Interact: getting a slider to change its range

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Since this functionality has yet to appear explicitly, one solution is to nest interacts. Here's a slider that depends on a slider (live example):

@interact
def _( n=slider(1,10) ):

  @interact
  def _( m=slider(0,n,default=n/2) ):

        show( 'n=', n )
        show( 'm=', m )

And here's a slider that depends on an input box as per the original question (live example):

@interact
def _( n=input_box(10) ):

  @interact
  def _( m=slider(0,n,default=n/2) ):

        show( 'n=', n )
        show( 'm=', m )

An alternative; if yon't mind getting your hands dirt (i.e. side effects)
The return is a tuple (master, secondary, secondary limit) The last is just for debugging. An alternative is to not allow the "illegal" selection.

@interact
def myfunc(x=(0,10)): 
    #sage_interactive(myfunc1, y=(0,floor(x/2)))
    pass
@interact
def myfunc1(y=(0,10)):
    return y

def get_value():
    gg=myfunc.widget.children[0].value
    #print('gg= ',gg,' floor= ',floor(gg/2))
    myfunc1.widget.children[0].max=floor(gg/2)
    return myfunc.widget.children[0].value,myfunc1.widget.children[0].value, myfunc1.widget.children[0].max

I left some debugging junk in.
Tip: The secret is to use
f.?
f.children?
f.widget.children?
Often!

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