Révision 78 pobysoPythonSage/src/sageSLZ/sagePolynomialOperations.sage

sagePolynomialOperations.sage (revision 78)
25 25 
    # We work from p^0 * N^alpha to p^alpha * N^0
26 26 
    for pPower in xrange(0, alpha + 1):
27 27 
        # pPower == 0 is a special case. We introduce all the monomials but one
28 
        # in, those in t necessary to be able to introduce
28 
        # in i and those in t necessary to be able to introduce
29 29 
        # p. We arbitrary choose to introduce the highest degree monomial in i
30 30 
        # with p. We also introduce all the mixed i^k * t^l monomials with
31 31 
        # k < p.degree(i) and l <= p.degree(t).
32 
        # Mixed terms introduction is necessary before we start "i shifts" in
33 
        # the next iteration.
32 
        # Mixed terms introduction is necessary here before we start "i shifts"
33 
        # in the next iteration.
34 34 
        if pPower == 0:
35 
            # iter1: power of i
36 
            # Notice how i^pIdegree is excluded.
35 
            # Notice that i^pIdegree is excluded as the bound of the xrange is
36 
            # pIdegree
37 37 
            for iPower in xrange(0, pIdegree):
38 
                # iter5: power of t.
39 38 
                for tPower in xrange(0, pTdegree + 1):
40 39 
                    if columnsWidth != 0:
41 40 
                        print "->", spo_expression_as_string(iPower,
......
44 43 
                                                             alpha)
45 44 
                    currentExpression = iVariable^iPower * \
46 45 
                                        tVariable^tPower * nAtPower
47 
                    # polynomialAtPower == 1 here. Next line should be commented out but it does not work!
48 
                    # Some convertion problem?
46 
                    # polynomialAtPower == 1 here. Next line should be commented
47 
                    # out but it does not work! Some conversion problem?
49 48 
                    currentPolynomial = pRing(currentExpression) * \
50 49 
                                        polynomialAtPower
51 50 
                    pMonomials = currentPolynomial.monomials()
......
55 54 
                                                        knownMonomials,
56 55 
                                                        protoMatrixRows,
57 56 
                                                        columnsWidth)
58 
                # End iter5.
59 
            # End for iter1.
60
57 
                # End tPower.
58 
            # End for iPower.
61 59 
        else: # pPower > 0: (p^1..p^alpha)
62 
            # This where we introduce the p^iPower * N^(alpha-iPower)
60 
            # This where we introduce the p^pPower * N^(alpha-pPower)
63 61 
            # polynomial.
64 62 
            # This step could technically be fused as the first iteration
65 63 
            # of the next loop (with iPower starting at 0).
......
97 95 
            # We want now to introduce a t * p^pPower polynomial. But before
98 96 
            # that we must introduce some mixed monomials.
99 97 
            # This loop is no triggered before pPower == 2.
100 
            # It introduces a first set of mixed monomials.
98 
            # It introduces a first set of high i degree mixed monomials.
101 99 
            for iPower in xrange(1, pPower):
102 100 
                tPower = pPower - iPower + 1
103 101 
                if columnsWidth != 0:
......
115 113 
                                                    protoMatrixRows,
116 114 
                                                    columnsWidth)
117 115 
            # End for iPower
118 
            # This is the main loop. It introduces:
116 
            #
117 
            # This is the mixed monomials main loop. It introduces:
119 118 
            # - the missing mixed monomials needed before the
120 
            #   t * p^pPower * N^(alpha-pPower)  polynomial;
121 
            # - the t * p^pPower * N^(alpha-pPower) itself;
122 
            # - the missing mixed monomials needed before each of the
123 
            #   i^k * t^l * p^pPower * N^(alpha-pPower) polynomials;
124 
            # - the i^k * t^l * p^pPower * N^(alpha-pPower) themselves.
119 
            #   t^l * p^pPower * N^(alpha-pPower) polynomial;
120 
            # - the t^l * p^pPower * N^(alpha-pPower) itself;
121 
            # - for each of i^k * t^l * p^pPower * N^(alpha-pPower) polynomials:
122 
            #   - the the missing mixed monomials needed  polynomials,
123 
            #   - the i^k * t^l * p^pPower * N^(alpha-pPower) itself.
124 
            # The t^l * p^pPower * N^(alpha-pPower) is introduced when
125 
            #
125 126 
            for iShift in xrange(0, pIdegree):
126 127 
                # When pTdegree == 1, the following loop only introduces
127 128 
                # a single new monomial.
......
144 145 
                                                        protoMatrixRows,
145 146 
                                                        columnsWidth)
146 147 
                    #print "+++++"
147 

