class encapsulates monomials and polynomials

**bartonc** · Jan 4 '07, 01:35 AM

Originally posted by badech

Hello ,
can you explain me what does this function ( class ) do ?

Code:

class Doublet:
    def __init__(self,referenceMonome,refSuiv):
        self.refMon = referenceMonome
        self.suiv = refSuiv
    def __repr__(self):
        res=''
        cour=self
        while cour!=None:
            res+=str(cour.refMon)
            cour=cour.suiv
        if res[0]=='+':
            return res[1:]
        return res

thank you

I don't know French and don't know many who do, and much of this lacks any context, but:
If suiv is "next" then this it looks like this is a linked list of some type and when this object's repr() is called, it returns referenceMonome from each member in the chain. It then removes the "+" from the head of the result.
It would be very helpful if you could translate your posts for us (non-bilingual) experts. Thanks,
Barton

**bvdet** · Jan 4 '07, 02:24 AM

Originally posted by badech

Hello ,
can you explain me what does this function ( class ) do ?

Code:

class Doublet:
    def __init__(self,referenceMonome,refSuiv):
        self.refMon = referenceMonome
        self.suiv = refSuiv
    def __repr__(self):
        res=''
        cour=self
        while cour!=None:
            res+=str(cour.refMon)
            cour=cour.suiv
        if res[0]=='+':
            return res[1:]
        return res

thank you

Monome - Monomial? Like Barton, I don't know French.
It looks like the class is accumulating a series of monomials - similar to another of your threads. A monomial is an algebraic expression containing only one term as in:

Code:

7*x**2

Just guessing.

**bartonc** · Jan 4 '07, 02:26 AM

Originally posted by bvdet

Monome - Monomial? Like Barton, I don't know French.
It looks like the class is accumulating a series of monomials - similar to another of your threads. A monomial is an algebraic expression containing only one term as in:

Code:

7*x**2

Just guessing.

I thought maybe it's collecting friends. Could be.

**badech** · Jan 5 '07, 02:15 AM

Hello
i'm sorry , I had not given many details which could have
helped you to better include/understand my question
here is my problem
the framed functions are given
# Polynomials with two variables:
# the choices:
# the monomials which make a polynomial make only this polynomial:
# they do not compose of another polynomial
# if two polynomials contain the same monomial, this monomial exists in two specimens
# the monomials of a polynomial NEVER have null coefficient

_______________ _______________ _______________ _______________ _____

Code:

class Monome: # monome =monomial
    def __init__(self, coefficient, exposantX, exposantY): #exposant = power
        self.coeff = coefficient 
        self.expoX = exposantX 
        self.expoY = exposantY 
    def __repr__(self): 
        s=str(self.coeff)+"*x^"+str(self.expoX)+"*y^"+str(self.expoY) 
        if self.coeff<0: return s 
        return "+"+s 
    def __lt__(self, autre):  #autre=other
        return (self.expoX < autre.expoX) or ((self.expoX == 
autre.expoX) and (self.expoY < autre.expoY)) 
    def __gt__(self,autre): 
        return (self.expoX > autre.expoX) or ((self.expoX == 
autre.expoX) and (self.expoY >autre.expoY))

_______________ _______________ _______________ _______________ _____

_______________ _______________ _______________ _______________ _____

Code:

class Doublet: 
    def __init__(self,referenceMonome,refSuiv):   # suiv=next
        self.refMon = referenceMonome 
        self.suiv = refSuiv 
    def __repr__(self): 
        res=''  # res=result
        cour=self  # cour = current
        while cour!=None: 
            res+=str(cour.refMon) 
            cour=cour.suiv 
        if res[0]=='+': 
            return res[1:] 
        return res

_______________ _______________ _______________ _______________ _____

_______________ _______________ _______________ _______________ _____

Code:

def degre(mon): #degré = degree
    return(mon.expoX + mon.expoY)

