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last edited 11 years ago by test1 |
Edit detail for NumericalIntegration revision 2 of 2
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Editor: test1
Time: 2013/05/23 17:43:46 GMT+0 |
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changed: - romberg(x+->exp1()^x,0.0,1.0,0.1,0.1,6,10) romberg(x+->exp(x),0.0,1.0,0.1,0.1,6,10) changed: - simpson(x+->exp1()^x,0.0,1.0,0.1,0.1,6,10) simpson(x+->exp(x),0.0,1.0,0.1,0.1,6,10) changed: - trapezoidal(x+->exp1()^x,0.0,1.0,0.1,0.1,6,10) trapezoidal(x+->exp(x),0.0,1.0,0.1,0.1,6,10) changed: - exp1()$Float exp(1)$Float
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
(1) -> 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}}, \: \right.
\
\
\displaystyle
\left.{totalpts ={129}}, \:{success = \mbox{\rm true} }\right]](images/2158254069120508946-16.0px.png "\label{eq1}\begin{array}{@{}l}
\displaystyle
\left[{value ={1.7182818284 \_ 590452354}}, \:{error ={0.0}}, \: \right.
\
\
\displaystyle
\left.{totalpts ={129}}, \:{success = \mbox{\rm true} }\right]") | (1) |
Type: Record(value: Float,
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 \_ 590539174}}, \: \right.
\
\
\displaystyle
\left.{error ={2.1478522855 \_ 738173967}}, \:{totalpts ={102
5}}, \: \right.
\
\
\displaystyle
\left.{success = \mbox{\rm false} }\right]](images/8938519589538117742-16.0px.png "\label{eq2}\begin{array}{@{}l}
\displaystyle
\left[{value ={1.7182818284 \_ 590539174}}, \: \right.
\
\
\displaystyle
\left.{error ={2.1478522855 \_ 738173967}}, \:{totalpts ={102
5}}, \: \right.
\
\
\displaystyle
\left.{success = \mbox{\rm false} }\right]") | (2) |
Type: Record(value: Float,
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 \<u> 5826871994 \</u> 1097}}, \:{totalpts ={129}}, \: \right.
\
\
\displaystyle
\left.{success = \mbox{\rm true} }\right]](images/1268477483842938138-16.0px.png "\label{eq3}\begin{array}{@{}l}
\displaystyle
\left[{value ={1.7182905680 \_ 834782946}}, \: \right.
\
\
\displaystyle
\left.{error ={0.0000327734 \<u> 5826871994 \</u> 1097}}, \:{totalpts ={129}}, \: \right.
\
\
\displaystyle
\left.{success = \mbox{\rm true} }\right]") | (3) |
Type: Record(value: Float,
Note that for some reason
fricas
%pi::Float
 | (4) |
Type: Float
works, while
fricas
%e::Float
Cannot convert the value from type Expression(Integer) to Float .
fails. You have to use
fricas
exp(1)$Float
 | (5) |
Type: Float
instead.