Singular Manual: displayTropicalLifting

| #### D.13.6.2 displayTropicalLifting Procedure from library `tropical.lib` (see tropical_lib). Usage: displaytropcallifting(troplift[,#]); troplift list, # list Assume: troplift is the output of tropicalLifting; the optional parameter # can be the string 'subst' Return: none Note: - the procedure displays the output of the procedure tropicalLifting - if the optional parameter 'subst' is given, then the lifting is substituted into the ideal and the result is displayed Example:
    LIB "tropical.lib";
    ring r=0,(t,x,y,z),dp;
    ideal i=-y2t4+x2,yt3+xz+y;
    intvec w=2,-4,0,4;
    displayTropicalLifting(tropicalLifting(i,w,3),"subst");
    ==> LP algorithm being used: "cddgmp".
    ==> Groebner basis Engine being used: "gfan".
    ==> 0
    ==> 0
    ==> 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]; setring LIFTRing; LIFT;
    ==>
    ==> The lifting of the point in the tropical variety lives in the ring
    ==> Q[[t^(1/2)]]
    ==>
    ==> The lifting has the form:
    ==> x=(1)*t^(4/2)
    ==> y=(1)
    ==> z=(-1)*1/t^(4/2) + (-1)*t^(2/2)
    ==>
    ==> Substituting the solution into the ideal gives:
    ==> i[1]=0
    ==> i[2]=0

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