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D.15.1.35 transformationsAfterSplit
Procedure from library arnold.lib (see arnold_lib).
- Usage:
- transformationsAfterSplit(N); N NormalForm as given by @ref(determineNormalForm)
- Return:
- the transformations (and in some cases their inverses) that was transformed, after the degenerate part was splitted off, of N.phi.sourcegerm.value to transform it to a germ
with nondegenerate Newton boundary (in some cases the transformations normalize the Newton boundary is also given), is given up to filtration d, where d is a determinacy bound for N.source (returned as type RightEquivalenceChainWithPrecision as defined in @ref(polyclass.lib))
Example:
| | LIB "arnold.lib";
ring R = 0,(x,y,z),ds;
poly g = (x^2+y^2)^2+5*x^(10)+y^(11)+z^2;
poly phix = x+y^2+x^2+x*y+x^2*y+x*y^3;
poly phiy = y+y^2+2*x^2+x*y+y*x^2+y^2*x+x*y^4;
poly phiz = z+2*x+x^2+y^4*x;
map phi = R,phix,phiy,phiz;
g = phi(g);
Poly F = makePoly(g);
NormalForm N = determineNormalForm(F);
transformationsAfterSplit(N);
==>
==> The transformations are only given up to transforming the input polynomia\
l to a germ with a nondegenerate Newton boundary. The final transformatio\
ns to normalize the germ are not yet determined.
==>
==>
==> Source germ = x4+1/2x2y2+1/16y4+4x5-4x4y+4x3y2-5/4x2y3+3/4xy4-1/16y5+\
8x6-14x5y+59/4x4y2-17/2x3y3+129/32x2y4-1/2xy5+13/128y6+8x7-20x6y+49/2x5y2\
-133/8x4y3+55/8x3y4-63/64x2y5+11/32xy6+13/128y7+3x7y-95/8x6y2+55/4x5y3-11\
03/64x4y4+309/32x3y5-1165/256x2y6+45/32xy7-79/4096y8-28x9+114x8y-823/4x7y\
2+1777/8x6y3-5827/32x5y4+12139/128x4y5-2655/64x3y6+4547/512x2y7-1229/1024\
xy8+659/4096y9-91x10+795/2x9y-12157/16x8y2+7231/8x7y3-95653/128x6y4+27055\
/64x5y5-93169/512x4y6+10655/256x3y7-78291/8192x2y8+33/256xy9+3975/32768y1\
0
==>
==> Target germ = x2y2+(-7/8a+3)*x3y2+(7/8a+3)*x2y3+(-5/16a+179/64)*x4y2+7\
3/8*x3y3+(5/16a+179/64)*x2y4+(607/512a-167/64)*x6y+(-51/128a+79/32)*x5y2+\
(1511/512a+413/64)*x4y3+(-2067/512a+211/64)*x3y4+(-21/512a+233/64)*x2y5+(\
-607/512a-167/64)*xy6+(1011/512a-2465/1024)*x7y+(801/512a-24979/2048)*x6y\
2+(3267/512a+4779/512)*x5y3+(-635/512a-94887/4096)*x4y4+(-2487/256a+8137/\
1024)*x3y5+(-563/256a-13977/1024)*x2y6+(-1161/512a-1145/512)*xy7+(-22727/\
32768a-26197/4096)*x8y+(-219/4096a-1481/512)*x7y2+(320121/16384a+12423/10\
24)*x6y3+(370865/16384a-115155/2048)*x5y4+(-966427/32768a-245813/4096)*x4\
y5+(-81865/4096a-2843/2048)*x3y6+(1079/4096a-709/2048)*x2y7+(23677/32768a\
-31097/4096)*xy8+(-101369/65536a+76495/262144)*x10+(15883/32768a+244153/3\
2768)*x9y+(-185881/32768a-1720781/131072)*x8y2+(564611/16384a+1847149/327\
68)*x7y3+(697013/32768a-13965943/131072)*x6y4+(-418479/32768a-143549/3276\
8)*x5y5+(-87863/8192a-15067493/131072)*x4y6+(-557581/16384a+631401/16384)\
*x3y7+(837899/65536a-3574399/262144)*x2y8+(-15165/32768a+76915/16384)*xy9\
+(101369/65536a+76495/262144)*y10
==>
==> Precision = 10
==>
==> Transformations:
==>
==> Transformation:
==> x-->1/2*x+1/2*y
==> y-->(1/2a)*x+(-1/2a)*y
==>
==> Transformation:
==> x-->x+(-3/16a+1/2)*y2
==> y-->y
==>
==> Transformation:
==> x-->x+(-1/16a-29/32)*y3
==> y-->y
==>
==> Transformation:
==> x-->x
==> y-->y+(3/16a+1/2)*x2
==>
==> Transformation:
==> x-->x
==> y-->y+(1/16a-29/32)*x3
==>
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