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facts-load

facts();

(load(fourie), facts...

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facts-load-pi

( load(fourie),facts(...

fourier(x,x,pi);

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facts-load-pi-ratsimp

( load(fourie),facts(...

ratsimp(fourier(x^2,...

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facts-load-sin

( load(fourie),facts(...

fourier(A*sin(S*t)*(1...

Calculate

facts-load-pi-ratsimp

( load(fourie),facts(...

ratsimp(fourier(x,x,...

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facts-load-pi

( load(fourie),facts(...

fourier(x,x,%pi);

Calculate

facts-load-pi

( load(fourie),facts(...

(fourier(x^2,x,pi));

Calculate

facts-load-sin

( load(fourie),facts(...

fourier(A*sin(S*t),n,1);

Calculate

facts

Run Example
(%i1)eq: diff(r(t),t,2)-C*r(t)=0;
                             2
                            d
(%o1)                       --- (r(t)) - r(t) C = 0
                              2
                            dt
(%i2) eq2:diff(r(t), t, 2)=0;
                                 2
                                d
(%o2)                           --- (r(t)) = 0
                                  2
                                dt
(%i3) assume(C<
0);
(%o3)                               [C < 0]
(%i4) ode2(eq, r(t), t);
(%o4)         r(t) = %i %k1 sinh(t sqrt(C)) + %k2 cosh(t sqrt(C))
(%i5) forget(facts());
(%o5)                              [[C < 0]]
(%i6) assume(C>
0);
(%o6)                               [C > 0]
(%i7) ode2(eq, r(t), t),demoivre;
                               t sqrt(C)         - t sqrt(C)
(%o7)             r(t) = %k1 %e          + %k2 %e
(%i8) ode2(eq2, r(t), t);
(%o8)                         r(t) = %k2 t + %k1
(%i9) 
Run Example
eq1:x*4+y-2=y;
(%o1)                           y + 4 x - 2 = y
(%i2) eq2:x+2=y;
(%o2)                              x + 2 = y
(%i3) linsolve([eq1,eq2],[x,y]);
                                     1      5
(%o3)                           [x = -, y = -]
                                     2      2
(%i4) assume(notequal(n, -1));
(%o4)                         [notequal(n, - 1)]
(%i5)  	integrate(x^n, x);
                                     n + 1
                                    x
(%o5)                               ------
                                    n + 1
(%i6) facts();
(%o6)                         [notequal(n, - 1)]
(%i7) forget(notequal(n, -1));
(%o7)                         [notequal(n, - 1)]
(%i8) assume(a>
0);
(%o8)                               [a > 0]
(%i9) integrate(1/(x^2+a), x);
                                         x
                                 atan(-------)
                                      sqrt(a)
(%o9)                            -------------
                                    sqrt(a)
(%i10) integrate(log(cos(x^2)), x, 0, 1);
                               1
                              /
                              [           2
(%o10)                        I  log(cos(x )) dx
                              ]
                              /
                               0
(%i11) quad_qags(log(cos(x^2)), x, 0, 1);
(%o11)        [- 0.11151210243615, 3.3310015826528369E-11, 21, 0]
(%i12) 
Run Example
eq: diff(r(t),t,2)-C*r(t)=0;
                             2
                            d
(%o1)                       --- (r(t)) - r(t) C = 0
                              2
                            dt
(%i2) eq2:diff(r(t), t, 2)=0;
                                 2
                                d
(%o2)                           --- (r(t)) = 0
                                  2
                                dt
(%i3) assume(C<
0);
(%o3)                               [C < 0]
(%i4) ode2(eq, r(t), t);
(%o4)         r(t) = %i %k1 sinh(t sqrt(C)) + %k2 cosh(t sqrt(C))
(%i5) ode2(eq, r(t), t);
(%o5)         r(t) = %i %k1 sinh(t sqrt(C)) + %k2 cosh(t sqrt(C))
(%i6) forget(facts());
(%o6)                              [[C < 0]]
(%i7) assume(C>
0);
(%o7)                               [C > 0]
(%i8) ode2(eq, r(t), t);
                               t sqrt(C)         - t sqrt(C)
(%o8)             r(t) = %k1 %e          + %k2 %e
(%i9) ode2(eq2, r(t), t);
(%o9)                         r(t) = %k2 t + %k1
(%i10) eq3: diff(r(t), t, 2)+m*r(t)/r(t)^3;
                               2
                              d              m
(%o10)                        --- (r(t)) + -----
                                2           2
                              dt           r (t)
(%i11) ode2(eq3, r(t), r(t));
                               2
                              d              m
(%t11)                        --- (r(t)) + -----
                                2           2
                              dt           r (t)

                                     msg1

(%o11)                               false
(%i12) 

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