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SYMBMATH.H04
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1993-04-15
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7.2 Calculation
SymbMath gives the exact value of calculation when the switch
numerical=off (default), or the approximate value of calculation when
the switch numerical=on or by the function num().
SymbMath can manipulate units as well as numbers, be used as
a symbolic calculator, and do exact computation. The range of real
numbers is from -infinity to infinity, e.g. ln(-inf), exp(inf+pi*i),
etc. SymbMath contains many built-in algorithms for performing
numerical calculations when the switch numerical=on, e.g. ln(-9), i^i,
(-2.3)^(-3.2), 2^3^4^5^6^7^8^9, etc.
Warming that SymbMath only gives a principle value if there
are multi-values, except for the function solve().
Example 7.2.1. Find the values of sin(x) when x=pi/2
and x=90 degree.
Input:
num(sin(pi/2))
num(sin(90*degree))
end
Output:
1
1
end
Example 7.2.2. Set the units converter from the minute to
the second, then calculate numbers with different units.
Input:
minute=60*second
v=2*meter/second
t=2*minute
d0=10*meter
v*t+d0
end
Output:
250 meter
Example 7.2.3
Input:
1/2+1/3
end
Output:
5/6
Example 7.2.4. Assign sqrt(x) to z, then evaluate z
when x=3 and y=4.
Input:
z=sqrt(x)
subs(z, x=3) # evaluate z by substituting x=3
x=4 # assign 4 to x
z # evaluate z
end
Output:
z = sqrt(x)
sqrt(3)
x=4
2
Note that after assignment by x=4, x should be cleared from
memory by clear(x) before differentiation of the new function.
Otherwise the values of x still is 4 until new values assigned. If
evaluating z by the function subs(z, x=3), the variable x is
automatically cleared after evaluation, i.e. the variable x in subs()
is local variable. This rule applies to other functions.