2.1 Maple,,Maple. Maple,,,. > ; > 21-4/3; 59 3 > 32(2-1/2)(3+1/3)/21; :, Maple., Maple,, ;,Maple. > ( )*12 Warning, inc

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1 . Maple,,Maple. Maple,,,. > ; 4474 > -4/3; 59 3 > 3*(-/)*(3+/3)/; 60 :, Maple., Maple,, ;,Maple. > (+34-4)* Warning, incomplete statement or missing semicolon :Maple *,,, : > (+)(3+4);. *. > (+)*(3+4); 3 Maple, , 9 9 = Maple.,Maple,. : intpos integer i 0 integer i integer i n :, n +. n + i 0, i,, i n. B, i 0 + i B + i B + i 3 B i n B n

2 . 3 Maple B :B 0, B, 3,B = 0 4., Maple,.Maple 7, 7, 4(( 7 ) ) = 9 9. Maple,,. > ^ ; Error, object too large,maple.,. > ^ ; Error, object too large > number:=0^3-0^6-; number := > isprime(number); false > settime:=time(): > ifactor(number); ( ) ( ) ( 5393) > cpu_time:=(time()-settime)*seconds; cpu time := 7.0 seconds > nextprime(number); > isqrt(number); ,. Maple time.. Maple. abs sign max min factorial irem iquo modp mods mod isqrt iroot isprime ifactor ifactors igcd ilcm igcdex iratrecon rand

3 4,,. > a:=34: b:=56: > q:=iquo(a,b); q := > r:=irem(a,b); r := > a=q*b+r; 34 = 34 > igcd(a,b); > igcdex(a,b, s, t ); > s; > t; > a*s+b*t; igcdex,maple ; a, b, s, t as + bt = gcd(a, b). igcdex, s,t,,, igcdex.,.maple mod, modp, mods. mod > mod 7; 4 > mod (,7); 4

4 . 5 mod,. mod, mod.. mod, mod modp. > modp(,7); 4 modp. n, [0, n ]. mod mods, mods, 0 n > mod :=mods: > mod (,7); n,...,, 0,,...,, 3 n Maple, iratrecon, m u. iratrecon(u,m,n,d, n, d ) N, D. iratrecon, n, d : n/d u (mod m) n N, d D. : > readlib(iratrecon): m := ; m := > u := / mod m; u := 6 > iratrecon(u,m,,, n, d ); true > n/d;,maple, readlib.readlib(iratrecon).

5 6.,,Maple.,Maple.. : > 5^(/6); 5 /6 > simplify(%); 5 /3 > evalf(%%); > convert(%%%, float ); , 5^(/6),Maple (, ), simplify. 5, Maple 5^(/6), evalf.convert, Maple,, convert., %,. Maple,. Maple V Release 4 ", Maple V Release 5, %., Maple,.,Maple. : > 5.0^(/6); > %^6; > 00045*0.5; Maple Digits,,Digits Digits,.Maple evalf,. : > evalf(sqrt());.44356

6 . 7 > Digits; 0 > Digits:=0: evalf(sqrt()); > evalf(pi,50); \ \ evalf,, Digits. Maple, π. constants.,, constants. > constants; false, γ,, true, Catalan, FAIL, π > constants:=constants,a,b,c; constants := false, γ,, true, Catalan, FAIL, π, A, B, C,false, true, F AIL, γ, : ( n ) γ = lim n k ln n ( ) n Catalan : (n + ). n=0 k=,maple, :.?inifcns.,,, : binomial(n,m) 0 m n, ( ) n n! m=, Γ m!(n m)! Γ(n+) :binomial(n, m) = Γ(m+)Γ(n m+) GAMMA(z) Γ, :Γ(z) = e t t z dt. 0 GAMMA(z,a) Γ, :Γ(z, a) = e t t a dt. 0 d dx Psi(z) Γ, :Ψ(x) = Γ(x) Γ(x). Psi(n,z) n Γ ( Γ n ), :Ψ(n, x) = Beta(x,y) Zeta(x) Zeta(n,x) d n dx Ψ(x). n β, :β(x, y) = Γ(x)Γ(y) Γ(x+y) ζ n, :ζ(x) = i= /ix, ζ(n, x) = d n ζ(x) dx. n

