I have the following package:
)abbrev package GGLC GeographicLibCoefficients
GeographicLibCoefficients() : Exports == Implementation where
L ==> List
I ==> Integer
P ==> PositiveInteger
EXPR ==> Expression(I)
RAT ==> Fraction(I)
PLY ==> Polynomial(RAT)
UPLY(var) ==> UnivariatePolynomial(var, RAT)
RATFUNC ==> Fraction(PLY)
TAY(var) ==> UnivariateTaylorSeries(EXPR, var, 0)
Exports ==> with
tau1_m_sigma: () -> EXPR
Implementation ==> add
maxpow(): P ==
8
tau1_m_sigma(): EXPR ==
integrand: EXPR := sqrt(1 + 'k2 * sin('sigma)^2)
I1: TAY('eps) := integrate(taylor(
subst(integrand,
'k2 = 4 * 'eps
/ (1 - 'eps)^2) *
(1 - 'eps),
'eps = 0),
'sigma)
I1_truncated: EXPR := reduce(_+,
[coefficient(I1, n) *
'eps^n for
n in 0..maxpow()])
A1: UPLY('eps) := simplify(subst(I1_truncated,
'sigma = 2*%pi) /
(2*%pi))
tau1: EXPR := I1_truncated / A1
tau1 - sigma
This is me trying to compile the package:
(1) -> )compile test.spad
Compiling FriCAS source code from file /tmp/spad_test/test.spad
using old system compiler.
GGLC abbreviates package GeographicLibCoefficients
------------------------------------------------------------------------
initializing NRLIB GGLC for GeographicLibCoefficients
compiling into NRLIB GGLC
compiling local maxpow : () -> PositiveInteger
GGLC;maxpow is replaced by 8
Time: 0.00 SEC.
compiling exported tau1_m_sigma : () -> Expression Integer
****** comp fails at level 7 with expression: ******
error in function tau1_m_sigma
(SEQ
(|:=| (|:| |integrand| (|Expression| (|Integer|)))
(|sqrt| (+ 1 (* '|k2| (^ | << | (|sin| '|sigma|) | >> | 2)))))
(|:=| (|:| I1 (|UnivariateTaylorSeries| (|Expression| (|Integer|)) '|eps| 0))
(|integrate|
(|taylor|
(* (|subst| |integrand| (= '|k2| (/ (* 4 '|eps|) (^ (- 1 '|eps|) 2))))
(- 1 '|eps|))
(= '|eps| 0))
'|sigma|))
(|:=| (|:| |I1_truncated| (|Expression| (|Integer|)))
(|reduce| +
(COLLECT (IN |n| (SEGMENT 0 (|maxpow|)))
(* (|coefficient| I1 |n|) (^ '|eps| |n|)))))
(|:=| (|:| A1 (|UnivariatePolynomial| '|eps| (|Fraction| (|Integer|))))
(|simplify|
(/ (|subst| |I1_truncated| (= '|sigma| (* 2 |%pi|))) (* 2 |%pi|))))
(|:=| (|:| |tau1| (|Expression| (|Integer|))) (/ |I1_truncated| A1))
(|exit| 1 (- |tau1| |sigma|)))
****** level 7 ******
$x:= (sin (QUOTE sigma))
$m:= $EmptyMode
$f:=
((((|integrand| #) (|maxpow| #) (* #) (+ #) ...)))
>> Apparent user error:
Cannot coerce (QUOTE sigma)
of mode (Symbol)
to mode (Expression (Integer))
I notice that Fricas says that it can't coerce a Symbol to an
Expression. Is that a bug, or do I really have to convert symbols into
expressions explicitly?
Thanks,
Neven
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