40 lines
1.1 KiB
Coq
40 lines
1.1 KiB
Coq
From mathcomp Require Import ssreflect ssrfun ssrbool eqtype ssrnat seq choice.
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From mathcomp Require Import fintype div tuple bigop prime finset fingroup.
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From mathcomp Require Import ssralg poly polydiv morphism action finalg zmodp.
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From mathcomp Require Import cyclic center pgroup abelian matrix mxpoly vector.
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From mathcomp Require Import falgebra fieldext separable galois.
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From mathcomp Require ssrnum ssrint algC cyclotomic.
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(* Identity of a group *)
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Check 1%g.
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Check 1%R.
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Check ringType.
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Check fieldType.
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(* Got +1,+2,+3,+4 and -1,-2 *)
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Compute 3.+4.
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(* = 7 : nat *)
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Print injective.
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(*
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injective =
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fun (rT aT : Type) (f : aT -> rT) =>
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forall x1 x2 : aT, f x1 = f x2 -> x1 = x2
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: forall rT aT : Type, (aT -> rT) -> Prop
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*)
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(* Check fieldExtType. *)
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Locate "0".
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Check 0%g.
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(* Check R. *)
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(* Factorial *)
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Compute 0`!. (* = 1 : nat *)
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Compute 1`!. (* = 1 : nat *)
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Compute 2`!. (* = 2 : nat *)
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Compute 3`!. (* = 6 : nat *)
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Compute 4`!. (* = 24 : nat *)
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(* Summation. ie, Σ *)
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Compute \sum_ (1 <= i < 5) i. (* 1+2+3+4+5 *)
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Compute \sum_ (1 <= i < 3) (2*i). (* 2*(1+2+3) *)
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