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Commit ed48502b authored by Mouhcine's avatar Mouhcine
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construct lagP1

parent b024f694
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......@@ -31,9 +31,12 @@ Geometries using P2 or higher are left aside... *)
Variable d : nat.
Lemma lt_minus_1 : forall (j : 'I_(S d)), (j - 1 < d)%nat.
Lemma lt_minus_1 : forall (j : 'I_(S d)),
j <> ord0 -> (j - 1 < d)%nat.
Proof.
move => [j Hj] /=.
move => [j Hj] H /=.
lia.
(* lia. does not work *)
Admitted.
......@@ -41,7 +44,7 @@ Admitted.
Definition LagP1 : '('R^d -> R)^(S d) :=
fun j x => match (eq_nat_dec j (@ord0 d)) with
| left _ => 1 - (*comb_lin x (fun _ => 1)*) \big[+%R/0]_(i < d) (x i)
| right H => x (Ordinal (lt_minus_1 j))
| right H => x (Ordinal (lt_minus_1 j H))
end.
Definition vtxP1 : '('R^d)^(S d) :=
......@@ -50,6 +53,12 @@ Definition vtxP1 : '('R^d)^(S d) :=
| right H => kronecker (Ordinal (lt_minus_1 j)) i
end.
Definition vtxP1_aux : '('R^d)^(S d) :=
fun j i => match (eq_nat_dec j (@ord0 d)) with
| left _ => 0
| right H => kronecker (j - 1) i
end.
Lemma LagP1_kron : forall i j,
LagP1 j (vtxP1 i) = kronecker i j.
Proof.
......
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