[Scilab-users] Strange behaviour of prod on rationals

classic Classic list List threaded Threaded
7 messages Options
fmiyara fmiyara
Reply | Threaded
Open this post in threaded view
|

[Scilab-users] Strange behaviour of prod on rationals


Dear all,

Look at this code (the coefficients are actually the result of pevious calculations):

NUM = [5.858D-09 + 2.011D-08*%s + 4.884D-08*%s^2 ...
       5.858D-09 + 8.796D-10*%s + 7.028D-10*%s^2]
DEN
= [0.1199597 + 7.2765093*%s + %s^2 ...
       8.336136 +  7.0282601*%s + %s^2]
q = NUM
./DEN
 
Running it yields

   5.858D-09 +2.011D-08s +4.884D-08s²  5.858D-09 +8.796D-10s +7.028D-10s² 
   ----------------------------------  ---------------------------------- 
       0.1199597 +7.2765093s +s²            8.336136 +7.0282601s +s²      

This is, correctly, a two-component rational vector with the expected numerators and denominators.

Now let's evaluate

q = prod(NUM./DEN)

The prod documantation sys that the argument may be "an array of reals, complex, booleans, polynomials or rational fractions". It should provide the rational obtained by multiplying the twonumrators and the two denominators. However, we get

   3.432D-17 +1.230D-16s +3.079D-16s² +5.709D-17s³ +3.432D-17s⁴ 
   ------------------------------------------------------------ 
                                1                               

The numeratoris right, but the expected denominator has been just replaced by 1

However, rewriting the command as

prod(NUM)/prod(DEN)

we get the expected result:

   3.432D-17 +1.230D-16s +3.079D-16s² +5.709D-17s³ +3.432D-17s⁴ 
   ------------------------------------------------------------ 
       1.0000004 +61.501079s +59.597296s² +14.304769s³ +s⁴      

This is quite strange!

Now we repeat with simpler polynomials:

NUM = [1-%s 2-%s]
DEN = [1+%s 2+%s]
q = NUM./DEN

We get

   1 -s  2 -s 
   ----  ---- 
   1 +s  2 +s

Now evaluate

prod(NUM./DEN)

The result is the expected one!
             
   2 -3s +s² 
   --------- 
   2 +3s +s² 

The behavior seems to depend on the type of polynomials.

Is this a bug or there is something I'm not interpreting correctly?

Regards,

Federico Miyara

_______________________________________________
users mailing list
[hidden email]
http://lists.scilab.org/mailman/listinfo/users
Perrichon Perrichon
Reply | Threaded
Open this post in threaded view
|

Re: Strange behaviour of prod on rationals

Hello Federico

 

I have met few months or years ago this problem when i was developping my  « OPTSIM Solution » software to fix parameters of a PID for turbines (30 mw to 2 gw) in Nyquist and Bode Plans with hydraulic parameters site

So I’ve seen instability of the denominator, witch damage calculus.

I don ‘t remember what I’ve done to get a cool solution, but it  has been a hard and severe problem with syslin, tf2ss and ss2tf instructions

 

Sincerely

 

Pierre P.

 

 

De : users <[hidden email]> De la part de Federico Miyara
Envoyé : mardi 17 mars 2020 10:31
À : Users mailing list for Scilab <[hidden email]>
Objet : [Scilab-users] Strange behaviour of prod on rationals

 


Dear all,

Look at this code (the coefficients are actually the result of pevious calculations):

NUM = [5.858D-09 + 2.011D-08*%s + 4.884D-08*%s^2 ...
       5.858D-09 + 8.796D-10*%s + 7.028D-10*%s^2]
DEN = [0.1199597 + 7.2765093*%s + %s^2 ...
       8.336136 +  7.0282601*%s + %s^2]
q = NUM./DEN
 
Running it yields

   5.858D-09 +2.011D-08s +4.884D-08s²  5.858D-09 +8.796D-10s +7.028D-10s² 
   ----------------------------------  ---------------------------------- 
       0.1199597 +7.2765093s +s²            8.336136 +7.0282601s +s²      

This is, correctly, a two-component rational vector with the expected numerators and denominators.

