| | LIB "tropical.lib";
==> Welcome to polymake version
==> Copyright (c) 1997-2015
==> Ewgenij Gawrilow, Michael Joswig (TU Darmstadt)
==> http://www.polymake.org
printlevel=1;
ring r=0,(x,y),ds;
poly f=x2-y4+x5y7;
puiseuxExpansion(f,3,"subst");
==> The procedure has created a list of lists. The jth entry of this list
==> contains a ring, an integer and an intvec.
==> In this ring lives an ideal representing the wanted lifting,
==> if the integer is N then in the parametrisation t has to be replaced by t\
^1/N,
==> and if the ith component of the intvec is w[i] then the ith component in \
LIFT
==> should be multiplied by t^-w[i]/N in order to get the parametrisation.
==>
==> Suppose your list has the name L, then you can access the 1st ring via:
==>
==> def LIFTRing=L[1][1]; setring LIFTRing; LIFT;
==>
==> !!!! WARNING: The number of terms computed in the Puiseux expansion were
==> !!!! not enough to find all branches of the curve singularity!
==> [1]:
==> [1]:
==> // coefficients: QQ
==> // number of vars : 1
==> // block 1 : ordering ls
==> // : names t
==> // block 2 : ordering C
==> [2]:
==> 2
==> [3]:
==> (11/8)*t^(30/2) + (5/4)*t^(43/2) + (139/256)*t^(56/2) + (35/256)*t^\
(69/2) + (21/1024)*t^(82/2) + (7/4096)*t^(95/2) + (1/16384)*t^(108/2)
==> [2]:
==> [1]:
==> // coefficients: QQ
==> // number of vars : 1
==> // block 1 : ordering ls
==> // : names t
==> // block 2 : ordering C
==> [2]:
==> 2
==> [3]:
==> (11/8)*t^(30/2) + (-5/4)*t^(43/2) + (139/256)*t^(56/2) + (-35/256)*\
t^(69/2) + (21/1024)*t^(82/2) + (-7/4096)*t^(95/2) + (1/16384)*t^(108/2)
==> [3]:
==> [1]:
==> // coefficients: QQ(a)
==> // number of vars : 1
==> // block 1 : ordering ls
==> // : names t
==> // block 2 : ordering C
==> [2]:
==> 2
==> [3]:
==> (-a4+1)*t^(4/2) + (a7-a3)*t^(17/2) + (14a6-3a2)/8*t^(30/2) + (21a5-\
a)/16*t^(43/2) + (140a4-1)/256*t^(56/2) + (35a3)/256*t^(69/2) + (21a2)/10\
24*t^(82/2) + (7a)/4096*t^(95/2) + (1/16384)*t^(108/2)
displayPuiseuxExpansion(puiseuxExpansion(f,3));
==> The procedure has created a list of lists. The jth entry of this list
==> contains a ring, an integer and an intvec.
==> In this ring lives an ideal representing the wanted lifting,
==> if the integer is N then in the parametrisation t has to be replaced by t\
^1/N,
==> and if the ith component of the intvec is w[i] then the ith component in \
LIFT
==> should be multiplied by t^-w[i]/N in order to get the parametrisation.
==>
==> Suppose your list has the name L, then you can access the 1st ring via:
==>
==> def LIFTRing=L[1][1]; setring LIFTRing; LIFT;
==>
==> !!!! WARNING: The number of terms computed in the Puiseux expansion were
==> !!!! not enough to find all branches of the curve singularity!
==> =============================
==> 1. Expansion:
==>
==> The Puiseux expansion lives in the ring
==> Q[[t^(1/2)]]
==>
==> The expansion has the form:
==> y=(1)*t^(1/2) + (1/4)*t^(14/2)
==>
==> =============================
==> 2. Expansion:
==>
==> The Puiseux expansion lives in the ring
==> Q[[t^(1/2)]]
==>
==> The expansion has the form:
==> y=(-1)*t^(1/2) + (1/4)*t^(14/2)
==>
==> =============================
==> 3. Expansion:
==>
==> The Puiseux expansion lives in the ring
==> Q[a]/0[[t^(1/2)]]
==>
==> The expansion has the form:
==> y=(a)*t^(1/2) + (1/4)*t^(14/2)
==>
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