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#338 'eval' misses main variable ←	↑	→ #34 Axiom missing rm, cat

#339 interpreter gives up in loop

Edit detail for #339 interpreter gives up in loop revision 1 of 2

	1 2
Editor: Time: 2007/11/17 22:29:28 GMT-8
Note: No, Axiom is smart enough :-)

changed:
-
The following is a very surprising for a novice, and a bit surprising for me:

\begin{axiom}
c 0==1; c 1==1; c n==c(n-1)+s*(reduce(+,[q^k*c(k)*c(n-1-k) for k in 1..n-1]));
c 5
\end{axiom}

Note that the type of 'c 5' is 'FRAC POLY INT'. This is, because Axiom is not smart enough to realize inside the loop that $q^k$ is a polynomial if $k$ is nonnegative. The following is more surprising, though:

\begin{axiom}
coefficient(univariate(c(5),s),3)
\end{axiom}

Axiom manages - after a *lot* of trying-  to coerce 'univariate(c(5),s)' to a 'SUP FRAC POLY INT'. Wow. 

\begin{axiom}
[coefficient(univariate(c(n),s),1) for n in 0..4]
\end{axiom}

But why does it give up here?

Martin

\begin{axiom}
Zq:=SUP(INT)
q:Zq := monomial(1,1)
Zqs:=SUP(Zq)
s:Zqs := monomial(1$Zq,1)
macro mac(n) == c(n-1) + s*(reduce(+,[q^k*c(k)*c(n-1-k) for k in 1..n-1]))
c(n: Integer): Zqs == (n=0 or n=1 => 1; mac n)
c 0
c 1
c 2
mac 2
\end{axiom}

I don't know but the output of c(2) is wrong. I would have expected "? ? + 1" in accordance to mac(2).
So the typed form of you example doesn't work. And the output looks ugly anyway. :-(

Ralf



From greg Thu Feb 22 11:08:42 -0600 2007
From: greg
Date: Thu, 22 Feb 2007 11:08:42 -0600
Subject: No, Axiom is smart enough :-)
Message-ID: <20070222110842-0600@wiki.axiom-developer.org>

In your function you are using the '-' operation for the upper bound, it is not defined for NNI or PI. Axiom is smart enough to detect the types of the step and the bounds. Because of that it is assumed that the result of (n-1) is an Integer.

Here I even don't define the type of the function:

\begin{axiom}
)clear all
c 0==1; c 1==1; c n==c(n-1)+s*(reduce(+,[q^k*c(k)*c(n-1-k) for k in 1..(n-1)::NNI]));
[coefficient(univariate(c(n),s),1) for n in 0..4]
\end{axiom}

I don't know why it gives up in your exemple though.

Greg

The following is a very surprising for a novice, and a bit surprising for me:

fricas

c 0==1; c 1==1; c n==c(n-1)+s*(reduce(+,[q^k*c(k)*c(n-1-k) for k in 1..n-1]));

Type: Void

fricas

c 5

fricas

Compiling function c with type Integer -> Fraction(Polynomial(
      Integer))

$\label{eq1}\begin{array}{@{}l} \displaystyle {{{q}^{10}}\ {{s}^{4}}}+{{\left({{q}^{9}}+{2 \ {{q}^{8}}}+{2 \ {{q}^{7}}}+{3 \ {{q}^{6}}}+{2 \ {{q}^{4}}}\right)}\ {{s}^{3}}}+ \ \ \displaystyle {{\left({{q}^{7}}+{2 \ {{q}^{6}}}+{5 \ {{q}^{5}}}+{4 \ {{q}^{4}}}+{5 \ {{q}^{3}}}+{3 \ {{q}^{2}}}\right)}\ {{s}^{2}}}+ \ \ \displaystyle {{\left({{q}^{4}}+{2 \ {{q}^{3}}}+{3 \ {{q}^{2}}}+{4 \ q}\right)}\ s}+ 1$

(1)

Type: Fraction(Polynomial(Integer))

Note that the type of c 5 is FRAC POLY INT. This is, because Axiom is not smart enough to realize inside the loop that is a polynomial if is nonnegative. The following is more surprising, though:

fricas

coefficient(univariate(c(5),s),3)

$\label{eq2}{{q}^{9}}+{2 \ {{q}^{8}}}+{2 \ {{q}^{7}}}+{3 \ {{q}^{6}}}+{2 \ {{q}^{4}}}$

(2)

Type: Fraction(Polynomial(Integer))

Axiom manages - after a lot of trying- to coerce univariate(c(5),s) to a SUP FRAC POLY INT. Wow.