Now let's evaluate

q = prod(NUM./DEN)

The prod documantation sys that the argument may be "an array of reals, complex, booleans, polynomials or rational fractions". It should provide the rational obtained by multiplying the twonumrators and the two denominators. However, we get

   3.432D-17 +1.230D-16s +3.079D-16s² +5.709D-17s³ +3.432D-17s⁴ 
   ------------------------------------------------------------ 
                                1                               

The numeratoris right, but the expected denominator has been just replaced by 1

However, rewriting the command as

prod(NUM)/prod(DEN)

we get the expected result:

   3.432D-17 +1.230D-16s +3.079D-16s² +5.709D-17s³ +3.432D-17s⁴ 
   ------------------------------------------------------------ 
       1.0000004 +61.501079s +59.597296s² +14.304769s³ +s⁴      

This is quite strange!

Now we repeat with simpler polynomials:

NUM = [1-%s 2-%s]
DEN = [1+%s 2+%s]
q = NUM./DEN

We get

   1 -s  2 -s 
   ----  ---- 
   1 +s  2 +s

Now evaluate

prod(NUM./DEN)

The result is the expected one!
             
   2 -3s +s² 
   --------- 
   2 +3s +s² 

The behavior seems to depend on the type of polynomials.

Is this a bug or there is something I'm not interpreting correctly?

Regards,

Federico Miyara


_______________________________________________
users mailing list
[hidden email]
http://lists.scilab.org/mailman/listinfo/users
Perrichon Perrichon
Reply | Threaded
Open this post in threaded view
|

Re: Strange behaviour of prod on rationals

In reply to this post by fmiyara

Here are examples of my process in Open loop (FTBO) or Close loop (FTBF)

Depending of managemat, D can have s14 …

 

 

 

De : Perrichon <[hidden email]>
Envoyé : mardi 17 mars 2020 10:49
À : 'Users mailing list for Scilab' <[hidden email]>
Objet : RE: [Scilab-users] Strange behaviour of prod on rationals

 

Hello Federico

 

I have met few months or years ago this problem when i was developping my  « OPTSIM Solution » software to fix parameters of a PID for turbines (30 mw to 2 gw) in Nyquist and Bode Plans with hydraulic parameters site

So I’ve seen instability of the denominator, witch damage calculus.

I don ‘t remember what I’ve done to get a cool solution, but it  has been a hard and severe problem with syslin, tf2ss and ss2tf instructions

 

Sincerely

 

Pierre P.

 

 

De : users <[hidden email]> De la part de Federico Miyara
Envoyé : mardi 17 mars 2020 10:31
À : Users mailing list for Scilab <[hidden email]>
Objet : [Scilab-users] Strange behaviour of prod on rationals

 


Dear all,

Look at this code (the coefficients are actually the result of pevious calculations):

NUM = [5.858D-09 + 2.011D-08*%s + 4.884D-08*%s^2 ...
       5.858D-09 + 8.796D-10*%s + 7.028D-10*%s^2]
DEN = [0.1199597 + 7.2765093*%s + %s^2 ...
       8.336136 +  7.0282601*%s + %s^2]
q = NUM./DEN
 
Running it yields

   5.858D-09 +2.011D-08s +4.884D-08s²  5.858D-09 +8.796D-10s +7.028D-10s² 
   ----------------------------------  ---------------------------------- 
       0.1199597 +7.2765093s +s²            8.336136 +7.0282601s +s²      

This is, correctly, a two-component rational vector with the expected numerators and denominators.

