在python中乘以多项式

Question

我做了加法和减法,但我很难在python中乘以多项式.

例如,如果我有:

2X^2 + 5X + 1 [1,5,2]

和...

3X^3 + 4X^2 + X + 6 [6,1,4,3]

我们得到:

6X^5 + 23X^4 + 25X^3 + 21X^2 + 31X + 6 [6,31,21,25,23,6]

我很绝望.我已经在这里工作了好几天.任何帮助,将不胜感激

Answer 1

s1 = [1,5,2]
s2 = [6,1,4,3]
res = [0]*(len(s1)+len(s2)-1)
for o1,i1 in enumerate(s1):
    for o2,i2 in enumerate(s2):
        res[o1+o2] += i1*i2

编辑:为了纪念@katrielalex:

import collections
import itertools

class Polynomial(object):
    def __init__(self, *args):
        """
        Create a polynomial in one of three ways:

        p = Polynomial(poly)           # copy constructor
        p = Polynomial([1,2,3 ...])    # from sequence
        p = Polynomial(1, 2, 3 ...)    # from scalars
        """
        super(Polynomial,self).__init__()
        if len(args)==1:
            val = args[0]
            if isinstance(val, Polynomial):                # copy constructor
                self.coeffs = val.coeffs[:]
            elif isinstance(val, collections.Iterable):    # from sequence
                self.coeffs = list(val)
            else:                                          # from single scalar
                self.coeffs = [val+0]
        else:                                              # multiple scalars
            self.coeffs = [i+0 for i in args]
        self.trim()

    def __add__(self, val):
        "Return self+val"
        if isinstance(val, Polynomial):                    # add Polynomial
            res = [a+b for a,b in itertools.izip_longest(self.coeffs, val.coeffs, fillvalue=0)]
        else:                                              # add scalar
            if self.coeffs:
                res = self.coeffs[:]
                res[0] += val
            else:
                res = val
        return self.__class__(res)

    def __call__(self, val):
        "Evaluate at X==val"
        res = 0
        pwr = 1
        for co in self.coeffs:
            res += co*pwr
            pwr *= val
        return res

    def __eq__(self, val):
        "Test self==val"
        if isinstance(val, Polynomial):
            return self.coeffs == val.coeffs
        else:
            return len(self.coeffs)==1 and self.coeffs[0]==val

    def __mul__(self, val):
        "Return self*val"
        if isinstance(val, Polynomial):
            _s = self.coeffs
            _v = val.coeffs
            res = [0]*(len(_s)+len(_v)-1)
            for selfpow,selfco in enumerate(_s):
                for valpow,valco in enumerate(_v):
                    res[selfpow+valpow] += selfco*valco
        else:
            res = [co*val for co in self.coeffs]
        return self.__class__(res)

    def __neg__(self):
        "Return -self"
        return self.__class__([-co for co in self.coeffs])

    def __pow__(self, y, z=None):
        raise NotImplemented()

    def _radd__(self, val):
        "Return val+self"
        return self+val

    def __repr__(self):
        return "{0}({1})".format(self.__class__.__name__, self.coeffs)

    def __rmul__(self, val):
        "Return val*self"
        return self*val

    def __rsub__(self, val):
        "Return val-self"
        return -self + val

    def __str__(self):
        "Return string formatted as aX^3 + bX^2 + c^X + d"
        res = []
        for po,co in enumerate(self.coeffs):
            if co:
                if po==0:
                    po = ''
                elif po==1:
                    po = 'X'
                else:
                    po = 'X^'+str(po)
                res.append(str(co)+po)
        if res:
            res.reverse()
            return ' + '.join(res)
        else:
            return "0"

    def __sub__(self, val):
        "Return self-val"
        return self.__add__(-val)

    def trim(self):
        "Remove trailing 0-coefficients"
        _co = self.coeffs
        if _co:
            offs = len(_co)-1
            if _co[offs]==0:
                offs -= 1
                while offs >= 0 and _co[offs]==0:
                    offs -= 1
                del _co[offs+1:]

Answer 2

In [1]: from numpy import convolve

In [2]: convolve([1,5,2],[6,1,4,3])
Out[2]: array([ 6, 31, 21, 25, 23,  6])

Answer 3

q = [6,1,4,3]
p = [1,5,2]
qa = zip(q, [3,2,1,0])
pa = zip(p, [2,1,0])
res = {}
for a in qa:
for b in pa:
    if a[1] + b[1] in res:
        res[a[1] + b[1]] += a[0]*b[0]
    else:
        res[a[1] + b[1]] = a[0]*b[0]
print res

当然，您需要添加更多内容才能使其适用于一般多项式。您还可以使用他们用于 FFT 的一些东西来使其更快（我认为）。