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If you need exact results, you can use: x = PolynomialRing(QQbar, 'x').gen() f = x^4 + 1 rs = f.roots(ring=QQbar,multip

Use: l = [1.4312706585e12, -1.4575266189e12, 4.9459419278e11, -4.8146621292e12] list_plot(l,frame=True)

This version looks nicer: complex_plot((3 * x + 7) / (-3 * x - 9), (-4,-1.5), (-1,1), contoured=True,plot_points=30

This version looks nicer: complex_plot((3 * x + 7) / (-3 * x - 9), (-4,-1.5), (-1,1), contoured=True,plot_points=30

A more compact introduction of squared metric is: M = Manifold(4, 'M') X.<t,x,y,z> = M.chart() g = M.lorentzian_m

Make the following modification: %display latex M = Manifold(4, 'M', latex_name=r'\mathcal{M}', structure='Lorentzian')

This version works better: %display latex M = Manifold(4, 'M', latex_name=r'\mathcal{M}', structure='Lorentzian') X.<

Using numerical computations with 100 decimals precision in GP/Pari one can check that the product A is equal 0.9999999

Using numerical computations with 100 decimals precision in GP/Pari one ca check that the product A is equal 0.99999999

On the unit disc g can be replaced by g = u + abs (1 - u**2 - v**2)**(3/2) and this version should work on older versio

Also: from sympy import Integral from sympy.abc import x Integral(1/x, (x, -1, 1)).principal_value()

Some workaround: E = EuclideanSpace(3) cylindrical.<rh,ph,z> = E.cylindrical_coordinates() cartesian.<x,y,z>

Using python from sage distribution (and full path to sage) $ ../sage/sage -python Untitled1.py one can execute the

Using giac: giac('assume(x>0);assume(y>0);assume(y>x)'); giac('max(19*x,20*y)') 20*y

giac('assume(x>0);assume(y>0);assume(y>x)'); giac('max(19x,20y)') 20*y

Some way to make them go is: from matplotlib import rcParams rcParams['xtick.major.size'] = rcParams['xtick.minor.size'

Some way to make them go is: from matplotlib import rcParams rcParams['xtick.major.size'] = rcParams['xtick.minor.size'

Some way to make them go is: from matplotlib import rcParams rcParams['xtick.major.size'] = rcParams['xtick.minor.size'

Some way to make them go is: from matplotlib import rcParams rcParams['xtick.major.size'] = rcParams['xtick.minor.size'

Some way to make them go is: from matplotlib import rcParams rcParams['xtick.major.size'] = rcParams['xtick.minor.size'

Some way to make them go away is: from matplotlib import rcParams rcParams['xtick.major.size'] = rcParams['xtick.minor.

If you accept arguments, then try matrix(3,3,lambda i,j: mymatrix[i,j].expr())

If you accept arguments, the try matrix(3,3,lambda i,j: mymatrix[i,j].expr())

The linear part can be rewritten as follows maxima('taylor(4/3*x + 2/3*y + 1/3,[x,1,1],[y,2,1])') ((2*(y-2))/3+3)+(4*(

When x is defined as [x_0,...,x_9] (no dots) the polynomial f can be computed but frank_wolfe remains unevaluated

When x is replaced by [x_0,...,x_9] the polynomial f can be computed but frank_wolfe remains unevaluated

When x is replaced by [x_0,...,x_9] the polynomial f can be computed by frank_wolfe remains unevaluated

A workaround: cmap='jet'

The color can be changed as follows: var('x,y,z,r,t') L = [(2*cos(t+pi/4),2*sin(t+pi/4), 4*sin(t+pi/4)^2) for t i

After t=var('t') g(t)=t^2 you can diff(g(t),t) or diff(g,t)(t) Also: g=t^2 diff(g,t)

Check https://www-fourier.ujf-grenoble.fr/~parisse/giac/cascmd_en.pdf, page 421. Giac is shipped with sage

In line3d(... arrow_head = True,...) try radius=0.02 (for example).

Try this version: reset() Man=Manifold(4, 'Man', r'\mathcal{M}') BL.<t,r,th,ph> = Man.chart(r't r:(0,+oo) th:(0,p

The problem is that SageManifolds and canonicalize_radical make different choice of square root. I think that your meth

One way is: var('k') assume(x>-1) assume(x<1) (4*sum(x^(2*k), k, 0, oo)+sum(x^(2*k+1), k, 0, oo)/4).combine() -1

One way is: var('k') assume(x>-1) assume(x<1) (4*sum(x^(2*k), k, 0, oo)+sum(x^(2*k+1), k, 0, oo)/4).combine() -1

One way is: var('k') assume(x>-1) assume(x<1) (4*sum(x^(2*k), k, 0, oo)+sum(x^(2*k+1), k, 0, oo)/4).combine() -1

One way is: var('k') assume(x>-1) assume(x<1) (4*sum(x^(2*k), k, 0, oo)+sum(x^(2*k+1), k, 0, oo)/4).combine() -1

For example giac('normal(sum((1+(-1)^k)*x^k,k,0,inf))').sage() -2/(x^2 - 1)

For example var('k x') giac('normal(sum((1+(-1)^k)*x^k,k,0,inf))').sage() -2/(x^2 - 1)

The problem is that SageManifolds and canonicalize_radical make different choice of square root. I think that your meth

Notice that canonicalize_radical is not always right. In this case the sign of H is needed to simplify. What is worse, S

canonicalize_radical is not always right. In this case the sign of H is needed to simplify. What is worse, sage is not g

canonicalize_radical is not always right. In this case the sign of H is needed to simplify. What is worse, sage is not g