Révision 78

pobysoPythonSage/src/sageSLZ/sagePolynomialOperations.sage (revision 78)
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    # We work from p^0 * N^alpha to p^alpha * N^0
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    for pPower in xrange(0, alpha + 1):
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        # pPower == 0 is a special case. We introduce all the monomials but one
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        # in, those in t necessary to be able to introduce
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        # in i and those in t necessary to be able to introduce
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        # p. We arbitrary choose to introduce the highest degree monomial in i
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        # with p. We also introduce all the mixed i^k * t^l monomials with
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        # k < p.degree(i) and l <= p.degree(t).
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        # Mixed terms introduction is necessary before we start "i shifts" in
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        # the next iteration.
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        # Mixed terms introduction is necessary here before we start "i shifts"
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        # in the next iteration.
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        if pPower == 0:
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            # iter1: power of i
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            # Notice how i^pIdegree is excluded.
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            # Notice that i^pIdegree is excluded as the bound of the xrange is
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            # pIdegree
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            for iPower in xrange(0, pIdegree):
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                # iter5: power of t.
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                for tPower in xrange(0, pTdegree + 1):
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                    if columnsWidth != 0:
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                        print "->", spo_expression_as_string(iPower,
......
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                                                             alpha)
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                    currentExpression = iVariable^iPower * \
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                                        tVariable^tPower * nAtPower
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                    # polynomialAtPower == 1 here. Next line should be commented out but it does not work!
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                    # Some convertion problem?
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                    # polynomialAtPower == 1 here. Next line should be commented
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                    # out but it does not work! Some conversion problem?
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                    currentPolynomial = pRing(currentExpression) * \
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                                        polynomialAtPower
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                    pMonomials = currentPolynomial.monomials()
......
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                                                        knownMonomials,
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                                                        protoMatrixRows,
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                                                        columnsWidth)
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                # End iter5.
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            # End for iter1.
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                # End tPower.
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            # End for iPower.
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        else: # pPower > 0: (p^1..p^alpha)
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            # This where we introduce the p^iPower * N^(alpha-iPower)
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            # This where we introduce the p^pPower * N^(alpha-pPower)
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            # polynomial.
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            # This step could technically be fused as the first iteration
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            # of the next loop (with iPower starting at 0).
......
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            # We want now to introduce a t * p^pPower polynomial. But before
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            # that we must introduce some mixed monomials.
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            # This loop is no triggered before pPower == 2.
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            # It introduces a first set of mixed monomials.
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            # It introduces a first set of high i degree mixed monomials.
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            for iPower in xrange(1, pPower):
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                tPower = pPower - iPower + 1
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                if columnsWidth != 0:
......
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                                                    protoMatrixRows,
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                                                    columnsWidth)
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            # End for iPower
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            # This is the main loop. It introduces:
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            #
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            # This is the mixed monomials main loop. It introduces:
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            # - the missing mixed monomials needed before the
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            #   t * p^pPower * N^(alpha-pPower)  polynomial;
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            # - the t * p^pPower * N^(alpha-pPower) itself;
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            # - the missing mixed monomials needed before each of the
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            #   i^k * t^l * p^pPower * N^(alpha-pPower) polynomials;
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            # - the i^k * t^l * p^pPower * N^(alpha-pPower) themselves.
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            #   t^l * p^pPower * N^(alpha-pPower) polynomial;
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            # - the t^l * p^pPower * N^(alpha-pPower) itself;
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            # - for each of i^k * t^l * p^pPower * N^(alpha-pPower) polynomials:
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            #   - the the missing mixed monomials needed  polynomials,
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            #   - the i^k * t^l * p^pPower * N^(alpha-pPower) itself.
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            # The t^l * p^pPower * N^(alpha-pPower) is introduced when
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            #
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            for iShift in xrange(0, pIdegree):
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                # When pTdegree == 1, the following loop only introduces
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                # a single new monomial.
......
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                                                        protoMatrixRows,
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                                                        columnsWidth)
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                    #print "+++++"
147 

  		





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


  		





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


  		





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                    # introducing the  


  		





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


  		





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


  		





  
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                    # before introducing the  


  		





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


  		





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                    # polynomial.


  		





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                    # It introduces smaller i degree monomials than the


  		





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


  		





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


  		





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


  		





  
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                    # The innerTpower loop does not produce anything before


  		





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


  		





  
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                    # p.


  		





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                    if iShift > 0:


  		





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                        iPower = pIdegree + iShift


  		





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


  		





  ......




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                            iPower += pIdegree


  		





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                        # End for innerTpower


  		





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                    # End of if iShift > 0


  		





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


  		





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


  		





  
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                    # been introduced (followed by a string of 


  		





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


  		





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


  		





  
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                    # 


  		





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                    # Eventually, the following section introduces the 


  		





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


  		





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                    # polynomials.


  		





  ......




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                                                        columnsWidth)


  		





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                # End for outerTpower 


  		





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                #print "++++++++++"


  		





  196
  
  
    

  		





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            # End for iShift


  		





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        polynomialAtPower *= p  


  		





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        nAtPower /= N


  		





  ......




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


  		





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                     monomials


  		





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


  		





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                     do display anything.


  		





  
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                     do not display anything.


  		





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    """


  		





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


  		





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    pMonomials.reverse()


  		












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