Robert M. Corless
Department of Applied Mathematics
University of Western Ontario
London, Canada

Copyright 2001 by Robert M. Corless
All rights reserved

Basics

Основы

Evaluation rules 

Правила оценивания
Inert functions  Инертные функции

> restart;
> Digits := 30;

Digits := 30
> ratio := Vector(10):
> for k to 10 do
> n := rand()/10^13;
> m := rand()/10^13;
> tn := time( evalf(int( t*tan(n*t), t=0..1)) );
> tm := time( evalf(Int( t*tan(m*t), t=0..1)) );
> ratio[k] := evalf(tn/tm,3);
    end do:
> seq( ratio[k], k=1..10 );

2.00, 1.54, 1.10, 1.87, 1.95, 2.02, 1.95, 1.82, 1.7...
> restart;
> with( LinearAlgebra ):
> A := RandomMatrix( 5, 5 );

A := _rtable[14274828]
> Eigenvalues( A );
> Eigenvalues( evalf(A) );

_rtable[14251708]
> SingularValues( evalf(A) );

_rtable[14251788]
> S := Sum( 1/k^2, k=1..infinity );

S := Sum(1/(k^2),k = 1 .. infinity)
> evalf( S );

1.644934067
> S := Sum(1/sqrt(k),k=1..infinity);

S := Sum(1/(sqrt(k)),k = 1 .. infinity)
> value( S );

infinity
> evalf( S );

-1.460354509
> B := Int( ln(x)/(1-x^2), x );

B := Int(ln(x)/(1-x^2),x)
> value( B );

1/2*dilog(x)+1/2*dilog(x+1)+1/2*ln(x)*ln(x+1)
> p := x^5 + x^3 + x;

p := x^5+x^3+x
> Factor(p) mod 2;

(x^2+x+1)^2*x
> q := diff(p,x) mod 2;

q := x^4+x^2+1
> Gcd(p, q);

Gcd(x^5+x^3+x,x^4+x^2+1)
> Gcd(p,q) mod 2;

x^4+x^2+1

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