- #1

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i, for example wanted to factorize-

216x

^{2}y

^{2}+150x

^{2}+6y

^{2}+72xy

^{2}+360x

^{2}y+48xy+40x+8y+7

- Thread starter chhitiz
- Start date

- #1

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i, for example wanted to factorize-

216x

- #2

CRGreathouse

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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+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
```

- #3

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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?

- #4

CRGreathouse

Science Advisor

Homework Helper

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Only the first two lines were input. The following lines were the output I got.

- #5

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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?

- #6

Chronos

Science Advisor

Gold Member

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It doesnt, as i suspect you alredy knew.

- #7

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are there more sites like the above mentioned magma?