# Is this a 4-linear form ?

1. Aug 23, 2007

### Sangoku

Is this a 4-linear form ??

rather a silly question, but i am a bit confused , could we consider the expression

$$x^{2}-y^{2}+3xy-x^{4}+5y^{4}+ z^{4}-2t^{4}+3xyzt-6x^{2}tz+ 5x^{2}y^{2}$$

or even in general $$A_{i,j}x^{i}x^{j}-Q_{i,j,k,l}x^{i}x^{j}x^{k}x^^{l}$$

could be considered a 4-linear form??.. i believe this is linear on every argument x^{i} but there seems to be 'mixed up' a 2-from plus a 4-form so i,m not sure what exactly is the proposed object.

2. Aug 23, 2007

### mathman

The usual label for such expressions is 4th degree polynomial in 4 variables.