Now let's evaluate

q = prod(NUM./DEN)

The prod documantation sys that the argument may be "an array of reals, complex, booleans, polynomials or rational fractions". It should provide the rational obtained by multiplying the twonumrators and the two denominators. However, we get

   3.432D-17 +1.230D-16s +3.079D-16s² +5.709D-17s³ +3.432D-17s⁴ 
   ------------------------------------------------------------ 
                                1                               

The numeratoris right, but the expected denominator has been just replaced by 1

However, rewriting the command as

prod(NUM)/prod(DEN)

we get the expected result:

   3.432D-17 +1.230D-16s +3.079D-16s² +5.709D-17s³ +3.432D-17s⁴ 
   ------------------------------------------------------------ 
       1.0000004 +61.501079s +59.597296s² +14.304769s³ +s⁴      

This is quite strange!

Now we repeat with simpler polynomials:

NUM = [1-%s 2-%s]
DEN = [1+%s 2+%s]
q = NUM./DEN

We get

   1 -s  2 -s 
   ----  ---- 
   1 +s  2 +s

Now evaluate

prod(NUM./DEN)

The result is the expected one!
             
   2 -3s +s² 
   --------- 
   2 +3s +s² 

The behavior seems to depend on the type of polynomials.

Is this a bug or there is something I'm not interpreting correctly?

Regards,

Federico Miyara


_______________________________________________
users mailing list
[hidden email]
http://lists.scilab.org/mailman/listinfo/users
fmiyara fmiyara
Reply | Threaded
Open this post in threaded view
|

Re: Strange behaviour of prod on rationals

In reply to this post by Perrichon

Pierre,

Thanks for your answer.

However, I believe no involved computatins are required to get the correct result. The multiplication of the two polynomials from the denominators is straightforward, no need to solve any system, no risk of ill-conditioned or badly-scaled matrices.

This must be another kind of problem.

Regards,

Federico Miyara

On 17/03/2020 06:48, Perrichon wrote:

Hello Federico

 

I have met few months or years ago this problem when i was developping my  « OPTSIM Solution » software to fix parameters of a PID for turbines (30 mw to 2 gw) in Nyquist and Bode Plans with hydraulic parameters site

So I’ve seen instability of the denominator, witch damage calculus.

I don ‘t remember what I’ve done to get a cool solution, but it  has been a hard and severe problem with syslin, tf2ss and ss2tf instructions

 

Sincerely

 

Pierre P.

 

 

De : users [hidden email] De la part de Federico Miyara
Envoyé : mardi 17 mars 2020 10:31
À : Users mailing list for Scilab [hidden email]
Objet : [Scilab-users] Strange behaviour of prod on rationals

 


Dear all,

Look at this code (the coefficients are actually the result of pevious calculations):

NUM = [5.858D-09 + 2.011D-08*%s + 4.884D-08*%s^2 ...
       5.858D-09 + 8.796D-10*%s + 7.028D-10*%s^2]
DEN = [0.1199597 + 7.2765093*%s + %s^2 ...
       8.336136 +  7.0282601*%s + %s^2]
q = NUM./DEN
 
Running it yields

   5.858D-09 +2.011D-08s +4.884D-08s²  5.858D-09 +8.796D-10s +7.028D-10s² 
   ----------------------------------  ---------------------------------- 
       0.1199597 +7.2765093s +s²            8.336136 +7.0282601s +s²      

This is, correctly, a two-component rational vector with the expected numerators and denominators.

Now let's evaluate

q = prod(NUM./DEN)

The prod documantation sys that the argument may be "an array of reals, complex, booleans, polynomials or rational fractions". It should provide the rational obtained by multiplying the twonumrators and the two denominators. However, we get

   3.432D-17 +1.230D-16s +3.079D-16s² +5.709D-17s³ +3.432D-17s⁴ 
   ------------------------------------------------------------ 
                                1                               

The numeratoris right, but the expected denominator has been just replaced by 1

However, rewriting the command as

prod(NUM)/prod(DEN)

we get the expected result:

   3.432D-17 +1.230D-16s +3.079D-16s² +5.709D-17s³ +3.432D-17s⁴ 
   ------------------------------------------------------------ 
       1.0000004 +61.501079s +59.597296s² +14.304769s³ +s⁴      

This is quite strange!

