Internal Error: Unexpected error in call to system function compColon

[nsajko]

Moving on from the mailing list, since now I stumbled upon an actual bug in Fricas. This is the diagnostic produced by )compile:

   compiling local trunc_taylor_integral : (Expression Integer,Expression Integer) -> Expression Integer
   Internal Error
   Unexpected error in call to system function compColon

This is the code:

)abbrev package GGLC GeographicLibCoefficients
GeographicLibCoefficients() : Exports == Implementation where

        SYM ==> Symbol

        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

                trunc_taylor_integral(integrand: EXPR, factor: EXPR): EXPR ==
                        subs_eq: Equation(EXPR) := 'k2::SYM::EXPR = 4 * 'eps::SYM::EXPR /
                                                                     (1 - 'eps::SYM::EXPR)^2
                        inte: EXPR := subst(integrand, subs_eq) * factor
                        tay: TAY('eps::SYM) := taylor(inte, 'eps:SYM = 0)
                        Inte: TAY('eps::SYM) := integrate(tay, 'sigma::SYM)
                        reduce(_+, [coefficient(Inte, n) * ('eps::SYM::EXPR)^n for n in 0..maxpow()])

                del_sigma(e: EXPR): UPLY('eps::SYM) ==
                        simplify(subst(e, 'sigma::SYM = 2*%pi) / (2*%pi))

                tau1_m_sigma(): EXPR ==
                        integrand: EXPR := sqrt(1 + 'k2::SYM::EXPR * sin('sigma::SYM::EXPR)^2)
                        I1_truncated: EXPR := trunc_taylor_integral(integrand,
                                                                          1 - 'eps::SYM::EXPR)
                        A1: UPLY('eps::SYM) := del_sigma(I1_truncated)
                        tau1: EXPR := I1_truncated / A1::EXPR
                        tau1 - 'sigma::SYM::EXPR

EDIT: the error is the same with this change:

                trunc_taylor_integral(integrand: EXPR, factor: EXPR): EXPR ==
                        subs_eq: Equation(EXPR) := 'k2::SYM::EXPR = 4 * 'eps::SYM::EXPR /
                                                                     (1 - 'eps::SYM::EXPR)^2
                        inte: EXPR := subst(integrand, subs_eq) * factor
                        terms: L(EXPR) := [coefficient(taylor(inte, 'eps:SYM = 0), n) *
                                             ('eps::SYM::EXPR)^n for n in 0..maxpow()]
                        tay: EXPR := reduce(_+, terms)
                        integrate(tay, 'sigma::SYM)

[billpage]

You wrote: tay: TAY('eps::SYM) := taylor(inte, 'eps:SYM = 0) Perhaps you meant to write: tay: TAY('eps::SYM) := taylor(inte, 'eps::SYM::EXPR = 0) i.e. double colon and coercion. But you are right that "Internal Error" suggests that the compiler should have given a more meaningful error message.

…

On Thu, Aug 5, 2021 at 2:23 PM Neven Sajko ***@***.***> wrote: Moving on from the mailing list, since now I stumbled upon an actual bug in Fricas. This is the diagnostic produced by )compile: compiling local trunc_taylor_integral : (Expression Integer,Expression Integer) -> Expression Integer Internal Error Unexpected error in call to system function compColon This is the code: )abbrev package GGLC GeographicLibCoefficients GeographicLibCoefficients() : Exports == Implementation where SYM ==> Symbol 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 trunc_taylor_integral(integrand: EXPR, factor: EXPR): EXPR == inte: EXPR := subst(integrand, 'k2::SYM::EXPR = 4 * 'eps::SYM::EXPR / (1 - 'eps::SYM::EXPR)^2) * factor tay: TAY('eps::SYM) := taylor(inte, 'eps:SYM = 0) I: TAY('eps::SYM) := integrate(tay, 'sigma::SYM) reduce(_+, [coefficient(I, n) * ('eps::SYM::EXPR)^n for n in 0..maxpow()]) del_sigma(e: EXPR): UPLY('eps::SYM) == simplify(subst(e, 'sigma::SYM = 2*%pi) / (2*%pi)) tau1_m_sigma(): EXPR == integrand: EXPR := sqrt(1 + 'k2::SYM::EXPR * sin('sigma::SYM::EXPR)^2) I1_truncated: EXPR := trunc_taylor_integral(integrand, 1 - 'eps::SYM::EXPR) A1: UPLY('eps::SYM) := del_sigma(I1_truncated) tau1: EXPR := I1_truncated / A1::EXPR tau1 - 'sigma::SYM::EXPR — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub <#62>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ABGCUQDFHBCKPNSWUXTA5VDT3LJLTANCNFSM5BUMJB6A> . Triage notifications on the go with GitHub Mobile for iOS <https://apps.apple.com/app/apple-store/id1477376905?ct=notification-email&mt=8&pt=524675> or Android <https://play.google.com/store/apps/details?id=com.github.android&utm_campaign=notification-email> .