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assume-define-plot2d-sin-sqrt-subst
plot2d((p(x)),[x,0,10]);

assume(s > 0);

assume(m > 0);

t(x):=sqrt(2*((x*m)-0...

Calculate

assume-log-taylor

assume(eps >0);

t1: (1 - eps)^2*(log...

taylor(t1, eps, 0, 5);

Calculate

assume-domain-facts-linsolve

domain:real;

eq1:n=d*q+r;

eq2:d=r*p^2;

Calculate

assume-draw-draw3d-explicit-kill-load
draw3d(key = "U",color = blue,contour = both , /* rzutowanie na p3aszczyzne */explicit(y,x1, 1, 100, x2,1, 100));

load(draw);

kill(all);

assume(x1>0,x2>...

Calculate

assume-constant-cos-declare-diff-let-letsimp-sin-solve-trigsimp

x(t) := r(t) * sin(th...

y(t) := r(t) * cos(th...

declare (slope,consta...

Calculate

assume-matrix-nullspace

assume(a1>0);

assume(b2>0);

assume(c3>0);

Calculate

assume-diff-plot2d-solve
plot2d(f(x),[x,-5,5]);

assume(x>=1);

f(x):=5/(2*x^2+1);

solve(f(x)=y,x);

Calculate

assume-diff-ev-integrate-sin

/* Problema_Base_Cuad...

dy(x):=diff(y(x),x);

ddy(x):=diff(dy(x),x);

Calculate

assume-cos-integrate-plot2d-sin-sqrt
plot2d([ax,ay,ta],[t,0,tmax]);

w1:2*%pi/7;

w2:2*%pi/4;

w3:0;

Calculate

assume-diff-integrate-phi-sin-solve

assume(r0>0,h>0...

phi:c1*(r0^2-r^2)*sin...

eq:(1/r)*diff(r*diff(...

Calculate

assume

Run Example
(%i1)assume(A>
0,d>
0,y>
0,%lambda>
0,D>
0);
(%o1)              [A > 0, d > 0, y > 0, %lambda > 0, D > 0]
(%i2) test:4*A^2*cos(%pi*d*y/(%lambda*D))^2;
                                2    2  %pi d y
(%o2)                        4 A  cos (---------)
                                       %lambda D
(%i3) l:diff(test,y,1);
                             2      %pi d y        %pi d y
                    8 %pi d A  cos(---------) sin(---------)
                                   %lambda D      %lambda D
(%o3)             - ----------------------------------------
                                   %lambda D
(%i4) solve(l=0,y);

solve: using arc-trig functions to get a solution.
Some solutions will be lost.
                                        %lambda D
(%o4)                       [y = 0, y = ---------]
                                           2 d
(%i5)
Run Example
assume(r>
0);
(%o1)                               [r > 0]
(%i2) assume(d>
0);
(%o2)                               [d > 0]
(%i3) assume(b>
0);
(%o3)                               [b > 0]
(%i4) rr(t):=sqrt(r*r+rp*rp-2*r*rp*cos(t));
(%o4)           rr(t) := sqrt(r r + rp rp + (- 2) r rp cos(t))
(%i5) x(t):=rr(t)/(2*d);
                                         rr(t)
(%o5)                            x(t) := -----
                                          2 d
(%i6) f(t):=1/d*(6/5-2*x(t)^2+3/2*x(t)^3-5*x(t)^5);
                        1  6      2      3  3             5
(%o6)           f(t) := - (- - 2 x (t) + - x (t) + (- 5) x (t))
                        d  5             2
(%i7) expand(f(t)*sin(t));
                               2    2 5/2
        5 (- 2 r rp cos(t) + rp  + r )    sin(t)
(%o7) - ----------------------------------------
                             6
                         32 d
                          2    2 3/2                                 2
   3 (- 2 r rp cos(t) + rp  + r )    sin(t)   r rp cos(t) sin(t)   rp  sin(t)
 + ---------------------------------------- + ------------------ - ----------
                        4                              3                 3
                    16 d                              d               2 d
    2
   r  sin(t)   6 sin(t)
 - --------- + --------
        3        5 d
     2 d
(%i8) integrate(expand(f(t)*sin(t)),t);
                               2    2 7/2                          2    2 5/2
        5 (- 2 r rp cos(t) + rp  + r )      3 (- 2 r rp cos(t) + rp  + r )
(%o8) - --------------------------------- + ---------------------------------
                        6                                  4
                   224 d  r rp                         80 d  r rp
                                       2        2           2
                               r rp cos (t)   rp  cos(t)   r  cos(t)   6 cos(t)
                             - ------------ + ---------- + --------- - --------
                                      3             3           3        5 d
                                   2 d           2 d         2 d
(%i9) integrate(f(t)*sin(t),t);
                                2    2 7/2                          2    2 5/2
         5 (- 2 r rp cos(t) + rp  + r )      3 (- 2 r rp cos(t) + rp  + r )
(%o9) (- --------------------------------- + ---------------------------------
                         5                                  3
                    224 d  r rp                         80 d  r rp
                                    2        2           2
                          - r rp cos (t) + rp  cos(t) + r  cos(t)   6 cos(t)
                        + --------------------------------------- - --------)/d
                                              2                        5
                                           2 d
(%i10)
Run Example
assume(x>
0);
(%o1)                               [x > 0]
(%i2) f(x):=integrate(1/sqrt(-1+exp(x)*erfc(sqrt(x)) + 2*sqrt(x/%pi)),x);
                                              1
(%o2) f(x) := integrate(----------------------------------------------, x)
                                                                  x
                        sqrt(- 1 + exp(x) erfc(sqrt(x)) + 2 sqrt(---))
                                                                 %pi
(%i3) define(f1(x),diff(f(x),x,1));
                                           1
(%o3)          f1(x) := ---------------------------------------
                                             x   2 sqrt(x)
                        sqrt(erfc(sqrt(x)) %e  + --------- - 1)
                                                 sqrt(%pi)
(%i4) f1(0.01);
                                      1
(%o4)                 ----------------------------------
                              0.2
                      sqrt(--------- - 0.10354302003087)
                           sqrt(%pi)
(%i5)
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