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If you can't solve this problem, then you are a brainlet who needs to get off this board.
Consider a function [math] F:\mathbb{C}^2\to\mathbb{C}^2 [/math] of the form F(x,y)=(p(x,y), q(x,y)) where the components p and q are polynomials.
Suppose the Jacobian determinant [math] p_xq_y-p_yq_x [/math] is a non-zero complex number.
Show that the components of G^{-1} are polynomials.
If you've taken any real analysis course this should not be difficult.
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>>8419375
Whoops. Meant to write
>Show that the components of F^{-1} are polynomials
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>Linear algebra, complex analysis
>"If you've taken any real analysis course this should not be difficult."
I don't even know why I'm responding to this. OP is a faggot. Do your own damn homework OP.
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Isn't this an unsolved math problem?
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>>8419362
polynomials are a spook
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>>8420556
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>>8419362
>is a non-zero complex number.
you mean it's constant?
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>>8421101
Yes
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>>8420556
>>8420701
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https://en.wikipedia.org/wiki/Jacobian_conjecture
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>>8419362
I have not taken a real analysis course, I am still working on its prerequisites. Not being at your level in mathematics does not make me a brainlet. Intelligence is not a function of knowledge, it is the capacity to gain, retain and use it.
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>>8419362
Let F be a polynomial.
Then F^-1 is 1 divided by that polynomial and therefore also a polynomial.
QED
Now hand over the Fields Medal.
Thread posts: 15
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