Now we repeat with simpler polynomials:

NUM = [1-%s 2-%s]
DEN = [1+%s 2+%s]
q = NUM./DEN

We get

   1 -s  2 -s 
   ----  ---- 
   1 +s  2 +s

Now evaluate

prod(NUM./DEN)

The result is the expected one!
             
   2 -3s +s² 
   --------- 
   2 +3s +s² 

The behavior seems to depend on the type of polynomials.

Is this a bug or there is something I'm not interpreting correctly?

Regards,

Federico Miyara


_______________________________________________
users mailing list
[hidden email]
http://lists.scilab.org/mailman/listinfo/users


_______________________________________________
users mailing list
[hidden email]
http://lists.scilab.org/mailman/listinfo/users
mottelet mottelet
Reply | Threaded
Open this post in threaded view
|

Re: Strange behaviour of prod on rationals

In reply to this post by fmiyara

Hello Frederico,

The problem is in simp() :

---> rlist(prod(a.num),prod(a.den),a.dt)
 ans  =

                                      2            3            4 
   3.432D-17 + 1.230D-16s + 3.079D-16s + 5.709D-17s + 3.432D-17s  
   -------------------------------------------------------------- 
                                          2            3   4      
       1.0000004 + 61.501079s + 59.597296s + 14.304769s + s       


---> simp(rlist(prod(a.num),prod(a.den),a.dt))
 ans  =

                                      2            3            4 
   3.432D-17 + 1.230D-16s + 3.079D-16s + 5.709D-17s + 3.432D-17s  
   -------------------------------------------------------------- 
                                                                  
                                 1         

S.

Le 17/03/2020 à 10:30, Federico Miyara a écrit :

Dear all,

Look at this code (the coefficients are actually the result of pevious calculations):

NUM = [5.858D-09 + 2.011D-08*%s + 4.884D-08*%s^2 ...
       5.858D-09 + 8.796D-10*%s + 7.028D-10*%s^2]
DEN
= [0.1199597 + 7.2765093*%s + %s^2 ...
       8.336136 +  7.0282601*%s + %s^2]
q = NUM
./DEN
 
Running it yields

   5.858D-09 +2.011D-08s +4.884D-08s²  5.858D-09 +8.796D-10s +7.028D-10s² 
   ----------------------------------  ---------------------------------- 
       0.1199597 +7.2765093s +s²            8.336136 +7.0282601s +s²      

This is, correctly, a two-component rational vector with the expected numerators and denominators.

Now let's evaluate

q = prod(NUM./DEN)

The prod documantation sys that the argument may be "an array of reals, complex, booleans, polynomials or rational fractions". It should provide the rational obtained by multiplying the twonumrators and the two denominators. However, we get

   3.432D-17 +1.230D-16s +3.079D-16s² +5.709D-17s³ +3.432D-17s⁴ 
   ------------------------------------------------------------ 
                                1                               

The numeratoris right, but the expected denominator has been just replaced by 1

However, rewriting the command as

prod(NUM)/prod(DEN)

we get the expected result:

   3.432D-17 +1.230D-16s +3.079D-16s² +5.709D-17s³ +3.432D-17s⁴ 
   ------------------------------------------------------------ 
       1.0000004 +61.501079s +59.597296s² +14.304769s³ +s⁴      

This is quite strange!

Now we repeat with simpler polynomials:

NUM = [1-%s 2-%s]
DEN = [1+%s 2+%s]
q = NUM./DEN

We get

   1 -s  2 -s 
   ----  ---- 
   1 +s  2 +s

Now evaluate

prod(NUM./DEN)

The result is the expected one!
             
