Polynomials can be factored with
factor. Factorization works in polynomial rings over prime finite fields, ZZ, or QQ.
i1 : R = ZZ/10007[a,b];
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i2 : f = (2*a+3)^4 + 5
4 3 2
o2 = 16a + 96a + 216a + 216a + 86
o2 : R
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i3 : g = (2*a+b+1)^3
3 2 2 3 2 2
o3 = 8a + 12a b + 6a*b + b + 12a + 12a*b + 3b + 6a + 3b + 1
o3 : R
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i4 : S = factor f
2
o4 = (a - 402)(a + 405)(a + 3a - 2301)(16)
o4 : Expression of class Product
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i5 : T = factor g
3
o5 = (a - 5003b - 5003) (8)
o5 : Expression of class Product
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The results have been packaged for easy viewing. The number of factors is obtained using
Each factor is represented as a power (exponents equal to 1 don't appear in the display.) The parts can be extracted with
#.
i7 : T#0
3
o7 = (a - 5003b - 5003)
o7 : Expression of class Power
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i8 : T#0#0
o8 = a - 5003b - 5003
o8 : R
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i9 : T#0#1
o9 = 3
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