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FriCAS Syntax

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Editor: test1 Time: 2016/05/28 15:34:45 GMT+0
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changed:
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On January 19, 2006 5:53 AM Fabio Stumbo wrote:

if-then-else: what is wrong?

  I am having some problem with the if-then-else syntax in the
.input  files.

**Problem 1:** I refer to the axiom book which ships with the program 
(version 2005/09). At page 204 it says that the usual rules for piling are 
suspended in conditional expressions and it gives 5 different ways which 
should be equivalent, namely::

  if i>0 then output("positive") else output("nonpositive")

  if i > 0 then output("positive")
    else output("nonpositive")

  if i > 0 then output("positive")
  else output("nonpositive")

  if i > 0
  then output("positive")
  else output("nonpositive")

  if i > 0
    then output("positive")
    else output("nonpositive")

Well, I tried all of them, creating each time a blank r.input file with 
inside only:
\begin{axiom}
  i := 2
\end{axiom}

followed by one of the "if...".

The result is that the first two are ok, where as the other three give 
some syntax error (different each time).

\begin{axiom}

for i in 2..2 repeat
  if i>0 then output("positive") else output("nonpositive")
\end{axiom}

\begin{axiom}
for i in 2..2 repeat
  if i > 0 then output("positive")
    else output("nonpositive")
\end{axiom}

\begin{axiom}
for i in 2..2 repeat
  if i > 0 then output("positive")
  else output("nonpositive")
\end{axiom}

\begin{axiom}
for i in 2..2 repeat
  if i > 0
  then output("positive")
  else output("nonpositive")
\end{axiom}

\begin{axiom}
for i in 2..2 repeat
  if i > 0
    then output("positive")
    else output("nonpositive")
\end{axiom}

So: what is happening? Is the book wrong?!?!

\begin{axiom}
for i in 2..2 repeat
  if i > 0 then
    output(i)
    output("positive")
  else
    output(i)
    output("nonpositive")
\end{axiom}

\begin{axiom}
i:=1.5
a :=
  if i > 0 then
    j := sin(i * pi())
    exp(j + 1/j)
  else
    j := cos(i * 0.5 * pi())
    log(abs(j)**5 + 1)
\end{axiom}


**Problem 2:** again with if then else, in a complex function
I noticed a wrong result (the function itself was ok... ;-)
Simplifying, you can produce the same error with something like:

\begin{axiom}
test: (INT,INT) -> List(INT)
test(a,b) ==
  x := 0; y := 0
  if (a rem b = 0) and b < 0 then
    x := 1
    y := 1
  [x,y]
\end{axiom}

Then,
\begin{axiom}
4 rem -2
test(4,-2)
\end{axiom}

returns correctly '[1,1]', but
\begin{axiom}
4 rem -3
test(4,-3)
\end{axiom}
or
\begin{axiom}
4 rem 2
test(4,2)
\end{axiom}

returns wrongly '[0,1]'.  Actually the result is '[0, 0]' which is correct.

The same happens if I write

\begin{axiom}
test: (INT,INT) -> List(INT)
test(a,b) ==
  x := 0; y := 0
  if (a rem b = 0) and b < 0 then  x := 1 ; y := 1
  [x,y]
\end{axiom}

Why?

**Another small question.** Is there a way to obtain on line the syntax
of a command in a more extensive way? I mean, for example, that writing
\begin{axiom}
)di op extendedEuclidean
\end{axiom}

which is not too useful. Moreover, how can I just ask about, say, the 
second function extendedEuclidean?

If I wanted to ask about the syntax of if-then-else, I would like
to write something like::

  )? if
  or
  )ap if

but nothing gives clues on how to use it.


Thank you for all your help

On January 19, 2006 5:53 AM Fabio Stumbo wrote:

if-then-else: what is wrong?

I am having some problem with the if-then-else syntax in the .input files.

Problem 1: I refer to the axiom book which ships with the program (version 2005/09). At page 204 it says that the usual rules for piling are suspended in conditional expressions and it gives 5 different ways which should be equivalent, namely:

  if i>0 then output("positive") else output("nonpositive")

  if i > 0 then output("positive")
    else output("nonpositive")

  if i > 0 then output("positive")
  else output("nonpositive")

  if i > 0
  then output("positive")
  else output("nonpositive")

  if i > 0
    then output("positive")
    else output("nonpositive")

Well, I tried all of them, creating each time a blank r.input file with inside only:

fricas

i := 2

$\label{eq1}2$

(1)

Type: PositiveInteger?

followed by one of the "if...".