   2 -3s +s² 
   --------- 
   2 +3s +s² 

The behavior seems to depend on the type of polynomials.

Is this a bug or there is something I'm not interpreting correctly?

Regards,

Federico Miyara

_______________________________________________
users mailing list
[hidden email]
https://antispam.utc.fr/proxy/1/c3RlcGhhbmUubW90dGVsZXRAdXRjLmZy/lists.scilab.org/mailman/listinfo/users
-- 
Stéphane Mottelet
Ingénieur de recherche
EA 4297 Transformations Intégrées de la Matière Renouvelable
Département Génie des Procédés Industriels
Sorbonne Universités - Université de Technologie de Compiègne
CS 60319, 60203 Compiègne cedex
Tel : +33(0)344234688
http://www.utc.fr/~mottelet

_______________________________________________
users mailing list
[hidden email]
http://lists.scilab.org/mailman/listinfo/users
mottelet mottelet
Reply | Threaded
Open this post in threaded view
|

Re: Strange behaviour of prod on rationals

(num,den) calling style seems to be OK:

--> [a,b]=simp(prod(q.num),prod(q.den))
 a  =

                                    2            3            4
   3.432D-17 +1.230D-16s +3.079D-16s  +5.709D-17s  +3.432D-17s

 b  =

                                    2            3   4
   1.0000004 +61.501079s +59.597296s  +14.304769s  +s

The problem is in %r_simp code, which does a cleaning, but not a complete one. If fact we should have the same result when the cleaning is done afterwards :

--> clean(a/b)
 ans  =

      
   0  
   -- 
      
   1 

which is OK to me when you see this:

--> w=10^(1:6); abs(horner(a/b,%i*w))
 ans  =

   2.224D-17   3.415D-17   3.432D-17   3.432D-17   3.432D-17   3.432D-17

S.


Le 20/03/2020 à 14:10, Stéphane Mottelet a écrit :

Hello Frederico,

The problem is in simp() :

---> rlist(prod(a.num),prod(a.den),a.dt)
 ans  =

                                      2            3            4 
   3.432D-17 + 1.230D-16s + 3.079D-16s + 5.709D-17s + 3.432D-17s  
   -------------------------------------------------------------- 
                                          2            3   4      
       1.0000004 + 61.501079s + 59.597296s + 14.304769s + s       


---> simp(rlist(prod(a.num),prod(a.den),a.dt))
 ans  =

                                      2            3            4 
   3.432D-17 + 1.230D-16s + 3.079D-16s + 5.709D-17s + 3.432D-17s  
   -------------------------------------------------------------- 
                                                                  
                                 1         

S.

Le 17/03/2020 à 10:30, Federico Miyara a écrit :

Dear all,

Look at this code (the coefficients are actually the result of pevious calculations):

NUM = [5.858D-09 + 2.011D-08*%s + 4.884D-08*%s^2 ...
       5.858D-09 + 8.796D-10*%s + 7.028D-10*%s^2]
DEN
= [0.1199597 + 7.2765093*%s + %s^2 ...
       8.336136 +  7.0282601*%s + %s^2]
q = NUM
./DEN
 
Running it yields

   5.858D-09 +2.011D-08s +4.884D-08s²  5.858D-09 +8.796D-10s +7.028D-10s² 
   ----------------------------------  ---------------------------------- 
       0.1199597 +7.2765093s +s²            8.336136 +7.0282601s +s²      

This is, correctly, a two-component rational vector with the expected numerators and denominators.

