As a helpful and smart assistant, your task is to parse a given text in any language to Universal Dependency (UD) format including POS tags and dependency relations (HEAD and DEPREL).
Key Components of UD Annotation:
1. Tokens: The fundamental units within UD are tokens. These can be individual words, punctuation marks, or even parts of multi-word expressions. Each token has several associated attributes.
2. UPOS Tags: The UPOS field in the CoNLL-U format represents the universal part-of-speech tag assigned to each word. This tag is part of a universal POS tag set designed to be applicable across different languages. The UPOS tags include categories such as NOUN, VERB, ADJ (adjective), ADV (adverb), PRON (pronoun), DET (determiner), and more. 
3. Dependency Relations: Dependency relations are the core of the syntactic representation. They form a tree structure over the tokens in a sentence. Here's how they work:
    - HEAD: This field indicates the head of the current word. The head is the word that the current word is connected to in the dependency parse tree. The value is an integer that corresponds to the ID of the head word within the same sentence. A value of zero (0) indicates that the word is the root of the sentence.
    - DEPREL: The DEPREL field specifies the type of dependency relation between the current word and its head (as specified in the HEAD field). The value is a universal dependency relation or a language-specific subtype of such a relation.
Note: Blank lines are used to mark the boundaries between sentences.
Example:
Let's analyze this sentence with its UD annotation:
"The big dog chased the cat."
1. Tokenization:
- The
- big
- dog
- chased
- the
- cat
- .
2. UPOS Tags:
- The: DET
- big: ADJ
- dog: NOUN
- chased: VERB
- the: DET
- cat: NOUN
- .: PUNCT
3. Head node (parent):
- The: the parent of this word is "dog" at position 3
- big: the parent of this word is "dog" at position 3
- dog: the parent of this word is "chased" at position 4
- chased: this is the root node, therefore its head is 0
- the: the parent of this word is "cat" at position 6
- cat: the parent of this word is "chased" at position 4
- .: the parent of this word is "chased" at position 4
3. Dependency Relations:
- root(ROOT, chased)
- det(dog, The)
- amod(dog, big)
- nsubj(chased, dog)
- det(cat, the)
- obj(chased, cat)
Combining the above annotations, the final output in UD format is:
Position	Tokenization	UPOS	Head	Deprel
1	The	DET	3	det
2	big	ADJ	3	amod
3	dog	NOUN	4	nsubj
4	chased	VERB	0	ROOT
5	the	DET	6	det
6	cat	NOUN	4	obj
7	.	PUNCT	4	punct
Generate UD annotations for the following tokenized text:
Une des méthodes utilisées en calcul numérique pour calculer des valeurs approchées des racines d'un polynôme est d'en construire la matrice compagnon puis de calculer des valeurs approchées des valeurs propres de cette matrice à l'aide d'une méthode itérative.
Postion	Tokenization
1	Une
2	des
3	de
4	les
5	méthodes
6	utilisées
7	en
8	calcul
9	numérique
10	pour
11	calculer
12	des
13	valeurs
14	approchées
15	des
16	de
17	les
18	racines
19	d'
20	un
21	polynôme
22	est
23	d'
24	en
25	construire
26	la
27	matrice
28	compagnon
29	puis
30	de
31	calculer
32	des
33	valeurs
34	approchées
35	des
36	de
37	les
38	valeurs
39	propres
40	de
41	cette
42	matrice
43	à
44	l'
45	aide
46	d'
47	une
48	méthode
49	itérative
50	.
Position	Tokenization	UPOS	Head	Deprel
1	Une	PRON	20	nsubj
2	des	_	None	_
3	de	ADP	4	case
4	les	DET	4	det
5	méthodes	NOUN	1	nmod
6	utilisées	VERB	4	acl
7	en	ADP	7	case
8	calcul	NOUN	5	obl:mod
9	numérique	ADJ	7	amod
10	pour	ADP	10	mark
11	calculer	VERB	5	advcl
12	des	DET	12	det
13	valeurs	NOUN	10	obj
14	approchées	ADJ	12	amod
15	des	_	None	_
16	de	ADP	16	case
17	les	DET	16	det
18	racines	NOUN	12	nmod
19	d'	ADP	19	case
20	un	DET	19	det
21	polynôme	NOUN	16	nmod
22	est	VERB	0	root
23	d'	ADP	23	mark
24	en	PRON	25	nmod
25	construire	VERB	20	ccomp:pred
26	la	DET	25	det
27	matrice	NOUN	23	obj
28	compagnon	NOUN	25	appos
29	puis	ADV	29	cc
30	de	ADP	29	mark
31	calculer	VERB	23	conj
32	des	DET	31	det
33	valeurs	NOUN	29	obj
34	approchées	ADJ	31	amod
35	des	_	None	_
36	de	ADP	35	case
37	les	DET	35	det
38	valeurs	NOUN	32	obl:arg
39	propres	ADJ	35	amod
40	de	ADP	39	case
41	cette	DET	39	det
42	matrice	NOUN	35	nmod
43	à	ADP	42	case
44	l'	DET	42	det
45	aide	NOUN	29	obl:mod
46	d'	ADP	45	case
47	une	DET	45	det
48	méthode	NOUN	42	nmod
49	itérative	ADJ	45	amod
50	.	PUNCT	20	punct