7 8 BesselJ(n,z) BesselI(n,z) BesselY(n,z) BesselK(n,z) LegendreF(x,k) LegendreE(x,k) LegendreKc(k) LegendreEc(k) Si(z),Ci(z) Ei(z),Li(z) FresnelS(z) FresnelC(z) with(orthopoly) BesselJ ;BesselI ;BesselY (Weber );BesselK (Macdonald ). LegendreF LegendreE ;LegendreKc LegendreEc. Si(z) : z sin(t) 0 t dt;ci(z) :γ + ln(iz) Iπ + z cos(t) 0 t dt; Ei(z) z e t t dt;li(z) Ei(ln(z)). Fresnel, : z 0 sin ( ) πt dt z 0 cos ( ) πt dt. x n. P(n,x) erf(x), :erf(x) = x π dt. 0 e t, orthopoly, numtheory, combinat, stats.,maple,,maple π, π 4, π 8, π 0. ζ,maple , Maple, expand., evalf. > sin(pi/0),cos(pi/0); > Zeta(0); 5 4 4, π0 > Zeta(50); ζ(50) > expand(%); π50 > Zeta(3); ζ(3) > evalf(%);

8 .3 9. > sin(4)-*sin()*cos(); sin(4) sin() cos() > combine(%, trig ); 0 > evalf(%%);. 0 9 > (+sqrt())^-*(+sqrt())-; ( + ) 3 > simplify(%); 0 > evalf(%%); ,.,Maple,.. > (/+/*sqrt(5))^; ( + 5) > expand(%); > (-8)^(/3); ( 8) /3 > simplify(%); + I 3 > %^3; ( + I 3) 3 > expand(%); 8

9 30, ( 8) 3.,, Maple,,. x, x 8 40x x 4 960x + 576, 3 8 x , x 5 + x + α, Maple α.,maple. RootOf, : > alpha:=rootof(z^-,z); α := RootOf( Z ) > alpha^; RootOf( Z ) > simplify(%); > simplify(/(+alpha)); RootOf( Z ) Maple Z. simplify α = α., alias. > alias(beta=rootof(z^-,z)): > /(beta+)+/(beta-); > simplify(%); + β + β convert RootOf. > convert((-8)^(/3), RootOf ); β RootOf( Z 3 + 8) > convert(%, radical ); ( 8) /3 α, β x, allvalues. > allvalues(alpha);,

10 .4 3.4,. i ( ) Maple I.. > complex_num:=(+3*i)+(4-5*i)*(-i); complex num := 6 I > Re(%); > Im(%%); 6 > conjugate(%%%); + 6 I > argument(complex_num); arctan(6) > /complex_num; I Maple,. > cos(i),ln(i),arccoth(0); cosh(), I π, I π > GAMMA(+*I); Γ( + I) > evalf(%); I

11 3 > plot3d(abs(gamma(x+y*i)),x=-pi..pi,y=-pi..pi, view=0..5,grid=[30,30], > orientation=[-0,45],axes=framed,style=patch contour); y x 3 plot3d,,,., evalc.evalc a + bi. > /(3+a-b*I); > evalc(%); > abs(%%); > evalc(%); 3 + a I b 3 + a (3 + a) + b + I b (3 + a) + b 3 + a I b a + a + b > sqrt(a+b*i); a + I b > evalc(%); a + b + a + I csgn(b I a) a + b a

12 .4 33 csgn : I(z) > 0 (I(z) = 0, R(z) > 0); csgn(z) = z = 0;. a, b,evalc. > assume(a>0):assume(b>0): > evalc(sqrt(a+b*i)); a + b + a + I a + b a

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