Now let's evaluate

q = prod(NUM./DEN)

The prod documantation sys that the argument may be "an array of reals, complex, booleans, polynomials or rational fractions". It should provide the rational obtained by multiplying the twonumrators and the two denominators. However, we get

   3.432D-17 +1.230D-16s +3.079D-16s² +5.709D-17s³ +3.432D-17s⁴ 
   ------------------------------------------------------------ 
                                1                               

The numeratoris right, but the expected denominator has been just replaced by 1

However, rewriting the command as

prod(NUM)/prod(DEN)

we get the expected result:

   3.432D-17 +1.230D-16s +3.079D-16s² +5.709D-17s³ +3.432D-17s⁴ 
   ------------------------------------------------------------ 
       1.0000004 +61.501079s +59.597296s² +14.304769s³ +s⁴      

This is quite strange!

Now we repeat with simpler polynomials:

NUM = [1-%s 2-%s]
DEN = [1+%s 2+%s]
q = NUM./DEN

We get

   1 -s  2 -s 
   ----  ---- 
   1 +s  2 +s

Now evaluate

prod(NUM./DEN)

The result is the expected one!
             
   2 -3s +s² 
   --------- 
   2 +3s +s² 

The behavior seems to depend on the type of polynomials.

Is this a bug or there is something I'm not interpreting correctly?

Regards,

Federico Miyara

_______________________________________________
users mailing list
[hidden email]
https://antispam.utc.fr/proxy/1/c3RlcGhhbmUubW90dGVsZXRAdXRjLmZy/lists.scilab.org/mailman/listinfo/users
-- 
Stéphane Mottelet
Ingénieur de recherche
EA 4297 Transformations Intégrées de la Matière Renouvelable
Département Génie des Procédés Industriels
Sorbonne Universités - Université de Technologie de Compiègne
CS 60319, 60203 Compiègne cedex
Tel : +33(0)344234688
http://www.utc.fr/~mottelet

_______________________________________________
users mailing list
[hidden email]
https://antispam.utc.fr/proxy/1/c3RlcGhhbmUubW90dGVsZXRAdXRjLmZy/lists.scilab.org/mailman/listinfo/users
-- 
Stéphane Mottelet
Ingénieur de recherche
EA 4297 Transformations Intégrées de la Matière Renouvelable
Département Génie des Procédés Industriels
Sorbonne Universités - Université de Technologie de Compiègne
CS 60319, 60203 Compiègne cedex
Tel : +33(0)344234688
http://www.utc.fr/~mottelet

_______________________________________________
users mailing list
[hidden email]
http://lists.scilab.org/mailman/listinfo/users
fmiyara fmiyara
Reply | Threaded
Open this post in threaded view
|

Re: Strange behaviour of prod on rationals


Stéphane,

In the meantime, a workaround is to toggle simplification off:

simp_mode(%f).

This inhibits simplification.

Regards,

Federico Miyara


On 20/03/2020 10:42, Stéphane Mottelet wrote:

(num,den) calling style seems to be OK:

--> [a,b]=simp(prod(q.num),prod(q.den))
 a  =

                                    2            3            4
   3.432D-17 +1.230D-16s +3.079D-16s  +5.709D-17s  +3.432D-17s

 b  =

                                    2            3   4
   1.0000004 +61.501079s +59.597296s  +14.304769s  +s

The problem is in %r_simp code, which does a cleaning, but not a complete one. If fact we should have the same result when the cleaning is done afterwards :

--> clean(a/b)
 ans  =

      
   0  
   -- 
      
   1 

which is OK to me when you see this:

--> w=10^(1:6); abs(horner(a/b,%i*w))
 ans  =

   2.224D-17   3.415D-17   3.432D-17   3.432D-17   3.432D-17   3.432D-17

S.


Le 20/03/2020 à 14:10, Stéphane Mottelet a écrit :

Hello Frederico,

The problem is in simp() :

---> rlist(prod(a.num),prod(a.den),a.dt)
 ans  =

                                      2            3            4 
   3.432D-17 + 1.230D-16s + 3.079D-16s + 5.709D-17s + 3.432D-17s  
   -------------------------------------------------------------- 
                                          2            3   4      
       1.0000004 + 61.501079s + 59.597296s + 14.304769s + s       


---> simp(rlist(prod(a.num),prod(a.den),a.dt))
 ans  =

                                      2            3            4 
   3.432D-17 + 1.230D-16s + 3.079D-16s + 5.709D-17s + 3.432D-17s  
   -------------------------------------------------------------- 
                                                                  
                                 1         

S.

