Values with uncertanties: ValueWithError

One of the central object in ostap is C++ class Ostap::Math::ValutWithError, accessible in python via shortcut VE. This class stands fot r a combination of the value with uncertainties:

from ostap.math.ve import VE
a = VE( 10 , 10 ) ## the value & squared uncertainty - 'variance' 
b = VE( 20 , 20 ) ## the value & squared uncertainty - 'variance' 
print "a=%s" % a 
print "b=%s" % b 
print 'Value    of a is %s'  % a.value() 
print 'Effor    of b is %s'  % b.error() 
print 'Variance of b is %s'  % b.cov2 ()

A lot of math operations are predefined for VE-objects.

Challenge

Make a try with all binary operations (+,-,*,/,**) for the pair of VE objects and combinations of VE-objects with numbers, e.g. 

a + b 
a + 1 
1 - b
2 ** a 
a +=1   
b += a

Compare the difference for following expresssions: 

a/a      ## <--- HERE 
a/VE(a)  ## <--- HERE
a-a      ## <--- HERE 
a-VE(a)  ## <--- HERE

Note that for trivial cases the correlations are propertly taken into account

Additionally many math-functions are provided, carefully takes care on uncertainties

from ostap.math.math_ve import * 
sin(a)+cos(b)/tanh(b) 
atan2(a,b)/log(a)

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