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Numeric integration routines

fricas
)sh NumericalQuadrature
NumericalQuadrature is a package constructor Abbreviation for NumericalQuadrature is NUMQUAD This constructor is exposed in this frame. ------------------------------- Operations -------------------------------- aromberg : ((Float -> Float),Float,Float,Float,Float,Integer,Integer,Integer) -> Record(value: Float,error: Float,totalpts: Integer,success: Boolean) asimpson : ((Float -> Float),Float,Float,Float,Float,Integer,Integer,Integer) -> Record(value: Float,error: Float,totalpts: Integer,success: Boolean) atrapezoidal : ((Float -> Float),Float,Float,Float,Float,Integer,Integer,Integer) -> Record(value: Float,error: Float,totalpts: Integer,success: Boolean) romberg : ((Float -> Float),Float,Float,Float,Float,Integer,Integer) -> Record(value: Float,error: Float,totalpts: Integer,success: Boolean) rombergo : ((Float -> Float),Float,Float,Float,Float,Integer,Integer) -> Record(value: Float,error: Float,totalpts: Integer,success: Boolean) simpson : ((Float -> Float),Float,Float,Float,Float,Integer,Integer) -> Record(value: Float,error: Float,totalpts: Integer,success: Boolean) simpsono : ((Float -> Float),Float,Float,Float,Float,Integer,Integer) -> Record(value: Float,error: Float,totalpts: Integer,success: Boolean) trapezoidal : ((Float -> Float),Float,Float,Float,Float,Integer,Integer) -> Record(value: Float,error: Float,totalpts: Integer,success: Boolean) trapezoidalo : ((Float -> Float),Float,Float,Float,Float,Integer,Integer) -> Record(value: Float,error: Float,totalpts: Integer,success: Boolean)

Example

fricas
f(x) == sin(x)
Type: Void
fricas
-- aromberg(fn, a, b, epsrel, epsabs, nmin, nmax, nint)
-- uses the adaptive romberg method to numerically integrate function
-- \spad{fn} over the closed interval from \spad{a} to \spad{b},
-- with relative accuracy \spad{epsrel} and absolute accuracy
-- \spad{epsabs}, with the refinement levels for convergence checking
-- vary from \spad{nmin} to \spad{nmax}, and where \spad{nint}
-- is the number of independent intervals to apply the integrator.
-- The value returned is a record containing the value of the integral,
-- the estimate of the error in the computation, the total number of
-- function evaluations, and either a boolean value which is true if
-- the integral was computed within the user specified error criterion.
aromberg(f, -%pi, %pi, 0.0001, 0.001, 2, 5, 20)
fricas
Compiling function f with type Float -> Float

\label{eq1}\begin{array}{@{}l}
\displaystyle
\left[{value = -{0.8 E - 20}}, \:{error ={0.1993526932 \_ 47 E - 8}}, \: \right.
\
\
\displaystyle
\left.{totalpts ={161}}, \:{success =  \mbox{\rm true} }\right] (1)
Type: Record(value: Float,error: Float,totalpts: Integer,success: Boolean)




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