The result is that the first two are ok, where as the other three give some syntax error (different each time).

fricas

for i in 2..2 repeat
  if i>0 then output("positive") else output("nonpositive")

   positive

Type: Void

fricas

for i in 2..2 repeat
  if i > 0 then output("positive")
    else output("nonpositive")

   positive

Type: Void

fricas

for i in 2..2 repeat
  if i > 0 then output("positive")
  else output("nonpositive")

   positive

Type: Void

fricas

for i in 2..2 repeat
  if i > 0
  then output("positive")
  else output("nonpositive")

   positive

Type: Void

fricas

for i in 2..2 repeat
  if i > 0
    then output("positive")
    else output("nonpositive")

  Line   1: for i in 2..2 repeat
  Line   2:   if i > 0
           ..A
  Error  A: (from A and on) Ignored from here
  Line   3:     then output("positive")
           ....A
  Error  A: Improper syntax.
  Error  A: (from A and on) Ignored from here
  Line   4:     else output("nonpositive")
           .............................A
  Error  A: (up to A) to here.
  Error  A: Possibly missing a then 
  Error  A: (up to A) to here.
   6 error(s) parsing

So: what is happening? Is the book wrong?!?!

fricas

for i in 2..2 repeat
  if i > 0 then
    output(i)
    output("positive")
  else
    output(i)
    output("nonpositive")

   2
   positive

Type: Void

fricas

i:=1.5

$\label{eq2}1.5$

(2)

Type: Float

fricas

a :=
  if i > 0 then
    j := sin(i * pi())
    exp(j + 1/j)
  else
    j := cos(i * 0.5 * pi())
    log(abs(j)**5 + 1)

$\label{eq3}0.1353352832 \<u> 3661269189$

(3)

Type: Float

Problem 2: again with if then else, in a complex function I noticed a wrong result (the function itself was ok... ;-) Simplifying, you can produce the same error with something like:

fricas

test: (INT,INT) -> List(INT)

Type: Void

fricas

test(a,b) ==
  x := 0; y := 0
  if (a rem b = 0) and b < 0 then
    x := 1
    y := 1
  [x,y]

Type: Void

Then,

fricas

4 rem -2

$\label{eq4}0$

(4)

Type: NonNegativeInteger?

fricas

test(4,-2)

fricas

Compiling function test with type (Integer,Integer) -> List(Integer)

$\label{eq5}\left[ 1, \: 1 \right]$

(5)

Type: List(Integer)

returns correctly '[1,1]?', but

fricas

4 rem -3

$\label{eq6}1$

(6)

Type: PositiveInteger?

fricas

test(4,-3)

$\label{eq7}\left[ 0, \: 0 \right]$

(7)

Type: List(Integer)

fricas

4 rem 2

$\label{eq8}0$

(8)

Type: NonNegativeInteger?

fricas

test(4,2)

$\label{eq9}\left[ 0, \: 0 \right]$

(9)

Type: List(Integer)

returns wrongly '[0,1]?'. Actually the result is '[0, 0]?' which is correct.

The same happens if I write

fricas

test: (INT,INT) -> List(INT)

   Compiled code for test has been cleared.

Type: Void

fricas

test(a,b) ==
  x := 0; y := 0
  if (a rem b = 0) and b < 0 then  x := 1 ; y := 1
  [x,y]

   1 old definition(s) deleted for function or rule test

Type: Void

Why?

Another small question. Is there a way to obtain on line the syntax of a command in a more extensive way? I mean, for example, that writing

fricas

)di op extendedEuclidean

There are 2 exposed functions called extendedEuclidean :
   [1] (D,D,D) -> Union(Record(coef1: D,coef2: D),"failed") from D
            if D has EUCDOM
   [2] (D,D) -> Record(coef1: D,coef2: D,generator: D) from D if D has 
            EUCDOM

which is not too useful. Moreover, how can I just ask about, say, the second function extendedEuclidean?

If I wanted to ask about the syntax of if-then-else, I would like to write something like:

  )? if
  or
  )ap if

but nothing gives clues on how to use it.

Thank you for all your help