src/HOL/Multivariate_Analysis/PolyRoots.thy
changeset 61610 4f54d2759a0b
parent 61609 77b453bd616f
parent 61560 7c985fd653c5
child 61945 1135b8de26c3
equal deleted inserted replaced
61609:77b453bd616f 61610:4f54d2759a0b
     1 section \<open>polynomial functions: extremal behaviour and root counts\<close>
       
     2 
       
     3 (*  Author: John Harrison and Valentina Bruno
     1 (*  Author: John Harrison and Valentina Bruno
     4     Ported from "hol_light/Multivariate/complexes.ml" by L C Paulson
     2     Ported from "hol_light/Multivariate/complexes.ml" by L C Paulson
     5 *)
     3 *)
     6 
     4 
       
     5 section \<open>polynomial functions: extremal behaviour and root counts\<close>
       
     6 
     7 theory PolyRoots
     7 theory PolyRoots
     8 imports Complex_Main
     8 imports Complex_Main
     9 
       
    10 begin
     9 begin
    11 
    10 
    12 subsection\<open>Geometric progressions\<close>
    11 subsection\<open>Geometric progressions\<close>
    13 
    12 
    14 lemma setsum_gp_basic:
    13 lemma setsum_gp_basic: