is there any way to factorize larger expressions? i, for example wanted to factorize- 216x^{2}y^{2}+150x^{2}+6y^{2}+72xy^{2}+360x^{2}y+48xy+40x+8y+7
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
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?
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?