_______________ _______________ _______________ _______________ _____

_______________ _______________ _______________ _______________ _____

Code:

def degreX (mon): 
    return mon.expoX

_______________ _______________ _______________ _______________ _____

the functions which follow, I must correct them and/or supplement them

Code:

def insereMonome(coefficient, exposantX, exposantY, doublett) : #insere=insert
    # to seek the last monomial before this new monomial 
# to make insertion by creating the monomial which will be placed 
# placed well for the ascending order "
        newRefMon = Monome(coefficient, exposantX, exposantY) 
        print "nouveau monome : ",newRefMon  
                                                              # nouveau monome = new monomial
        return None 


def insereCopieMonome( refMon, doublett): 
    #DO NOT modify this function
    return insereMonome(refMon.coeff, refMon.expoX, refMon.expoY, 
doublett) 


def ajouteDoubletsRec(listeDoublet1, listeDoublet2): #ajoute=add
    # returns a new list of doublets obtained by 
    # fusion of the two lists in new one
    # ATTENTION: not to forget to treat the case where two opposite 
    # monomials are added!!!!! 
    # in this case, not to reveal a monomial with a null coefficient.
    return None 


def multMonomeMonome(refMon1, refMon2): #mult=multiply
    return Monome(refMon1.coeff * refMon2.coeff, refMon1.expoX + 
refMon2.expoX, refMon1.expoY + refMon2.expoY) 
def multMonomeListeDoublets(refMon, listeDoublets): 
    res = None 
    return res 


def multDeuxListesDoublets(ld1, ld2): 
# multDeuxListesDoublets = mulitply 2 lists of doublets
# doublet = list of monomials
    res = None 
    return res

_______________ _______________ _______________ _______________ _____

Code:

class Polynome: #polynome =polynomial
    def __init__(self,listePrincipale): #liste pricipale=main list
        self.lp = listePrincipale 
        self.lDegre = creerListeDegre(listePrincipale)  creerListe=create list
        triDegre(self.lDegre) # tri =sorting

    def __repr__(self): 
        doub = self.lp 
        res = " liste pour l'ordre < \n" #l ist for the order
        res = res + str(doub) 
        res = res + "\n \n " 
        res = res + " liste pour l'ordre du degré total \n" 
                                                              #list for the order of the total degree
        doub = self.lDegre 
        res = res + str(doub) 
        return res

_______________ _______________ _______________ _______________ _____

_______________ _______________ _______________ _______________ _____

Code:

def creerListeDegre(ld): 
    if ld == None: 
        return None 
    else: 
        return Doublet(ld.refMon, creerListeDegre(ld.suiv))

_______________ _______________ _______________ _______________ _______________ *__

Code:

def triDegre(doublett): #tri =sorting
    # we modify by exchange the values of the fields "refMon"of the listdoublett,
    # so that  the list doublett is increasing for the order of the degree 
    
return ...


def add(pol1, pol2): 
        return None 


def mul(pol1, pol2): 
        return None 



# END of the definition of the functions and methods
#  -------------------------------------------------------------- 
#tests on the monomials
#m1 = Monome(5,2,6) 
#m2 = Monome(6,2,8) 
#m3 = Monome(-4,3,1) 
#m4 = Monome(-6,0,1) 
#print "m1 : ",m1, "     m2 : ",m2 
#print "m3 : ",m3, "    m4 : ",m4 
#print m1 < m2 
#print m3 < m4 
#print 
#tests on the doublets 
#d1 = Doublet(m1,None) 
#print "doublet d1 : ",d1 
#doublet1 = Doublet(Monome(-4,7,1),Doublet(Monome(2,4,3),None)) 
#doublet2 = Doublet(m1,Doublet(m2,None)) 
#print 
#print"doublet1 : ",doublet1, "   doublet2 : ",doublet2 
#print 
# tests of the function insereMonome
#doub1 = insereMonome(5, 2, 6, None) 
#doub1 = insereMonome(6,3,8, doub1) 
#doub2 = insereMonome(5,10,3, None) 
#doub2 = insereMonome(4,2,6, doub2) 
#doub2 = insereMonome(-3,11,7, doub2) 
#doub2 = insereMonome(-6, 3,8, doub2) 
#doub2 = insereMonome(2,3,0, doub2) 
#print "doub1 : ",doub1 
#print"    doub2 : ",doub2 
# tests of the function ajouteDoubletsRec 
#listeAjout = ajouteDoubletsRec(doub1, doub2) 
#print "sum of 2 lists : ", listeAjout 


