CoCalc -- polynomial_division.ipynb

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Kernel: SageMath (system-wide)

In [22]:

dR.<d1,d2,d3,d4,d12,d13,d14,d23,d24,d34,d123,d124,d134,d234,d1234> \
    = PolynomialRing(ZZ,15,order='negdegrevlex')
denom=load('denom'); num=load('num')
dR

Multivariate Polynomial Ring in d1, d2, d3, d4, d12, d13, d14, d23, d24, d34, d123, d124, d134, d234, d1234 over Integer Ring

In [23]:

denom in dR

True

In [24]:

num in dR

True

In [25]:

denom.number_of_terms()

64

In [26]:

num.number_of_terms()

3197

In [33]:

(d12+1).divides(denom)

True

In [34]:

(d12+1).divides(num)

True

In [35]:

d12.divides(denom(d12=d12-1))

True

In [36]:

d12.divides(num(d12=d12-1))

False

In [41]:

dR.<d1,d2,d3,d4,d12,d13,d14,d23,d24,d34,d123,d124,d134,d234,d1234> \
    = PolynomialRing(ZZ,15,order='lex')

In [43]:

(d12+1).divides(denom)

True

In [44]:

(d12+1).divides(num)

False

In [28]:

num.reduce(Ideal([denom]))

0

In [29]:

F=num/denom

In [30]:

F.denominator()/denom

1

In [31]:

F.reduce()

In [32]:

F.denominator()/denom

1

In [0]:

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