<p>如果有任何python包可以提供帮助,那么它可能是<a href="https://en.wikipedia.org/wiki/SymPy" rel="nofollow noreferrer">Sympy</a>:</p>
<pre><code>from sympy import init_printing, symbols, simplify, collect, factor
e,n,p,tn,te,tp,N = symbols("e,n,p,tn,te,tp,N")
upperside = (e * e * n * p * tn * tn +
2 * e * e * n * p * tn * tp +
e * e * n * p * tp * tp +
2 * e * n * n * p * te * tn +
2 * e * n * n * p * te * tp +
N * e * n * n * tp * tp +
2 * e * n * p * p * te * tn +
2 * e * n * p * p * te * tp -
2 * N * e * n * p * tn * tp +
N * e * p * p * tn * tn +
n * n * n * p * te * te +
2 * n * n * p * p * te * te +
n * p * p * p * te * te)
print collect(upperside, e*n)
</code></pre>
<p>It输出:</p>
^{pr2}$
<p>在<a href="http://docs.sympy.org/dev/tutorial/simplification.html" rel="nofollow noreferrer">page</a>中描述的所有方法中,<code>collect</code>看起来最有希望。在</p>
<p>这里有一种快速而肮脏的方法来迭代所有符号组合并显示找到的最短表达式:</p>
<pre><code>from sympy import init_printing, symbols, collect, pprint
import itertools
init_printing()
e,n,p,tn,te,tp,big_n = symbols("e,n,p,tn,te,tp,big_n")
upperside = (e * e * n * p * tn * tn + 2 * e * e * n * p * tn * tp +
e * e * n * p * tp * tp + 2 * e * n * n * p * te * tn + 2 * e * n * n * p * te * tp +
big_n * e * n * n * tp * tp + 2 * e * n * p * p * te * tn +
2 * e * n * p * p * te * tp - 2 * big_n * e * n * p * tn * tp + big_n * e * p * p * tn * tn +
n * n * n * p * te * te + 2 * n * n * p * p * te * te + n * p * p * p * te * te)
my_symbols = [e, n, p, tn, te, tp, big_n]
min_length = float('inf')
for i in range(len(my_symbols)):
for symbol_subsets in itertools.combinations(my_symbols, i+1):
collect_by = '*'.join(str(symbol) for symbol in symbol_subsets)
expression = collect(upperside, collect_by)
length = len(str(expression))
if length < min_length:
min_length = length
print "With '%s' :" % collect_by
pprint(expression)
print
</code></pre>
<p>It输出:</p>
<pre><code>With 'e' :
e**2*(n*p*tn**2 + 2*n*p*tn*tp + n*p*tp**2) + e*(big_n*n**2*tp**2 - 2*big_n*n*p*tn*tp + big_n*p**2*tn**2 + 2*n**2*p*te*tn + 2*n**2*p*te*tp + 2*n*p**2*te*tn + 2*n*p**2*te*tp) + n**3*p*te**2 + 2*n**2*p**2*te**2 + n*p**3*te**2
With 'n' :
big_n*e*p**2*tn**2 + n**3*p*te**2 + n**2*(big_n*e*tp**2 + 2*e*p*te*tn + 2*e*p*te*tp + 2*p**2*te**2) + n*(-2*big_n*e*p*tn*tp + e**2*p*tn**2 + 2*e**2*p*tn*tp + e**2*p*tp**2 + 2*e*p**2*te*tn + 2*e*p**2*te*tp + p**3*te**2)
With 'e*n' :
big_n*e*p**2*tn**2 + e**2*n*(p*tn**2 + 2*p*tn*tp + p*tp**2) + e*n**2*(big_n*tp**2 + 2*p*te*tn + 2*p*te*tp) + e*n*(-2*big_n*p*tn*tp + 2*p**2*te*tn + 2*p**2*te*tp) + n**3*p*te**2 + 2*n**2*p**2*te**2 + n*p**3*te**2
With 'e*n*p' :
big_n*e*n**2*tp**2 - 2*big_n*e*n*p*tn*tp + big_n*e*p**2*tn**2 + e**2*n*p*(tn**2 + 2*tn*tp + tp**2) + e*n**2*p*(2*te*tn + 2*te*tp) + e*n*p**2*(2*te*tn + 2*te*tp) + n**3*p*te**2 + 2*n**2*p**2*te**2 + n*p**3*te**2
</code></pre>