# tests of the function multMonomeListeDoublets
# TESTS TO BE BUILT ( we must write some tests of this 
# function ( multMonomeListeDoublets)

# tests of the function multDeuxListesDoublets 
# TESTS TO BE BUILT ( we must write some tests of this 
# function ( multDeuxListesDoublets)

# tests of the function creerListeDegre 
#TESTS TO BE BUILT ( we must write some tests of this 
# function ( creerListeDegre)

# tests of the function triDegre 
#TESTS TO BE BUILT ( we must write some tests of this 
# function ( triDegre )

# tests of polynomials: representation, addition, multiplication
# TESTS TO BE BUILT ( we must write some tests )

#pol1 = Polynome(doublet1) 
#pol2 = Polynome(doublet2) 
#som = add(pol1, pol2) 
#prod = mult(pol1, pol2) 
#print som 
#print prod

for example , the calss Doublet causes problems to me

Code:

>If, for example, I write

> >>> a=Monome(2,7,11) 
> >>> a 
> +2*x^7*y^11 
> >>> b=Monome(-1,17,35) 
> >>> b 
> -1*x^17*y^35 
> >>> c=Doublet(a,b) 
> >>> t 
> Traceback (most recent call last): 
>   File "<pyshell#5>", line 1, in <module> 
>     t 
>   File "C:\...\polynomesXY2_DEVOIR_Enonce.py", line 36, in __repr__ 
>     res+=str(cour.refMon) 
> AttributeError: Monome instance has no attribute 'refMon'

this returns an error message

could you help me PLEASE?
thank you in advance and I hope to have been clear ( understood )
thank you

**bartonc** · Jan 5 '07, 02:35 AM

I've added [ code] [ /code] tags. I'll take a look now. In the mean time, please learn to use these (without spaces) in "Posting Guidelines" in several places on this forum.

**badech** · Jan 6 '07, 12:12 PM

Hello bartonc ,
can you change the title please ?
thanks

**badech** · Jan 6 '07, 12:27 PM

thank you bartonc :)

**bvdet** · Jan 6 '07, 03:52 PM

I added spaces at the plus and minus signs so the polynomial is easier to read.

Code:

m1 = Monome(5,2,6) 
m2 = Monome(6,2,8) 
print "\nm1 : ", m1
print "m2 : ", m2 
d2 = Doublet(m1,Doublet(m2, Doublet(Monome(4,7,1), None)))
print "Doublet(m1,Doublet(m2, Doublet(Monome(-4,7,1), None))): ", d2

Output:

Code:

m1 :   + 5*x^2*y^6
m2 :   + 6*x^2*y^8
Doublet(m1,Doublet(m2, Doublet(Monome(-4,7,1), None))):   + 5*x^2*y^6 + 6*x^2*y^8 + 4*x^7*y^1

The first argument to Doublet is a Monome object and the second is None or a Doublet object

**bvdet** · Jan 7 '07, 12:51 AM

badech,

I was playing with an instance of your Doublet class and noticed there was no iteration method. I have never used 'yield' in code before:

Code:

# Doublet iterator
def iterDoub(d):
    while d:
        yield d.refMon
        d = d.suiv

Example:

Code:

>>> print "Doublet 'd1':", d1
Doublet 'd1':  + 9*x^2*y^6 + 2*x^3*y^0 + 5*x^3*y^9 - 2*x^4*y^2 + 5*x^10*y^3 - 3*x^11*y^7
>>> for d in iterDoub(d1):
... 	print d
... 	
 + 9*x^2*y^6
 + 2*x^3*y^0
 + 5*x^3*y^9
 - 2*x^4*y^2
 + 5*x^10*y^3
 - 3*x^11*y^7
>>>

It seems interestingly simple. Maybe you can use it.