Le 17/03/2020 à 10:30, Federico Miyara a écrit :

Dear all,

Look at this code (the coefficients are actually the result of pevious calculations):

NUM = [5.858D-09 + 2.011D-08*%s + 4.884D-08*%s^2 ...
       5.858D-09 + 8.796D-10*%s + 7.028D-10*%s^2]
DEN
= [0.1199597 + 7.2765093*%s + %s^2 ...
       8.336136 +  7.0282601*%s + %s^2]
q = NUM
./DEN
 
Running it yields

   5.858D-09 +2.011D-08s +4.884D-08s²  5.858D-09 +8.796D-10s +7.028D-10s² 
   ----------------------------------  ---------------------------------- 
       0.1199597 +7.2765093s +s²            8.336136 +7.0282601s +s²      

This is, correctly, a two-component rational vector with the expected numerators and denominators.

Now let's evaluate

q = prod(NUM./DEN)

The prod documantation sys that the argument may be "an array of reals, complex, booleans, polynomials or rational fractions". It should provide the rational obtained by multiplying the twonumrators and the two denominators. However, we get

   3.432D-17 +1.230D-16s +3.079D-16s² +5.709D-17s³ +3.432D-17s⁴ 
   ------------------------------------------------------------ 
                                1                               

The numeratoris right, but the expected denominator has been just replaced by 1

However, rewriting the command as

prod(NUM)/prod(DEN)

we get the expected result:

   3.432D-17 +1.230D-16s +3.079D-16s² +5.709D-17s³ +3.432D-17s⁴ 
   ------------------------------------------------------------ 
       1.0000004 +61.501079s +59.597296s² +14.304769s³ +s⁴      

This is quite strange!

Now we repeat with simpler polynomials:

NUM = [1-%s 2-%s]
DEN = [1+%s 2+%s]
q = NUM./DEN

We get

   1 -s  2 -s 
   ----  ---- 
   1 +s  2 +s

Now evaluate

prod(NUM./DEN)

The result is the expected one!
             
   2 -3s +s² 
   --------- 
   2 +3s +s² 

The behavior seems to depend on the type of polynomials.

Is this a bug or there is something I'm not interpreting correctly?

Regards,

Federico Miyara

_______________________________________________
users mailing list
[hidden email]
https://antispam.utc.fr/proxy/1/c3RlcGhhbmUubW90dGVsZXRAdXRjLmZy/lists.scilab.org/mailman/listinfo/users
-- 
Stéphane Mottelet
Ingénieur de recherche
EA 4297 Transformations Intégrées de la Matière Renouvelable
Département Génie des Procédés Industriels
Sorbonne Universités - Université de Technologie de Compiègne
CS 60319, 60203 Compiègne cedex
Tel : +33(0)344234688
http://www.utc.fr/~mottelet

_______________________________________________
users mailing list
[hidden email]
https://antispam.utc.fr/proxy/1/c3RlcGhhbmUubW90dGVsZXRAdXRjLmZy/lists.scilab.org/mailman/listinfo/users
-- 
Stéphane Mottelet
Ingénieur de recherche
EA 4297 Transformations Intégrées de la Matière Renouvelable
Département Génie des Procédés Industriels
Sorbonne Universités - Université de Technologie de Compiègne
CS 60319, 60203 Compiègne cedex
Tel : +33(0)344234688
http://www.utc.fr/~mottelet

_______________________________________________
users mailing list
[hidden email]
http://lists.scilab.org/mailman/listinfo/users


_______________________________________________
users mailing list
[hidden email]
http://lists.scilab.org/mailman/listinfo/users