'factor'yse this

  1. is there any way to factorize larger expressions?
    i, for example wanted to factorize-
    216x2y2+150x2+6y2+72xy2+360x2y+48xy+40x+8y+7
     
  2. jcsd
  3. CRGreathouse

    CRGreathouse 3,682
    Science Advisor
    Homework Helper

    Magma says it's irreducible:
    Code (Text):
    P<x,y> := PolynomialRing(IntegerRing(), 2);
    Factorization(216*x^2*y^2+150*x^2+6*y^2+72*x*y^2+360*x^2*y+48*x*y+40*x+8*y+7);

    [
        <216*x^2*y^2 + 360*x^2*y + 150*x^2 + 72*x*y^2 + 48*x*y + 40*x + 6*y^2 + 8*y
            + 7, 1>
    ]

    Total time: 0.140 seconds, Total memory usage: 7.28MB
     
  4. i entered the code:
    P<x,y> := PolynomialRing(IntegerRing(), 2);
    Factorization(216*x^2*y^2+150*x^2+6*y^2+72*x*y^2+360*x^2*y+48*x*y+40*x+8*y+2);

    [
    <216*x^2*y^2 + 360*x^2*y + 150*x^2 + 72*x*y^2 + 48*x*y + 40*x + 6*y^2 + 8*y
    + 2, 1>
    ]
    and got:
    [
    <2, 1>,
    <108*x^2*y^2 + 180*x^2*y + 75*x^2 + 36*x*y^2 + 24*x*y + 20*x + 3*y^2 + 4*y +
    1, 1>
    ]
    [
    <216*x^2*y^2 + 360*x^2*y + 150*x^2 + 72*x*y^2 + 48*x*y + 40*x + 6*y^2 + 8*y
    + 2, 1>
    ]

    Total time: 0.140 seconds, Total memory usage: 7.28
    even tried to put a 3 beside the Integering()(if, that is for no. of factors), to get the same result. but i know,that the above expression is:
    2(6xy+5x+y+1)(18xy+15x+3y+1)
    how does this work?
     
  5. CRGreathouse

    CRGreathouse 3,682
    Science Advisor
    Homework Helper

    Only the first two lines were input. The following lines were the output I got.
     
  6. i entered:
    P<x,y> := PolynomialRing(IntegerRing(), 2);
    Factorization(216*x^2*y^2+150*x^2+6*y^2+72*x*y^2+360*x^2*y+48*x*y+40*x+8*y+2);
    and got:
    [
    <2, 1>,
    <108*x^2*y^2 + 180*x^2*y + 75*x^2 + 36*x*y^2 + 24*x*y + 20*x + 3*y^2 + 4*y +
    1, 1>
    ]

    Total time: 0.140 seconds, Total memory usage: 7.28MB
    whereas above expressioon is:
    2(6xy+5x+y+1)(18xy+15x+3y+1)
    how does this work?
     
  7. Chronos

    Chronos 9,975
    Science Advisor
    Gold Member

    It doesnt, as i suspect you alredy knew.
     
  8. are there more sites like the above mentioned magma?
     
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