fricas

[coefficient(univariate(c(n),s),1) for n in 0..4]

   There are 8 exposed and 6 unexposed library operations named 
      coefficient having 2 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                           )display op coefficient
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.
   Cannot find a definition or applicable library operation named 
      coefficient with argument type(s) 
     Fraction(SparseUnivariatePolynomial(Fraction(Polynomial(Integer))))
                               PositiveInteger

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.
   FriCAS will attempt to step through and interpret the code.
   There are 8 exposed and 6 unexposed library operations named 
      coefficient having 2 argument(s) but none was determined to be 
      applicable. Use HyperDoc Browse, or issue
                           )display op coefficient
      to learn more about the available operations. Perhaps 
      package-calling the operation or using coercions on the arguments
      will allow you to apply the operation.

   Cannot find a definition or applicable library operation named 
      coefficient with argument type(s) 
     Fraction(SparseUnivariatePolynomial(Fraction(Polynomial(Integer))))
                               PositiveInteger

      Perhaps you should use "@" to indicate the required return type, 
      or "$" to specify which version of the function you need.

But why does it give up here?

Martin

fricas

Zq:=SUP(INT)

$\label{eq3}\hbox{\axiomType{SparseUnivariatePolynomial}\ } (\hbox{\axiomType{Integer}\ })$

(3)

Type: Type

fricas

q:Zq := monomial(1,1)

   Compiled code for c has been cleared.

$\label{eq4}?$

(4)

Type: SparseUnivariatePolynomial?(Integer)

fricas

Zqs:=SUP(Zq)

$\label{eq5}\hbox{\axiomType{SparseUnivariatePolynomial}\ } (\hbox{\axiomType{SparseUnivariatePolynomial}\ } (\hbox{\axiomType{Integer}\ }))$

(5)

Type: Type

fricas

s:Zqs := monomial(1$Zq,1)

$\label{eq6}?$

(6)

Type: SparseUnivariatePolynomial?(SparseUnivariatePolynomial?(Integer))

fricas

macro mac(n) == c(n-1) + s*(reduce(+,[q^k*c(k)*c(n-1-k) for k in 1..n-1]))

Type: Void

fricas

c(n: Integer): Zqs == (n=0 or n=1 => 1; mac n)

   Function declaration c : Integer -> SparseUnivariatePolynomial(
      SparseUnivariatePolynomial(Integer)) has been added to workspace.
   1 old definition(s) deleted for function or rule c

Type: Void

fricas

c 0

fricas

Compiling function c with type Integer -> SparseUnivariatePolynomial
      (SparseUnivariatePolynomial(Integer))

$\label{eq7}1$

(7)

Type: SparseUnivariatePolynomial?(SparseUnivariatePolynomial?(Integer))

fricas

c 1

$\label{eq8}1$

(8)

Type: SparseUnivariatePolynomial?(SparseUnivariatePolynomial?(Integer))

fricas

c 2

$\label{eq9}{{?}^{2}}+ 1$

(9)

Type: SparseUnivariatePolynomial?(SparseUnivariatePolynomial?(Integer))

fricas

mac 2

$\label{eq10}{? \ ?}+ 1$

(10)

Type: SparseUnivariatePolynomial?(SparseUnivariatePolynomial?(Integer))

I don't know but the output of c(2) is wrong. I would have expected "? ? + 1" in accordance to mac(2). So the typed form of you example doesn't work. And the output looks ugly anyway. :-(

Ralf

No, Axiom is smart enough :-) --greg, Thu, 22 Feb 2007 11:08:42 -0600 reply

In your function you are using the - operation for the upper bound, it is not defined for NNI or PI. Axiom is smart enough to detect the types of the step and the bounds. Because of that it is assumed that the result of (n-1) is an Integer.

Here I even don't define the type of the function:

fricas

)clear all

   All user variables and function definitions have been cleared.
c 0==1; c 1==1; c n==c(n-1)+s*(reduce(+,[q^k*c(k)*c(n-1-k) for k in 1..(n-1)::NNI]));

Type: Void

fricas

[coefficient(univariate(c(n),s),1) for n in 0..4]

fricas

Compiling function c with type Integer -> Polynomial(Integer)

$\label{eq11}\left[ 0, \: 0, \: q , \:{{{q}^{2}}+{2 \ q}}, \:{{{q}^{3}}+{2 \ {{q}^{2}}}+{3 \ q}}\right]$

(11)

Type: List(Polynomial(Integer))

I don't know why it gives up in your exemple though.

Greg