Solving 1.a using Maple
Define your f and find the partial derivatives wioth respect to x and y
> | f:=x^4+y^4-x^2; fx:=diff(f,x); fy:=diff(f,y); |
Now we find the singular points:
> | solvefor[x](f,fx,fy); |
find its Taylor series around the singular point (0,0) up to the third term which is of degree 2
> | f2:=mtaylor(f,[x=0,y=0],3); |
Solving 1.b using Maple
Now we define an equation g and take its partial derivatives with respect to x and y
> | g:=x^6+y^6-x*y; gx:=diff(g,x); gy:=diff(g,y); |
Find the singular points
> | solvefor[x](g,gx,gy); |
find its Taylor series around the singular point (0,0) up to the third term which is of degree 2
> | g2:=mtaylor(g,[x=0,y=0],3); |