sage: maxima('1/100 + 1/101') 201/10100
sage: a = maxima('(1 + sqrt(2))^5'); a (sqrt(2) + 1)^5 sage: a.expand() 29*sqrt(2) + 41
sage: a = maxima('(1 + sqrt(2))^5') sage: float(a) 82.012193308819747 sage: a.numer() 82.01219330881975
sage: maxima.eval('fpprec : 100') '100' sage: a.bfloat() 8.2012193308819756415248973002081244278520484385931494122123712401731241875 4011041266612384955016056B1
sage: maxima('100!') 933262154439441526816992388562667004907159682643816214685929638952175999932 299156089414639761565182862536979208272237582511852109168640000000000000000 00000000
sage: f = maxima('(x + 3*y + x^2*y)^3') sage: f.expand() x^6*y^3 + 9*x^4*y^3 + 27*x^2*y^3 + 27*y^3 + 3*x^5*y^2 + 18*x^3*y^2 + 27*x*y^2 + 3*x^4*y + 9*x^2*y + x^3 sage: f.subst('x=5/z') (5/z + 25*y/z^2 + 3*y)^3 sage: g = f.subst('x=5/z') sage: h = g.ratsimp(); h (27*y^3*z^6 + 135*y^2*z^5 + (675*y^3 + 225*y)*z^4 + (2250*y^2 + 125)*z^3 + (5625*y^3 + 1875*y)*z^2 + 9375*y^2*z + 15625*y^3)/z^6 sage: h.factor() (3*y*z^2 + 5*z + 25*y)^3/z^6
sage: eqn = maxima(['a+b*c=1', 'b-a*c=0', 'a+b=5']) sage: s = eqn.solve('[a,b,c]'); s [[a = (25*sqrt(79)*%i + 25)/(6*sqrt(79)*%i - 34),b = (5*sqrt(79)*%i + 5)/(sqrt(79)*%i + 11),c = (sqrt(79)*%i + 1)/10],[a = (25*sqrt(79)*%i - 25)/(6*sqrt(79)*%i + 34),b = (5*sqrt(79)*%i - 5)/(sqrt(79)*%i - 11),c = - (sqrt(79)*%i - 1)/10]]
Here is an example of solving an algebraic equation:
sage: maxima('x^2+y^2=1').solve('y') [y = - sqrt(1 - x^2),y = sqrt(1 - x^2)] sage: maxima('x^2 + y^2 = (x^2 - y^2)/sqrt(x^2 + y^2)').solve('y') [y = - sqrt(( - y^2 - x^2)*sqrt(y^2 + x^2) + x^2),y = sqrt(( - y^2 - x^2)*sqrt(y^2 + x^2) + x^2)]
You can even nicely typeset the solution in latex:
sage: print latex(s) \left[\left[a = \frac{25\sqrt{79}i + 25}{6\sqrt{79}i - 34},b = \frac{5\sqrt{79}i + 5}{\sqrt{79}i + 11},c = \frac{\sqrt{79}i + 1}{10}\right],\left[a = \frac{25\sqrt{79}i - 25}{6\sqrt{79}i + 34},b = \frac{5\sqrt{79}i - 5}{\sqrt{79}i - 11},c = - \frac{\sqrt{79}i - 1}{10}\right]\right]
To have the above appear onscreen via xdvi
, type view(s)
.
(TODO: For OS X should create pdf output and use preview instead?)
sage: e = maxima('sin(u + v) * cos(u)^3'); e cos(u)^3*sin(v + u) sage: f = e.trigexpand(); f cos(u)^3*(cos(u)*sin(v) + sin(u)*cos(v)) sage: f.trigreduce() (sin(v + 4*u) + sin(v - 2*u))/8 + (3*sin(v + 2*u) + 3*sin(v))/8 sage: w = maxima('3 + k*%i') sage: f = w^2 + maxima('%e')^w sage: f.realpart() %e^3*cos(k) - k^2 + 9
sage: f = maxima('x^3 * %e^(k*x) * sin(w*x)'); f x^3*%e^(k*x)*sin(w*x) sage: f.diff('x') k*x^3*%e^(k*x)*sin(w*x) + 3*x^2*%e^(k*x)*sin(w*x) + w*x^3*%e^(k*x)*cos(w*x) sage: f.integrate('x') (((k*w^6 + 3*k^3*w^4 + 3*k^5*w^2 + k^7)*x^3 + (3*w^6 + 3*k^2*w^4 - 3*k^4*w^2 - 3*k^6)*x^2 + ( - 18*k*w^4 - 12*k^3*w^2 + 6*k^5)*x - 6*w^4 + 36*k^2*w^2 - 6*k^4)*%e^(k*x)*sin(w*x) + (( - w^7 - 3*k^2*w^5 - 3*k^4*w^3 - k^6*w)*x^3 + (6*k*w^5 + 12*k^3*w^3 + 6*k^5*w)*x^2 + (6*w^5 - 12*k^2*w^3 - 18*k^4*w)*x - 24*k*w^3 + 24*k^3*w)*%e^(k*x)*cos(w*x))/(w^8 + 4*k^2*w^6 + 6*k^4*w^4 + 4*k^6*w^2 + k^8)
sage: f = maxima('1/x^2') sage: f.integrate('x', 1, 'inf') 1 sage: g = maxima('f/sinh(k*x)^4') sage: g.taylor('x', 0, 3) f/(k^4*x^4) - 2*f/(3*k^2*x^2) + 11*f/45 - 62*k^2*f*x^2/945
sage: maxima.taylor('asin(x)','x',0, 10) x + x^3/6 + 3*x^5/40 + 5*x^7/112 + 35*x^9/1152
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