help links subscribe changes refresh edit

	OldWishList
Multivariate Resultants ←	↑	→ SandBoxCombinat

NumericalIntegration

Edit detail for NumericalIntegration revision 1 of 2

	1 2
Editor: 127.0.0.1 Time: 2007/11/08 06:22:01 GMT-8
Note:

changed:
-
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.

\begin{axiom}
   romberg(x+->exp1()^x,0.0,1.0,0.1,0.1,6,10)
\end{axiom}

\begin{axiom}
   simpson(x+->exp1()^x,0.0,1.0,0.1,0.1,6,10)
\end{axiom}

\begin{axiom}
   trapezoidal(x+->exp1()^x,0.0,1.0,0.1,0.1,6,10)
\end{axiom}

  Note that for some reason
\begin{axiom}
   %pi::Float
\end{axiom}
  works, while 
\begin{axiom}
   %e::Float
\end{axiom}
  fails. You have to use
\begin{axiom}
   exp1()$Float
\end{axiom}
  instead.

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.

axiom

romberg(x+->exp1()^x,0.0,1.0,0.1,0.1,6,10)

$\label{eq1}\begin{array}{@{}l} \displaystyle \left[{value ={1.7182818284590452354}}, \:{error ={0.1 E - 19}}, \: \right. \ \ \displaystyle \left.{totalpts ={129}}, \:{success = \mbox{\rm true} }\right]$

(1)

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

axiom

simpson(x+->exp1()^x,0.0,1.0,0.1,0.1,6,10)

$\label{eq2}\begin{array}{@{}l} \displaystyle \left[{value ={1.718281828494606636}}, \: \right. \ \ \displaystyle \left.{error ={0.66676075883179510874 E - 9}}, \:{totalpts ={1 29}}, \: \right. \ \ \displaystyle \left.{success = \mbox{\rm true} }\right]$

(2)

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

axiom

trapezoidal(x+->exp1()^x,0.0,1.0,0.1,0.1,6,10)

$\label{eq3}\begin{array}{@{}l} \displaystyle \left[{value ={1.7182905680834782946}}, \: \right. \ \ \displaystyle \left.{error ={0.000032773458268719941097}}, \:{totalpts ={12 9}}, \: \right. \ \ \displaystyle \left.{success = \mbox{\rm true} }\right]$

(3)

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

Note that for some reason

axiom

%pi::Float

$\label{eq4}3.1415926535897932385$

(4)

Type: Float

works, while

axiom

%e::Float

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

fails. You have to use

axiom

exp1()$Float

$\label{eq5}2.7182818284590452354$

(5)

Type: Float

instead.