MathAction NumericalIntegration

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The package NumericalQuadrature implements several operations for numerical integration. Here I provide just some examples. Documentation is to be found in the corresponding .spad or .pamphlet file.

fricas

romberg(x+->exp(x),0.0,1.0,0.1,0.1,6,10)

$\label{eq1}\begin{array}{@{}l} \displaystyle \left[{value ={1.7182818284_590452354}}, \:{error ={0.0}}, \:{totalpts ={129}}, \right. \ \ \displaystyle \left.\:{success = \mbox{\rm true} }\right]$

(1)

Type: Record(value: Float,error: Float,totalpts: Integer,success: Boolean)

fricas

simpson(x+->exp(x),0.0,1.0,0.1,0.1,6,10)

$\label{eq2}\begin{array}{@{}l} \displaystyle \left[{value ={1.7182818284_94606636}}, \: \right. \ \ \displaystyle \left.{error ={0.6667607588_1485444979 E - 9}}, \:{totalpts ={1 29}}, \: \right. \ \ \displaystyle \left.{success = \mbox{\rm true} }\right]$

(2)

Type: Record(value: Float,error: Float,totalpts: Integer,success: Boolean)

fricas

trapezoidal(x+->exp(x),0.0,1.0,0.1,0.1,6,10)

$\label{eq3}\begin{array}{@{}l} \displaystyle \left[{value ={1.7182905680_834782946}}, \: \right. \ \ \displaystyle \left.{error ={0.0000327734_5826871994_1097}}, \:{totalpts ={1 29}}, \: \right. \ \ \displaystyle \left.{success = \mbox{\rm true} }\right]$

(3)

Type: Record(value: Float,error: Float,totalpts: Integer,success: Boolean)

Note that for some reason

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%pi::Float

$\label{eq4}3.1415926535_897932385$

(4)

Type: Float

works, while

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%e::Float

   Cannot convert from type Expression(Integer) to Float for value
   %e

fails. You have to use

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exp(1)$Float

$\label{eq5}2.7182818284_590452354$

(5)

Type: Float

instead.

Subject: Be Bold !!

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