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Numerical Analysis in Coq
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Micaela Mayero
Numerical Analysis in Coq
Commits
ed48502b
Commit
ed48502b
authored
2 years ago
by
Mouhcine
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construct lagP1
parent
b024f694
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FEM/poly_Lagrange.v
+12
-3
12 additions, 3 deletions
FEM/poly_Lagrange.v
with
12 additions
and
3 deletions
FEM/poly_Lagrange.v
+
12
−
3
View file @
ed48502b
...
...
@@ -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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