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I two multivariate polynomials, 'num' and 'denom' such that denom divides num. But I have not been able to get Sagemath to simplify the quotient num/denom.

Sample code is below. The workbook and the two polynomials are available at https://cocalc.com/share/513993d46f58cd3c1c6c6b22d60962e425fecad2/polynomial_division.ipynb?viewer=share https://cocalc.com/share/6884a274c847cbf4780bf636290777ad5e710828/denom.sobj?viewer=share https://cocalc.com/share/d8904075cf0e67344ac25f47edfa8d38de104379/num.sobj?viewer=share

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

denom=load('denom'); num=load('num')

denom.divides(num)

True

num.reduce(Ideal([denom]))

0

F=num/denom

F.denominator()/denom

1

F.reduce()

F.denominator()/denom

1

num.number_of_terms()

3197

denom.number_of_terms()

64

num.degree()

24

I have two multivariate polynomials, 'num' and 'denom' such that denom divides num. But I have not been able to get Sagemath to simplify the quotient num/denom.

Sample code is below. The workbook and the two polynomials are available at https://cocalc.com/share/513993d46f58cd3c1c6c6b22d60962e425fecad2/polynomial_division.ipynb?viewer=share https://cocalc.com/share/6884a274c847cbf4780bf636290777ad5e710828/denom.sobj?viewer=share https://cocalc.com/share/d8904075cf0e67344ac25f47edfa8d38de104379/num.sobj?viewer=share

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

denom=load('denom'); num=load('num')

denom.divides(num)

True

num.reduce(Ideal([denom]))

0

F=num/denom

F.denominator()/denom

1

F.reduce()

F.denominator()/denom

1

num.number_of_terms()

3197

denom.number_of_terms()

64

num.degree()

24

I have two multivariate polynomials, 'num' num and 'denom' denom such that denom that denom divides num. num. But I have not been able to get Sagemath SageMath to simplify the quotient num/denom. num/denom.

Sample code is below. The workbook and the two polynomials are available at https://cocalc.com/share/513993d46f58cd3c1c6c6b22d60962e425fecad2/polynomial_division.ipynb?viewer=share https://cocalc.com/share/6884a274c847cbf4780bf636290777ad5e710828/denom.sobj?viewer=share https://cocalc.com/share/d8904075cf0e67344ac25f47edfa8d38de104379/num.sobj?viewer=sharebelow.

sage: dR.<d1, d2, d3, d4, d12, d13, d14, d23, d24, d34, d123, d124, d134, d234, d1234> = PolynomialRing(ZZ,15,order='lex')
PolynomialRing(ZZ, 15, order='lex')
  
denom=load('denom'); num=load('num')
 
denom.divides(num)
 
True
 
num.reduce(Ideal([denom]))
 
0
 
F=num/denom
 
F.denominator()/denom
 
1
 
F.reduce()
 
F.denominator()/denom
 
1
 
num.number_of_terms()
 
3197
 
denom.number_of_terms()
 
64
 
num.degree()
 
24sage: denom = load('denom')
sage: num = load('num')
sage: denom.divides(num)
True
sage: num.reduce(Ideal([denom]))
0
sage: F = num/denom
sage: F.denominator()/denom
1
sage: F.reduce()
sage: F.denominator() / denom
1
sage: num.number_of_terms()
3197
sage: denom.number_of_terms()
64
sage: num.degree()
24