3.2.3 Piecewise Functions
| Boole[expr] | give 1 if expr is True, and 0 if it is False |
Turning conditions into numbers. Boole[expr] is a basic function that turns True and False into 1 and 0. It is sometimes known as the characteristic function or indicator function. | This gives the area of a unit disk. | |
In[1]:=
Integrate[Boole[x^2 + y^2  1], {x, -1, 1}, {y, -1, 1}]
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Out[1]=
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Piecewise[{{ ,  }, { ,  }, ... }]
| | give the first  for which  is True | Piecewise[{{ ,  }, ... }, val] | give val if all  are False |
Piecewise functions. It is often convenient to have functions with different forms in different regions. You can do this using Piecewise. | This plots a piecewise function. | |
In[2]:=
Plot[Piecewise[{{x^2, x < 0}, {1-x, x > 0}}], {x, -1, 1}]
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Out[2]=
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Piecewise functions appear in systems where there is discrete switching between different domains. They are also at the core of many computational methods, including splines and finite elements. Special cases include such functions as Abs, UnitStep, Clip, Sign, Floor and Max. Mathematica handles piecewise functions in both symbolic and numerical situations.
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