:
f = xyzt + xyz + xy
1) * .
2) , , corank(f), codim(f) .
:
1) f = xyzt + xyz + xy
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K:
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2)
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K:
, , K*=K=(0,0).
codim. , , . xy 1,1. ³ ( . . 3.2).
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1. * .
1.1. f = x2 + 2xy + yz2
1.2. f = sin2xcosy y3cos2z
1.3. f = e x2(z2 + sin2y) + 2cosy(z4 + 1)
1.4. f = x(x/2 + sin3y)e - z^3
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1.5. f = (xy z3)(1 t2) + xz
1.6. f = xy(z + 1)(x y)z2
1.7. f = y2ex^2 xyz
1.8. f = xu2 + y(u + v2)
1.9. f = xyzt + ty + xyt
1.10. f = xy(z + 1) + (x - y)z2
1.11. f = sin2xcos2y y3cos2z
1.12. f = x3 + 2xy + yz
1.13. f = sin(x2y) + sin(y2z) sin(z2x)
1.14. f = x(x/3 - sin6y)e - z^3
1.15. f = sin2xcos4y y2cosz
2. , , corank(f),, codim(f) .
2.1. f = x4
2.2. f = x5
2.3. f = x6
2.4. f = x7
2.5. f = x2y + y4
2.6. f = x2y y5
2.7. f = x2y + y5
2.8. f = x3 + y4
2.9. f = sin(y2) cos(x2)
2.10. f = [cos(y2) - cosx]ln[(1 + y)2]
2.11. f = x2y - y4
2.12. f = x3y + y3
2.13. f = x2y + y6
2.14. f = x4y y3
2.15. f = xy3 + 4
³
1.
1.1. K* = (0,0,0), f = u2 v2 + (1/4)z4
1.2. K* = (0,0,z), f = u2 y3cos2z
1.3. K* = (x,0,0), K1* = (0,0,0) f = u2 + 2cosy + sin2ye - x^2
1.4. K* = (0,0,z), f = u2 (1/2)sin6ye - z^3
1.5. K* = (0,0,0,t), f = u2 v2 + z3(t2 - 1)
1.6. K* = (0,0,0), f = u2 v2 + w4
1.7. K* = (0,0,z), K1* = (0,0,0) f = u2 (1/4)x2z2e - x^2
1.8. K* = (x,0,0,0), f = s2 t2 + xv4
1.9. K* = (0,0,0,0), f = u2 v2
2.
2.1. ӳ
2.2.
2.3.
2.4. ³
2.5.
2.6.
2.7.
2.8.
2.9. ӳ
2.10.