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Dear all,

I am trying to define a piecewise function where the domains are parametrized by some variable:

import sage.all as sage
sage.var('x')
sage.var('x0')
sage.var('x1')
sage.assume( 0<x0)
sage.assume(x0<x1)
sage.assume(x1< 1)
sage.piecewise([((0,x0),0), ([x0,x1],1), ((x1,1),1)], var=x)

However, I cannot seem to get it to work:

TypeError: unable to simplify to a real interval approximation

Any idea how to make it work? Thanks!

Martin

Right. Sorry for lack of clarity. And thanks for trying to help. I am using sage in standalone python scripts. Is there a way for me to save all variables to a file, and load them in another script? Thanks!

Trying to save my sage session from a standalone python script, but I am getting the following error:

TypeError: argument of type 'NoneType' is not iterable

Can't find any information on that. Any idea what might be going on? Thanks!

A pointer to the doc? Thanks!

My advice: put import sage.all as sage at the beginning of each python file, and then use for instance sage.var('x') in your scripts.

Consider the following code:

sage.var(x)
f = (1-x) * sage.unit_step(x)
df = f.diff(x)    ->    -unit_step(x) + (1-x)*dirac_delta(x)

Trying to compute df.limit(x=0, dir="right"), which should return -1, but instead returns limit(-unit_step(x) + (1-x)*dirac_delta(x), x, 0, plus).

Even df.limit(x=0.5) return limit(-unit_step(x) + (1-x)*dirac_delta(x), x, 0.5) instead of -1.

Any idea on what might be going on? Thanks!

You can try minimizing d using sage.minimize.

You can try minimizing sqrt((sin(x)+y)**2 + (sin(x)-y)**2) using sage.minimize.

You can try minimizing sqrt(f1(a,b)**2 + f2(a,b)**2) using sage.minimize.

I need to define some function like f(x,y) = x * sin(y)/y if y != 0, x otherwise, such that f can be differentiated. Is there a way to do so? Thanks!

Thanks! Yes, I prefer python standalone (makes it easier to use other python libraries) with import sage.all as sage (makes it where each function comes from).

Thanks! Just updated my question. Any idea?

It works…thanks!

For the record, a workaround is to declare var('_C')right before solve(sol, _C).

Hi,

Consider the following code:

sage.var('R')

rho = sage.function('rho')(R)

r = rho(R=R).function(R)

Is there a way to assign some function to rho such that r is modified? For instance, if I do:

y = sage.function('y')(R)

rho = sage.desolve(sage.diff(y,R) - y(R), dvar=y, ivar=R, ics=[0,1]).function(R) -> R |--> e^R

Then I get:

r(0) -> rho(0)

rho(0) -> 1

So rho is of course modified, but not r.

Thanks!

Martin

Hi,

In my SMC project, I have two sagemath worksheet. I need to "import" the first one into the second one. Is there a way to do so? Can't figure it out. Thanks!

Martin

Hi,

I figured out how to import sage.all from a standalone python script, and everything seems to work, but I'm getting this warning/error:

Bug >>Could not get expanded executable from "/usr/lib/sagemath/local/lib/libSingular.so"<< at feResource.cc:429

Any idea what might be going on? Thanks!

Martin

Hi,

Consider the following code:

x = var('x')

f = function('f')(x)

sol = desolve(diff(f,x), [f,x])

print "sol =", sol

solve(sol, _C)

For which I'm getting NameError: name '_C' is not defined. What would be the right way to set the integration constant after the resolution of the differential equation?

Thanks!