**bartonc** · Jan 7 '07, 03:23 AM

Originally posted by bvdet

badech,

I was playing with an instance of your Doublet class and noticed there was no iteration method. I have never used 'yield' in code before:

Code:

# Doublet iterator
def iterDoub(d):
    while d:
        yield d.refMon
        d = d.suiv

Example:

Code:

>>> print "Doublet 'd1':", d1
Doublet 'd1':  + 9*x^2*y^6 + 2*x^3*y^0 + 5*x^3*y^9 - 2*x^4*y^2 + 5*x^10*y^3 - 3*x^11*y^7
>>> for d in iterDoub(d1):
... 	print d
... 	
 + 9*x^2*y^6
 + 2*x^3*y^0
 + 5*x^3*y^9
 - 2*x^4*y^2
 + 5*x^10*y^3
 - 3*x^11*y^7
>>>

It seems interestingly simple. Maybe you can use it.

Great post, B.V.! It's awesome that you are finding inspiration from members' questions.

**bvdet** · Jan 7 '07, 02:53 PM

Originally posted by bartonc

Great post, B.V.! It's awesome that you are finding inspiration from members' questions.

Thanks Barton. I am learning new things regularly by following threads and participating where I can.

badech - Have you made any progress on your assignment? Show us what you have accomplished. Try to solve it one step at a time. We should not write it for you, but I am sure we can help if you are having problems with your code.

**bvdet** · Jan 7 '07, 03:57 PM

I did not care for the way the multinomials were represented, so I reworked special methods '__repr__':

Code:

class Monome: # monome = monomial
    def __init__(self, coefficient, exposantX, exposantY): #exposant = power
        self.coeff = coefficient 
        self.expoX = exposantX 
        self.expoY = exposantY
        
    def __repr__(self):
        if abs(self.coeff) == 1:
            coeffStr = "("
        else:
            coeffStr = '%s(' % (abs(self.coeff))
        if self.coeff < 0:
            preStr = "-"
        else:
            preStr = "+"
        return '%s%sx^%s*y^%s)' % (preStr, coeffStr, self.expoX, self.expoY)
    
    def __lt__(self, autre):  #autre=other
        return (self.expoX < autre.expoX) or ((self.expoX == autre.expoX) and (self.expoY < autre.expoY)) 
    def __gt__(self,autre): 
        return (self.expoX > autre.expoX) or ((self.expoX == autre.expoX) and (self.expoY >autre.expoY))

class Doublet: 
    def __init__(self,referenceMonome,refSuiv):   # suiv=next
        self.refMon = referenceMonome 
        self.suiv = refSuiv
        
    def __repr__(self):
        res = str(self.refMon)
        a = self.suiv
        while a:
            res += str(a.refMon)
            a = a.suiv
        if res[0] == '+': 
            return res[1:] 
        return res

This is what it looks like now:

Code:

Doublet 'd1': 9(x^2*y^6)+2(x^3*y^0)+5(x^3*y^9)-2(x^4*y^2)+5(x^10*y^3)-3(x^11*y^7)
Iteration over Doublet 'd1':
+9(x^2*y^6)
+2(x^3*y^0)
+5(x^3*y^9)
-2(x^4*y^2)
+5(x^10*y^3)
-3(x^11*y^7)

6(x^3*y^8)+5(x^3*y^9)-2(x^4*y^2)
4(x^2*y^6)+2(x^3*y^0)-6(x^3*y^8)+5(x^10*y^3)-3(x^11*y^7)
-(x^-2*y^-3)+7(x^4*y^12)+4(x^5*y^6)+6(x^7*y^1)

**bartonc** · Jan 7 '07, 06:53 PM

Originally posted by bvdet

Thanks Barton. I am learning new things regularly by following threads and participating where I can.

badech - Have you made any progress on your assignment? Show us what you have accomplished. Try to solve it one step at a time. We should not write it for you, but I am sure we can help if you are having problems with your code.

I often wish that I had more time to play with some of these exercises. I'm right in the middle of good sized project with a deadline looming.

Maybe no progress, maybe just (less that avid poster) - I know that he checked in this morning.

**badech** · Jan 7 '07, 07:49 PM

Hello
I am blocked on the first question, I do not manage to write the function insereMonome because I do not understand how the "calss" function.
can you help me to write this first function , and then i'll do the others
thank you

class encapsulates monomials and polynomials

class encapsulates monomials and polynomials

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