Maple :, f (x), f (x), diff(f,x), diff(f(x),x,x), diff(f,x,x,y,y) simplify(f) f (x)dx int(f,x) f:=diff(log(sqrt((1-cos(x))/(1+cos(x)))),x); g:=simplify(f); sin(x) h:=int(g,x); ln(csc(x)-cot(x))

7 Maple : plot(sin(x)+sin(2*x)+sin(3*x),x=-1010); plot3d(xˆ3+yˆ3-3*x*y,x=-55,y=-55);

8 Maple : SyNRAC 1 SyNRAC Google 2 SyNRAC: SyNRAC 3 synrac 4 synrac synrac_startmw

9 Maple : SyNRAC f (x) = x 3 + 3x 2 9x y < x < a x, y (x y) f (a) + (a x) f (y), f (x) > a a y f(x):=xˆ3+3*xˆ2-9*x; u:=all([x,y],impl(and(y<x,x<a), f(x)>((x-y)*f(a)+(a-x)*f(y))/(a-y))); qe(u);

10 Maple : with(groebner); b:=[xˆ2+y*z+x*y-1,yˆ2+x*z+y*z-1,zˆ2+x*y+x*z-1]; ord:=plex(x,y,z); Basis(b,ord); [1-9 z + 27 z - 30 z + 9 z, z z z - 90 z + y, z z z - 45 z + x]

11 Maxima MIT (1968 ; Macsyma) (100 ) Maxima, etc Windows, Linux, Mac maximasourgeforgenet Windows : wxmaxima maxima-notepdf ( )

12 Maxima +, -, *( ), /, ˆ ( ),! ( ) ; ( ) $ ( ) Shift+Enter (%i1) 2ˆ100; (%o1) (%i2) 100!; (%o2) ,,

13 Maxima : (%i5) (x+y)ˆ2; 2 (%o5) (y + x) (%i6) expand((x+y)ˆ2); 2 2 (%o6) y + 2 x y + x (%i7) x:(y+zˆ2-2)ˆ3; 2 3 (%o7) (z + y - 2) (%i8) u:expand(x); (%o8) z + 3 y z - 6 z + 3 y z -, : (= ),

14 Maxima : (%i74) factor(xˆ20-1); 2 (%o74) (x - 1) (x + 1) (x + 1) (x +x +x +x+1) (x -x +x -x +1) Q

15 Maxima : f (x), f (n) (x), m+n f / x m y n diff(f(x),x), diff(f(x),x,n), diff(f(x,y),x,m,y,n) ( ) x = a subst(a,x,diff(f(x),x)) (%i2) f:diff(log(sqrt((1-cos(x))/(1+cos(x)))),x); (%o2) (%i3) g:ratsimp(f); sin(x) (%o3) cos (x) - 1

16 Taylor f (x) x = a n taylor(f(x),x,a,n) ( ) (%i3) taylor(cos(x)ˆ3,x,0,5); 2 4 3x 7x (%o3)/t/

17 Maxima : (%i34) integrate(sin(log(x)),x); x (sin(log(x)) - cos(log(x))) (%o34) (%i35) integrate(1/log(x),x); / [ 1 (%o35) I dx ( ) ] log(x) / (%i36) integrate(sqrt(1-xˆ2),x,0,1); %pi (%o36) (%i37) integrate(exp(-xˆ2),x,-inf,inf); (%o37) sqrt(%pi) %pi π, inf

18 Maxima : Help (\%i57)? integrate 0: integrate :(maximainfo)definitions 1: integrate_use_rootsof :Definitions Enter space-separated, all or none : 0 -- Function: integrate (<expr>, <x>) help?

19 KNOPPIX/Math KNOPPIX Klaus Knopper ( ), Live Linux CD/DVD Live Linux : Windows PC CD/DVD, OS (Linux) (Windows HDD ) KNOPPIX/Math ( ),, ( ) KNOPPIX DVD, USB ( ) Windows, Mac ( ) Maxima, GeoGebra ( )

20 GeoGebra GeoGebra = Geometry ( ) + Algebra ( ), Java Windows, Macintosh, Linux OK ( Linux (KNOPPIX/Math) ),,,,,,

21 GeoGebra 1 GeoGebra Google 2 3 WebStart 4 geogebrajnlp 5 geogebrajnlp

22 GeoGebra : :,, ( ) 2, 2, 3

23 GeoGebra,,, 2 A, B, A, B 2 A, B, A B,

24 1 : ( ), 1 2 3, 4, 5

25 2 : n ( ) 1, ( a ) ( b ) 2 y=xˆ3+a*x+b a, b 3 3 a, b 4,

26 3 : 1 y=a*xˆ2 (a ) 2, x 3 4, 4 5, 6 x, 3 7,

27 4 : = ( III) 0 30,, 0, 1 y=sin(x) y = sin x [sin(x),0,a], sin x

28 5 : ( ), sin(x), sin(x)+sin(2x)/2, 0 50, Sum[Sequence[sin(n*x)/n,n,1,a]]?? Sum[Sequence[sin(n*x)/n,n,1,a,2]], ( 2 n )??

29 KnoppixMath surfex : 3,, R : S, T E X, L A T E X : D E Knuth ( ), (The Art of Computer Programming) ( METAFONT )

30 : K502 Maple (SyNRAC), GeoGebra SyNRAC GeoGebra

topics KNOPPIX/Math DVD maxima KSEG GeoGebra Coq 2011 July 17 - Page 1

KNOPPIX/Math ( ) 2011/07/17 topics KNOPPIX/Math DVD maxima KSEG GeoGebra Coq 2011 July 17 - Page 1 (1) 2011 July 17 - Page 2 (2) 2011 July 17 - Page 3 KNOPPIX/Math KNOPPIX: Linux CD/DVD CD/DVD 1 Windows