  		





  148
  
  
    
                    # At iShift == 0, the following loop adds duplicate 


  		





  149
  
  
    
                    # monomials, since no extra i^l * t^k is needed before 


  		





  150
  
  
    
                    # introducing the  


  		





  
  148
  
    
                    # At iShift == 0, the following innerTpower loop adds  


  		





  
  149
  
    
                    # duplicate monomials, since no extra i^l * t^k is needed 


  		





  
  150
  
    
                    # before introducing the  


  		





  151
  151
  
    
                    # i^iShift * t^outerPpower * p^pPower * N^(alpha-pPower) 


  		





  152
  152
  
    
                    # polynomial.


  		





  153
  153
  
    
                    # It introduces smaller i degree monomials than the


  		





  154
  154
  
    
                    # one(s) added previously (no pPower multiplication).


  		





  155
  155
  
    
                    # Here the exponent of t decreases as that of i increases.


  		





  
  156
  
    
                    # This conditional is not entered before pPower == 1.


  		





  
  157
  
    
                    # The innerTpower loop does not produce anything before


  		





  
  158
  
    
                    # pPower == 2. We keep it anyway for other configuration of


  		





  
  159
  
    
                    # p.


  		





  156
  160
  
    
                    if iShift > 0:


  		





  157
  161
  
    
                        iPower = pIdegree + iShift


  		





  158
  162
  
    
                        for innerTpower in xrange(pPower, 1, -1):


  		





  ......




  174
  178
  
    
                            iPower += pIdegree


  		





  175
  179
  
    
                        # End for innerTpower


  		





  176
  180
  
    
                    # End of if iShift > 0


  		





  
  181
  
    
                    # When iShift == 0, just after each of the  


  		





  
  182
  
    
                    # p^pPower * N^(alpha-pPower) polynomials has 


  		





  
  183
  
    
                    # been introduced (followed by a string of 


  		





  
  184
  
    
                    # i^k * p^pPower * N^(alpha-pPower) polynomials) a


  		





  
  185
  
    
                    # t^l *  p^pPower * N^(alpha-pPower) is introduced here.


  		





  
  186
  
    
                    # 


  		





  177
  187
  
    
                    # Eventually, the following section introduces the 


  		





  178
  188
  
    
                    # i^iShift * t^outerTpower * p^iPower * N^(alpha-iPower) 


  		





  179
  189
  
    
                    # polynomials.


  		





  ......




  193
  203
  
    
                                                        columnsWidth)


  		





  194
  204
  
    
                # End for outerTpower 


  		





  195
  205
  
    
                #print "++++++++++"


  		





  196
  
  
    

  		





  197
  
  
    

  		





  198
  206
  
    
            # End for iShift


  		





  199
  207
  
    
        polynomialAtPower *= p  


  		





  200
  208
  
    
        nAtPower /= N


  		





  ......




  221
  229
  
    
    protoMatrixRows: a list of lists, each one holding the coefficients of the 


  		





  222
  230
  
    
                     monomials


  		





  223
  231
  
    
    columnWith     : the width, in characters, of the displayed column ; if 0, 


  		





  224
  
  
    
                     do display anything.


  		





  
  232
  
    
                     do not display anything.


  		





  225
  233
  
    
    """


  		





  226
  234
  
    
    # We have started with the smaller degrees in the first variable.


  		





  227
  235
  
    
    pMonomials.reverse()


  		












Formats disponibles :
  Unified diff